Best voting system to elect Prime Minister or Speaker of the House?

[Rob Wilson]

Consider a situation in which a body has to elect a leader. This body would be educated enough to understand any voting system along with the utility of any strategy that could be used with that particular system. Each member of the body knows the ideals of each other member and has a good idea of how they would vote if they were to vote honestly. What do you think would be the best voting system to use? In this situation, I don't like score or approval because I think it might have a good chance at devolving into plurality.

For right now, I think the best method of electing a head of such a body would to be to use Black's Condorcet method (using Borda to break cycle). The winner of the election would be the elected head of the body unless members of this body could get a majority to agree on a different candidate within 24 hours.

Instead of using Black's method, maybe you could make it more range-voting like. You could maybe allow a voter to give a candidate 1 to 3 points less than the candidate ranked above him.

What do you think is the best voting system to use in this situation and what considerations do you think we'd have watch out for?

[Jim Mueller]

The question ceases to have any relevance if one dumps the archaic,  patriarchally derived, zero sum game inducing singular leader and converts to a executive council with each member having voting power equal to the number votes that the candidate received.

The council would more perfectly represent the desires of the body than would a singular leader obtained through any voting system that restricts or denies the voter's choice . The Executive Council would choose a voting system to elect a Chair or Executive Committee for the Council. 

Sent from my iPhone

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[Warren D. Smith (CRV cofounder, http://RangeVoting.org)]

https://www.youtube.com/watch?v=kUS9uvYyn3A

[Rob Wilson]

On Sunday, September 7, 2014 6:42:09 AM UTC-5, Jim Mueller wrote:

The question ceases to have any relevance if one dumps the archaic,  patriarchally derived, zero sum game inducing singular leader and converts to a executive council with each member having voting power equal to the number votes that the candidate received.

The council would more perfectly represent the desires of the body than would a singular leader obtained through any voting system that restricts or denies the voter's choice . The Executive Council would choose a voting system to elect a Chair or Executive Committee for the Council. 

Sent from my iPhone

On Sep 6, 2014, at 6:10 PM, Rob Wilson <blahf...@gmail.com> wrote:

This is a bit off topic, but I very much agree with you. I wish the Senate would lose most of its legislative functions and gain much more executive powers. The President would be a special member of the Senate and any bill would require the approval of the majority of the Senate to become law. No official vote would need to take place, a senator would be able to approve a bill at any time after it is passed by the House.

Instead of approving candidates nominated by the President, the Senate would elect all appointments. The President would be able to nominate a candidate for any position. The relevant committee on the Senate would be able to nominate up to 3 additional candidates for the position and the Senate as a whole would vote on them. It would take the endorsement of over 25% of the committee to nominate each candidate.

The Senate would assign committee seats by using STV.

 

[Andy Jennings]

I've been thinking about this same question.

In the Arizona House and Senate, the majority party meets alone (a caucus meeting) and chooses the speaker without any input from the minority.  (They do have to make it official in a floor vote later.)  The speaker chooses the chairs of all the committees and controls the legislative schedule, so the minority party is essentially shut out.

Whatever method the majority caucus uses to choose the speaker (usually plurality), we assume that a majority dominates, so a majority of the majority (as little as 26% of the legislators) can control the body.  I'm assuming this is how it is in most legislatures.

If we want a system that chooses a chair more fairly, it has to compensate for this caucus system.  A majority, voting in lockstep, should not be able to completely control the outcome.

My ideal solution is to force one party to nominate 50% of the legislature and then let the other party choose among them.  Ignoring the fact that it only works for two parties, if you wrote this into the state constitution, could the legislature subvert it?  By RRoO, can they change their speaker at any time with a majority vote?  Would the majority party try to install a non-moderate speaker?

~ Andy

====Addendum====
As an academic exercise, I've wondered if any existing voting system is robust to caucusing, choosing a compromise even if the majority votes in lockstep.

Range/approval are not.  The majority can vote one person MAX and everyone else MIN and have their way no matter how the minority votes.

Condorcet is not.  The majority can put their winner first and they will be the Condorcet winner no matter how the minority votes.

The closest I can come is Borda, if you force the majority to vote first and let the minority see the vote totals before they vote.  (Borda's biggest weakness, not being robust if candidates are added or removed, is moot if all legislators are automatically candidates.)  According to my (preliminary) calculations, in a legislature of 100 (100 candidates and 100 voters), a majority of 52 has enough power to eliminate 9 candidates from winning.  A majority of 60 could eliminate 51 candidates from winning.  And a majority of 67 could choose the winner outright.  I've been wondering if you could achieve "fairness" by adjusting the Borda points or changing the weight of each voter in the voting order.

--

[Andy Jennings]

On Sun, Sep 7, 2014 at 4:42 AM, Jim Mueller <jimmue...@gmail.com> wrote:

The question ceases to have any relevance if one dumps the archaic,  patriarchally derived, zero sum game inducing singular leader and converts to a executive council with each member having voting power equal to the number votes that the candidate received.

The council would more perfectly represent the desires of the body than would a singular leader obtained through any voting system that restricts or denies the voter's choice . The Executive Council would choose a voting system to elect a Chair or Executive Committee for the Council. 

Jim,

I'm a fan of the Executive Council idea, where members have voting power equal to the number of votes they got, but as long as there are parties, I don't think it eliminates the winner-take-all aspect of choosing a speaker.  All legislative bodies operate according to Robert's Rules of Order, don't they?  Doesn't RRoO require a speaker/chair?  If the chair wants to freeze out a minority, then there's nothing anyone can do, right?

~ Andy

[Warren D Smith]

The problem with Andy's suggestion...
in legislatures, majority rules. Majorities can change the rules.
Majorities can select the leaders, select the committee heads.

Do you want to change that, so that, say, a majority CANNOT change the rules?
That's a dangerous path to take. Indeed in the US senate they made a
"minority rules"
deal with the "filibuster" which resulted in the least productive
congress in US history
and intentional gridlock.

If majorities can change rules, then everything else you say, has to
be thrown in the garbage since they'll overrule you. Now what happens
in the USA almost 100% of the time, is all party members of the
majority party vote in lockstep about every such issue, thus the
majority party unilaterally gets to choose all committee heads and the
speaker and so forth. Occasionally there is a fight and some majority
party member will vote against his party on such a vote, but this is
very rare. This in principle makes it possible for the speaker to
come NOT from the majority party, etc, but it is very rare.

Now certainly this kind of monopoly is probably not optimal, but I see
no way to cure the problem in such a way that the cure is not worse
than the disease, EXCEPT by removing the fact that a majority party
even EXISTS in the first place. If the USA had, say 10 big parties,
not 2, then single party majorities might become fairly rare, and then
such monopolies would naturally vanish. Range voting and PR both
could hope to accomplish that.

Jennings' "cut and choose" approach where the majority party nominates
more than the required number of chairs, etc, then the others choose
among the choices, is not going
to work. First of all, the majority party will change the rules to
get rid of that.
Second, this system still would yield a 100% monopoly. You could try
to argue it'd be a slightly kinder & gentler monopoly, but considering
the majority-party members
still were agreeing to vote in lockstep, obviously they all still want
to 100% use the iron fist to get 100% party control of everything in
the legislature, so I'm not terribly
impressed with the kindness & gentleness.










--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

[Warren D Smith]

And as a thought experiment, let's say that somehow, party A with 60%
of the house seats, got 60% of the chairs and party B with 40% got 40%
of the chairs.
Well then the speaker would simply refuse to allow anything that came
out of the 40% of the committees, to ever get on the house floor for a
vote, so the 40% of committees would be rendered nonexistent for
practical purposes.

Wouldn't matter that you claimed that the "monopoly has been busted."

At least with the monopoly chair control, when a committee does do
something, it
generally gets to go to the floor for a vote.

So long as the majority party gets to set the agenda, and agrees to
vote in lockstep,
no bill need ever be voted on, that they do not like. The only way to stop
this, is to prevent the majority from ruling about the agenda.
And that would seem harmful.

-----

Here's a possible semi-cure.

Each majority party member gives the majority leader "shekels" by
voting for him.
The minority leader gets fewer shekels in same way.
Then, whenever an agenda decision is made, whoever makes it expends shekels to
do so. The point would be that the minority leader then would be able to make
some fraction of agenda decisions.

[Andy Jennings]

On Sun, Sep 7, 2014 at 10:29 AM, Warren D Smith <warre...@gmail.com> wrote:

The problem with Andy's suggestion...
in legislatures, majority rules. Majorities can change the rules.
Majorities can select the leaders, select the committee heads.

Warren is right that such a rule is useless if the majority just reverts it.  That's why I suggested it would be done in a constitutional amendment.

Do you want to change that, so that, say, a majority CANNOT change the rules?
That's a dangerous path to take.   Indeed in the US senate they made a
"minority rules"
deal with the "filibuster" which resulted in the least productive
congress in US history
and intentional gridlock.

If majorities can change rules, then everything else you say, has to
be thrown in the garbage since they'll overrule you.  Now what happens
in the USA almost 100%  of the  time, is all party members of the
majority party vote in lockstep about every such issue, thus the
majority party unilaterally gets to choose all committee heads and the
speaker and so forth.  Occasionally there is a fight and some majority
party member will vote against his party on such a vote, but this is
very rare.   This in principle makes it possible for the speaker to
come NOT from the majority party, etc, but it is very rare.

Usually what happens is a few of the most moderate legislators in the majority party strike a deal with the minority party that one of them will be chair.

http://en.wikipedia.org/wiki/Kent_Williams_%28politician%29#Speaker

If you think it's better to have a moderate member of the majority party as chair than an extremist, then you should applaud such coups.  But usually, the other members of their party are so angry at them that trust and productivity suffer afterwards.  I just think it would be better if the "system" forced it, instead of having to rely on a coup.

Assuming a one-dimensional spectrum, the median candidate is the Condorcet winner.  So once someone near the median legislator gets to be chair, it is difficult to get a majority together to dislodge them.

 

Now certainly this kind of monopoly is probably not optimal, but I see
no way to cure the problem in such a way that the cure is not worse
than the disease, EXCEPT by removing the fact that a majority party
even EXISTS in the first place. If the USA had, say 10 big parties,
not 2, then single party majorities might become fairly rare, and then
such monopolies would naturally vanish.  Range voting and PR both
could hope to accomplish that.

In places with lots of parties, don't they just negotiate with each other until they form a majority coalition in the legislature?  Then they can do whatever they want.  If they want to freeze out all other parties, they can.  If they want to have a caucus and choose an extremist chair, they can.

 

Jennings' "cut and choose" approach where the majority party nominates
more than the required number of chairs, etc, then the others choose
among the choices, is not going
to work.  First of all, the majority party will change the rules to
get rid of that.
Second, this system still would yield a 100% monopoly.  You could try
to argue it'd be a slightly kinder & gentler monopoly, but considering
the majority-party members
still were agreeing to vote in lockstep, obviously they all still want
to 100% use the iron fist to get 100% party control of everything in
the legislature, so I'm not terribly
impressed with the kindness & gentleness.

You're right that it might not make a difference.  But the degree of "voting in lockstep" varies in different legislatures around the country.

In the Arizona Senate, the Republicans have a slight majority.  But the extreme Rs had a slight majority over the moderate Rs in the caucus and chose a pretty extreme speaker.  He was the one that stopped our Approval Voting legislation from passing last year.  Wouldn't let it get to the floor.  Wouldn't meet with us.  Turned it into a "study committee" which he then neglected to convene.

I think if any one of the moderate Rs was chair, the legislation would've passed.

So, yeah, I think it might make a difference, in some cases, to choose a chair that the whole legislature can agree on rather than having the majority party choose the chair behind closed doors.

~ Andy

 

--
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)

[Rob Wilson]

The problem with our system is that it revolves too much around party when it doesn't need to. It strongly incentives representatives to toe the party line.

Members of Congress could all vote on who gets assigned seats in a committee through STV. You could use STV to allocate time in the legislative schedule as well.

If you have a committee working on a bill to address an issue such as extending healthcare, you can have up to three different versions of the bill make it out of the committee provided that each version gets over 25% of the committee members endorsing it. For example, theoretically you could have the three following healthcare bills coming out of the committee:

(1) ACA

(2) ACA with public option

(3) Single Payer.

When voting for the bills, the house would be able to vote for none or all of the bills. If more than 1 bill gets approved by the majority, the representatives who voted to approve the bill would have another vote to determine which version passes.

You can also do a lot of things without even having to set a schedule and just automating the timing on everything. After a set of similar bills makes it out of committee, representatives could vote to approve the bill any time within the next 40 days. If it doesn't get enough approvals by then, the majority could actively vote to extend deadline.

We can save time by allowing members of congress to have their legislative debates on a publicity viewable message-board. They could debate point-by-point and it would be pretty easy for their constituency to see the arguments unfold at their own convenience.

If we had these reforms and a voting system that solved the spoiler problem, we would see a lot more independent thinking coming from our representatives.

[Warren D Smith]

On 9/7/14, Andy Jennings <abjen...@gmail.com> wrote:
> On Sun, Sep 7, 2014 at 10:29 AM, Warren D Smith <warre...@gmail.com>
> wrote:
>
>> The problem with Andy's suggestion...
>> in legislatures, majority rules. Majorities can change the rules.
>> Majorities can select the leaders, select the committee heads.
>>
>>
> Warren is right that such a rule is useless if the majority just reverts
> it. That's why I suggested it would be done in a constitutional amendment.

--yah... but these require supermajorities to enact, which is far harder
and certainly would be blocked...

> Usually what happens is a few of the most moderate legislators in the
> majority party strike a deal with the minority party that one of them will
> be chair.
>
> http://en.wikipedia.org/wiki/Kent_Williams_%28politician%29#Speaker
>
> If you think it's better to have a moderate member of the majority party as
> chair than an extremist, then you should applaud such coups. But usually,
> the other members of their party are so angry at them that trust and
> productivity suffer afterwards. I just think it would be better if the
> "system" forced it, instead of having to rely on a coup.

> In places with lots of parties, don't they just negotiate with each other
> until they form a majority coalition in the legislature? Then they can do
> whatever they want. If they want to freeze out all other parties, they
> can. If they want to have a caucus and choose an extremist chair, they
> can.

--yes, often coalitions are made. But there is no law, and hopefully
never will be a law, that all party members or all coalition members,
need to vote in lockstep. The party leaders of parties A,B,C,D can
get together and say "let's install a joint leader under a coalition
agreement and we'll all vote in lockstep to make that happen" but the
party members may decide to tell those leaders to go to hell.
The more parties there are, the less likely that these monopolies will
be set up and will hold together, and the less motivation to do so.
It is different in countries like the UK than in the USA, since they
actually have "votes of confidence" in coalitions etc which, if they
fail, cause there to be a new election; and the notion of a majority
in parliament behind a Prime Minister, is built into the rules of the
system, unlike in USA, where the rules of the system (constitution)
simply do not mention parties at all...

>> Jennings' "cut and choose" approach where the majority party nominates
>> more than the required number of chairs, etc, then the others choose
>> among the choices, is not going
>> to work. First of all, the majority party will change the rules to
>> get rid of that.
>> Second, this system still would yield a 100% monopoly. You could try
>> to argue it'd be a slightly kinder & gentler monopoly, but considering
>> the majority-party members
>> still were agreeing to vote in lockstep, obviously they all still want
>> to 100% use the iron fist to get 100% party control of everything in
>> the legislature, so I'm not terribly
>> impressed with the kindness & gentleness.

> You're right that it might not make a difference. But the degree of
> "voting in lockstep" varies in different legislatures around the country.

--really?

> In the Arizona Senate, the Republicans have a slight majority. But the
> extreme Rs had a slight majority over the moderate Rs in the caucus and
> chose a pretty extreme speaker. He was the one that stopped our Approval
> Voting legislation from passing last year. Wouldn't let it get to the
> floor. Wouldn't meet with us. Turned it into a "study committee" which he
> then neglected to convene.
>
> I think if any one of the moderate Rs was chair, the legislation would've
> passed.

--well, presumably, the moderate Rs could have got together with some Dems,
and between them formed a majority to elect a moderate R to be the Speaker.
This would have presumably been better for everybody. In principle
nothing stopped
that from happening. However, in practice, the R's essentially always
agree to vote 100% in lockstep, and always to elect whoever the
R-majority wants, even if it is not who
the legislature as a whole would prefer. In other words, 45% of the R's (say)
intentionally vote dishonestly in the official vote, and zero percent of the R's
try to make the true Condorcet winner win (if he is different).

This is not the fault of the AZ legislature's rules or the A
constitution. This is the fault of the republican robots.

Indeed the so called "Hastert rule," which was not actually a rule,
was that only bills
the majority of the majority (Republicans, at the time) wanted, would
ever come to the floor for a vote. This was the policy of
then-speaker Dennis Hastert.
It was directly opposed to the idea of majority rule in the
legislature and therefore hurt the USA tremendously. But again, by
voting in lockstep, the majority party can make this happen, often to
their own detriment but they do it anyhow since (a) they can and since
(b) they are robots.
http://en.wikipedia.org/wiki/Hastert_Rule


It then often happens that some bill cannot each the floor for a vote,
because the R leadership prevents that, because the majority of R's do
not want that bill. So then, even a bill supported by a large majority
of the legislature (e.g. a minority of the R's plus the Dems) cannot
reach the floor for a vote. We thus get "minority rule" in the
legislature to the detriment of all. Also, in the US senate they
often have SINGLE senators
exerting veto power in various ways and thus subverting the desires of
(sometimes even vast) majorities. These are not the fault of the US
constitution. It is due to rules the majority party set up, voting in
lockstep to do it, to make all that happen.

There is no rule in the constitution that the majority party should
make decisions
behind closed doors with the other parties excluded. (The rule in the
constitution is:
majority rules.) They only decided on their own to do that, because they could.
And they've gradually abused this more and more and time went on --
note the "Hastert rule" was a fairly recent development (mid-1990s)
which could have happened any time
in the preceding 200 years, but did not, because in earlier times they
had a little more
morals.

So anyway, the way I see to escape this, is:
(A) abolish the very existence of a majority party by making many parties.
A different idea is:
(B) abolish the very idea of a single entity that gets total control
over the legislature's agenda. Instead have some kind of rotating
time-shared control where there are multiple leaders who each control
a certain fraction of the time, using "shekels," or time measurement,
or something, to accomplish that.
As far as I am aware (B) has never been tried and it might well
lead to dysfunction and chaos worse than now. (A) has been tried and
has both been successful and not, depending when & where. Certainly
overall (A) has been more successful than the USA's legislature right
now, which is totally broken. However, there have been cases where
(A) has worked badly and certainly been worse than the USA's
legislature (at better times than now) has been.

[Andy Jennings]

On Mon, Sep 8, 2014 at 10:01 AM, Warren D Smith <warre...@gmail.com> wrote:

On 9/7/14, Andy Jennings <abjen...@gmail.com> wrote:
> On Sun, Sep 7, 2014 at 10:29 AM, Warren D Smith <warre...@gmail.com>
> wrote:
>
>> The problem with Andy's suggestion...
>> in legislatures, majority rules. Majorities can change the rules.
>> Majorities can select the leaders, select the committee heads.
>>
>>
> Warren is right that such a rule is useless if the majority just reverts
> it.  That's why I suggested it would be done in a constitutional amendment.

--yah... but these require supermajorities to enact, which is far harder
and certainly would be blocked...

At the state level, it would be done with an initiative.

Look, I admit it will be difficult.  I'm sorry that I don't have time to argue about where on the spectrum it lies between "difficult" and "impossible".  Talk about enactment would come later, if we happen to stumble upon a good algorithm.

I think these are the interesting mathematical questions:

- Can we design a system that elects the median legislator as speaker even if the majority votes in lockstep for someone more extreme?

- How do you extend the concept to more than one dimension, where median is meaningless?

Warren, if you're interested, then that's where I can use your help.  I'm not interested in debating these other, subjective, points.

 

[Andy Jennings]

Rob,

I agree that it would be better to have a version that didn't consider parties.

How about this:

1) Every senator submits a ranking of all senators.

2) One of the senators is chosen.  The last-ranked senator on his ballot is eliminated.

3) The ballot for the senator that just got eliminated is used to determine the next senator that gets eliminated (the lowest-ranked uneliminated senator).

4) Repeat step 3 until all senators but one are eliminated.

I'm thinking this would create a back-and-forth dynamic, eliminating the most extreme senators on each side until only one remains.

You could choose the senator in step 2 randomly.

Or maybe you would choose the senator with the most seniority.

Or maybe you would run the algorithm through for every starting ballot, keeping track of how many times each senator won as speaker.  Then choose the speaker who won the most times.

~ Andy

--

[Warren D Smith]

> At the state level, it would be done with an initiative.

--sounds good.

> I think these are the interesting mathematical questions:
>
> - Can we design a system that elects the median legislator as speaker even
> if the majority votes in lockstep for someone more extreme?

--no, you cannot, because that majority could be voting honestly, in
which case their choice WOULD be the median legislator (anyhow
Condorcet winner).

> - How do you extend the concept to more than one dimension, where median is
> meaningless?

--well, this already seems busted in 1 dimension, so forget about that.

The only ways out, I reiterate, seem to be (A) to get rid of the very
existence of a majority party, or (B) to get rid of single-entity
control over the agenda (i.e the one speaker).

By the way there already is a way around the speaker's agenda control
in the US House, which is a petition, which if it gets signed by a
majority, forces some item onto
the agenda for a floor vote, even if the speaker wanted it dead.
However, for some reason (logistical? psycho-robotical?) it is rare
that such petitions succeed.
If the reason is logistical then simply a computer system for allowing
the congressmen ease in signing such petitions, could go a long way.

In the US senate, they can keep stuff off the floor using the
"filibuster" and thus a minority of 40% can stop stuff, which is
absurd. I do not know what the analogue
of that is in various US states, if any. I believe I know the right
way to cure the filibuster problem -- which is good compared to your
problem whose cure is unclear.
Namely: the end of debate ("cloture") should indeed require a
supermajority, say 60% like now, but this threshhold should decline
with time at a specified rate until it eventually reaches 50%.
This cure causes the minority to be able to extend debate and get
media attention,
which is good (otherwise the majority could ram things thru with zero
debate and media), but it does not allow them to extend it forever and
thus allow a minority to stop stuff.
The present filibuster rule is the worst of all worlds, allowing
minorities to stop stuff with zero debate. That is just absurd.
So how about a constitutional amendment to enact this obvious
filibuster cure?

Returning to your speaker issue...
As I said, far as I know B (multiple agenda control) has not yet been
tried, but perhaps it could be done, and it might be
interesting/useful to try to design (B). We now have computers that
could be installed in legislatures, which allows algorithms to be used
that in previous eras might have been deemed too complicated and
nasty. That's the good news. The bad news is, nobody is going to
vote for your scheme if they do not understand it, which means it has
to be kept pretty simple anyhow.

So, let's see. There are various ways one could do (B).
One is: there is not one speaker, there are, say, 3. These 3 are
chosen using a PR
(proportional representation) voting scheme. Each of the 3
co-speakers controls the agenda 1/3 of the time according to a set
control schedule. (Or 5, and each gets 1 day per workweek MTWRF.)
They can divvy up stuff cooperatively. Point of this is, hopefully
enough diversity of views will arise that stuff that ought to be on
the agenda, will find a way to get on the agenda.

Also, it is probably not a great idea to have just 1 speaker, even
aside from monopoly issues -- because it is better to have more than 1
congressman acquire leadership experience.

There are numerous PR schemes that could be used. I assume you
already know them.

Now in countries with a "Prime Minister" that is different from the
USA's "Speaker" concept. The prime minster is like the US president,
he does executive stuff. The speaker does not do stuff, he just
controls the agenda for voting.
Having 3 co-prime-ministers on different work days likely would not
work, they might work at cross-purposes.

That would hopefully be less of a problem with mere speakers.

[Jameson Quinn]

I like this last "elimination order" algorithm. Note that it decently if parties vote in lock-step. That is, if there were a 60/40 split yellow/purple split, it would at worst elect the 41st yellowest member, and would in practice probably elect the most senior of the 20 least-yellow yellows, which is a pretty good result.

In fact, it almost works better if parties vote in lock-step. Otherwise, in that scenario, the last 20 eliminations would appear random, and potentially be gameable, with bad consequences for everyone if the strategy backfired.

Of course, it's politically untenable to do it publicly. Nobody wants to get labelled as the "least-Republican Republican," at least, not these days.

[Andy Jennings]

On Mon, Sep 8, 2014 at 1:19 PM, Warren D Smith <warre...@gmail.com> wrote:

> I think these are the interesting mathematical questions:
>
> - Can we design a system that elects the median legislator as speaker even
> if the majority votes in lockstep for someone more extreme?

--no, you cannot, because that majority could be voting honestly, in
which case their choice WOULD be the median legislator (anyhow
Condorcet winner).

For the general social choice problem, that is correct.  But we have more structure here, because every voter is a candidate and every candidate a voter.

[Warren D Smith]

>> > - Can we design a system that elects the median legislator as speaker
>> even
>> > if the majority votes in lockstep for someone more extreme?
>>
>> --no, you cannot, because that majority could be voting honestly, in
>> which case their choice WOULD be the median legislator (anyhow
>> Condorcet winner).
>>
>
> For the general social choice problem, that is correct. But we have more
> structure here, because every voter is a candidate and every candidate a
> voter.

--so?
I mean, the 55% could honestly say that Boehner was their top choice
and honestly say every other choice was super-horrible.
Or, that might have been an exaggeration.
In the honest case, how can you elect anybody beside Boehner?

[Andy Jennings]

On Mon, Sep 8, 2014 at 2:39 PM, Jameson Quinn <jameso...@gmail.com> wrote:

I like this last "elimination order" algorithm. Note that it decently if parties vote in lock-step. That is, if there were a 60/40 split yellow/purple split, it would at worst elect the 41st yellowest member, and would in practice probably elect the most senior of the 20 least-yellow yellows, which is a pretty good result.

In fact, it almost works better if parties vote in lock-step. Otherwise, in that scenario, the last 20 eliminations would appear random, and potentially be gameable, with bad consequences for everyone if the strategy backfired.

Of course, it's politically untenable to do it publicly. Nobody wants to get labelled as the "least-Republican Republican," at least, not these days.

Yes, it's definitely a liability in the next primary race.  Still, there are quite a few politicians who would risk it for a chance at being speaker.

 

[Bruce Gilson]

On Mon, Sep 8, 2014 at 5:39 PM, Jameson Quinn <jameso...@gmail.com> wrote:

​[...]

Of course, it's politically untenable to do it publicly. Nobody wants to get labelled as the "least-Republican Republican," at least, not these days.

 

​Well, Joe Manchin of West Virginia is pretty much considered the "least-Democratic Democrat" in the Senate. ​There are even rumors that he will switch parties if the GOP controls the Senate after this November's election, so he will still be on the majority side.

[Andy Jennings]

On Mon, Sep 8, 2014 at 2:39 PM, Jameson Quinn <jameso...@gmail.com> wrote:

I like this last "elimination order" algorithm. Note that it decently if parties vote in lock-step. That is, if there were a 60/40 split yellow/purple split, it would at worst elect the 41st yellowest member, and would in practice probably elect the most senior of the 20 least-yellow yellows, which is a pretty good result.

It might be worth finding a way to choose the next eliminated from the ballots of _everyone_ who's been eliminated so far, instead of just the last one eliminated.  We'd want to use something like anti-plurality (eliminate the person who's _last_ on the most ballots), though, because we want to choose an extremist, not a compromise candidate.  Would that add stability?  Make things better or worse?

Also, anti-plurality on the whole ballot set might be a good way to choose the first candidate to eliminate.

[Andy Jennings]

Well, if Boehner were _last_ on the ballots of all the other voters, then he can't be the median candidate.  Since every voter is a candidate, you can be sure that there's a better compromise candidate.

Also, you are correct that any such system would not pass the Condorcet criterion.  In general, I guess I believe that this is a weakness in the Condorcet criterion.  It forces susceptibility to total manipulation by a majority caucus.

Tyranny of the majority and all that.

[Warren D Smith]

> Well, if Boehner were _last_ on the ballots of all the other voters, then
> he can't be the median candidate. Since every voter is a candidate, you
> can be sure that there's a better compromise candidate.

--Not so!
(Well, I guess it depends what you consider a "median candidate" to be.)

One claim is, if Boehner is first on 51% of ballots, then he
automatically is median
no matter what the other 49% of voters do.

Why should we say that?
In a 1-dimensional situation where the candidates & voters lie on a
line, voters prefer candidates in distance order (closest = most
preferred) the usual claim is that the "median" candidate is one of
the two closest to the voter-median. If, say, the voters happen to
come in 2 clusters, 51% in one cluster, 49% in the other, and Boehner
is located in the big cluster, all the other 99 candidates are located
in other places, then Boehner would be the median candidate (he could,
in fact, lie exactly at the voter median!) even though he could also
be (fully honestly) ranked dead last on 49% of the ballots.

--I think maybe what you are trying to get at if, what is every voter
is herself a candidate,
the voter & canddt sets are the same set. In that case, every voter
would get exactly 1 top-rank vote (for herself)... only the two
extreme ones could ever be ranked last...
and if the set-cardinality were odd, then then median voter would
always be the condorcet winner (with honest votes). However, before
you rush to adopt Condorcet for
speaker elections, let me point out that (a) there will be dishonest
votes, and (b)
really, not every congressman wishes to be speaker and hence will not
even vote himself top, and that is the way is should be, and so this
entire model is bogus.
And indeed every condorcet system will be (according to you) bad for
speaker-electing purposes anyhow!

> Also, you are correct that any such system would not pass the Condorcet
> criterion. In general, I guess I believe that this is a weakness in the
> Condorcet criterion. It forces susceptibility to total manipulation by a
> majority caucus.
>
> Tyranny of the majority and all that.

--it is not so much the condorcet criterion I am worried about, as the
"51% top"
criterion, or actually, the "a majority has the power to get its
unanimously chosen winner" criterion. Any system obeying that, will
in your view, be bad for speaker-choosing purposes because a 51%
collusion can force a speaker. But any system disobeying that will be
highly dubious! Indeed almost every system ever proposed obeys the
"majority has the power to force a winner" criterion -- score,
approval, condorcet, IRV.

In the case of Borda voting, I claim

THEOREM:
With Borda, a 51 majority has power to force a winner, *but*
only if they know the other votes.
They cannot force him working in total ignorance of the other 49 votes.

PROOF:
Let's say the 51% majority all vote X top,
getting him summed score 51*(C-1)
in a C-candidate race with scores 0,1,2,...,C-1.
Then there necessarily will exist at least one rival candidate Y whose score is
at least the average among the C-1 rivals, namely his total will be at
least 51*(C-2)/2.
Now, the other 49% of the voters can respond with ballots ranking X last and
Y top. In that case at the end of the day, X's score will be
51*(C-1)
while Y's score will be
51*(C-1)/2 + 49*(C-1).
Y's score is greater provided C>98/47=2.08511.

That proves the 51% majority cannot force X to win, if they work in
ignorance of how
the other 49% will vote, the election is held using Borda, and there
are at least 3 candidates.

If the 51 have some knowledge about the other 49%, though, they may be
able to force X to win. In particular, let's say they have perfect
knowledge of the other 49 votes.
Then they can vote as follows:
(1) X is top.
(2) 49 of the 51 voters vote the same, except reversed, as a matching
member of the 49,
thus exactly cancelling out all their pairwise preferences among all X's rivals.
(3) the remaining 2 voters do something useful.
This forces X to win.
Q.E.D.

[Jameson Quinn]

You'd want to do anti-Bucklin, not anti-plurality, because the median of the eliminated votes is a meaningful concept. That would tend to get the "alternating one from each side" dynamic working, too.

[Andy Jennings]

On Thu, Sep 11, 2014 at 7:25 AM, Warren D Smith <warre...@gmail.com> wrote:

--it is not so much the condorcet criterion I am worried about, as the
"51% top"
criterion, or actually, the "a majority has the power to get its
unanimously chosen winner" criterion.   Any system obeying that, will
in your view, be bad for speaker-choosing purposes because a 51%
collusion can force a speaker.  But any system disobeying that will be
highly dubious!

Please define "highly dubious" mathematically and prove that any system disobeying the "51% top" criterion will be highly dubious.

In the meantime, yes, I'm trying to find a good one that meets the "51% top" criterion.  What do you think of the other system I proposed in this thread, "last eliminated chooses next eliminated"?


 

[Jameson Quinn]

I like the "eliminate the anti-Bucklin winner of the eliminated candidate's votes" idea. But it does break down a bit when there's a 51-49 split; the winner would basically be a nonentity. So honestly, I think you should stop the eliminations when 1/3 of the chamber is left, and take the (Bucklin?) winner among whoever's left. That would elect a generally centrist speaker, but still one who has some play with their own party.

(If the final rule were Bucklin, you'd have to use graded ballots, because with ranked ballots there would be dishonest incentives for the minority party to betray their own party for a moderate member of the other side. I think that 12 grade levels, A+ through F, would be about right). 

[Warren D Smith]

>> --it is not so much the condorcet criterion I am worried about, as the
>> "51% top"
>> criterion, or actually, the "a majority has the power to get its
>> unanimously chosen winner" criterion. Any system obeying that, will
>> in your view, be bad for speaker-choosing purposes because a 51%
>> collusion can force a speaker. But any system disobeying that will be
>> highly dubious!
>
>
> Please define "highly dubious" mathematically and prove that any system
> disobeying the "51% top" criterion will be highly dubious.

--well, one trivial answer is, if it disobeys it, it is highly dubious! :)
And I think a lot of people would say that, not just me.

> In the meantime, yes, I'm trying to find a good one that meets the "51%
> top" criterion. What do you think of the other system I proposed in this
> thread, "last eliminated chooses next eliminated"?

--I thought it was "highly dubious"! :)
It was nondeterministic, and fairly complicated, and pretty mysterious.

To me, anyhow, it is pretty clear you have to abandon the "one
speaker" paradigm and move to a multiple co-speaker set up, or abandon
the "there are only 2 parties" paradigm
those are the only acceptable ways out of the monopoly control mess
that I've been able to think of.

My remarks about "majority can force a winner" were intended to try to
clarify that, i.e. point out exactly what you would have to sacrifice
if you insist on keeping those two
paradigms. It would be a huge sacrifice, probably one that most
people would consider unacceptable. It's petty much an impossibility
proof like "Arrow's theorem" -- no "good" voting system can exist for
this purpose.

By the way, if you are going to be nondeterministic, why not at least
do it in a simple and non-mysterious way? Like, oh, pick a winner at
random with probability proportional to his total score. I'm not
advocating this, I'm just saying at least we'd easily understand what
was going on and what properties it had.

[Rob Wilson]

After thinking about this, I think the best solution would be to use a Condorcet method that handles a cycle with a restricted version of range voting. Every member of a legislature would rank each candidate. They would then score each candidate with the following rules.

1) You can't score a candidate higher than a candidate you ranked higher.

2) The score given to a candidate must be at minimum (number of candidates- rank of candidate)*3. For the first ranked candidate, this would also be the mandatory score and last place would have a mandatory score of 0 pts.

In a four candidate race, first place would get a score of 9 pts; second place could be 6 -9 pts; third place could be 3 to however many points you ranked the second candidate. fourth place would get 0 points

If this system had been used in the UK, do you think Nick Clegg would be Prime Minister right now?

[Andy Jennings]

On Thu, Sep 11, 2014 at 7:58 AM, Jameson Quinn <jameso...@gmail.com> wrote:

I like the "eliminate the anti-Bucklin winner of the eliminated candidate's votes" idea. But it does break down a bit when there's a 51-49 split; the winner would basically be a nonentity. So honestly, I think you should stop the eliminations when 1/3 of the chamber is left, and take the (Bucklin?) winner among whoever's left. That would elect a generally centrist speaker, but still one who has some play with their own party.

You're probably right, but I dislike the additional complexity.

It's tempting to allow some legislators to opt out of being a candidate for speaker, making fewer candidates than voters.  I can think of some ways to do it.  But I don't like it.  It's way too easy for the moderates to get their arms twisted in the caucus and to "choose" not to run for speaker.

I would much rather have everyone eligible, have a relatively moderate candidate win, and then if she declines, offer it to the next-to-last eliminated, and so on.  It's much harder to decline the leadership once it's offered.

 

[Warren D Smith]

is it reasonable to have 500 candidates?

[Andy Jennings]

On Sat, Sep 13, 2014 at 10:26 AM, Warren D Smith <warre...@gmail.com> wrote:

is it reasonable to have 500 candidates?

I think most legislatures are smaller than the US House, so there's no need to dwell on this outlier.  The AZ Senate has 30 members.  It is totally reasonable to require each of them to rank them all.

Even in the case of the US House, considering the importance of their position, I don't think it's unreasonable to ask them to rank all 435 representatives.  They can get help from other reps, consult their staff, use party lists, etc..  If it was required of them, I'm sure they could manage it.

[Warren D Smith]

> Even in the case of the US House, considering the importance of their
> position, I don't think it's unreasonable to ask them to rank all 435
> representatives. They can get help from other reps, consult their staff,
> use party lists, etc.. If it was required of them, I'm sure they could
> manage it.

--first of all, they'd probably "manage it" by getting the ordering
from party headquarters and all would use the same one. Utterly
defeating purpose.

Second, "they could manage it with assistance from staff" is not a
justification for using
a voting system. It is more like an admission of failure. I mean, if
they can't manage voting without help, the system is too damn hard,
and deserves to be rejected.

Third, let's take a look at the (ugly) system proposed:

"1) Every senator submits a ranking of all senators.
2) One of the senators is chosen. The last-ranked senator on his
ballot is eliminated.
3) The ballot for the senator that just got eliminated is used to
determine the next senator that gets eliminated (the lowest-ranked
uneliminated senator).
4) Repeat step 3 until all senators but one are eliminated.
I'm thinking this would create a back-and-forth dynamic, eliminating
the most extreme senators on each side until only one remains.
You could choose the senator in step 2 randomly."

Obviously this system is highly vulnerable to collusions, despite any
and all claims it is not. The Republican majority could very simply
collude to make sure every single Democrat is eliminated, by never
repeating a name in the last-place spots. (Do you think they are
complete idiots?) If they did not collude, they;d be at a huge
disadvantage,
so you've created a system which essentially forces massive collusion,
like it or not.
Whoopee.

The problem anyhow is not that somebody "extreme" is
elected speaker. The problem is robot lockstep voting causing 100%
control over the agenda by one side. This would happen no matter how
"extreme" or not the guy was.
Look at the vote they just had on the constitutional amendment to
overturn Citizens United. 100% lockstep republican vote against it,
even though many republicans had previously said they thought Citizens
United was a huge error, some in the strongest
terms possible, such as McCain said it was the worst supreme court
decision ever.
Tell me -- was there some "less extreme" Republican out there? Because in this
vote, all were exactly the same.

Do you think Hastert or Boehner were the most extreme members of
congress? Not even close. So you are trying to solve the wrong
problem, by a ugly complicated method, which does not work anyway.

[Andy Jennings]

 

Utterly
defeating purpose.

 

Third, let's take a look at the (ugly) system proposed:
"1) Every senator submits a ranking of all senators.
2) One of the senators is chosen.  The last-ranked senator on his
ballot is eliminated.
3) The ballot for the senator that just got eliminated is used to
determine the next senator that gets eliminated (the lowest-ranked
uneliminated senator).
4) Repeat step 3 until all senators but one are eliminated.
I'm thinking this would create a back-and-forth dynamic, eliminating
the most extreme senators on each side until only one remains.
You could choose the senator in step 2 randomly."

Obviously this system is highly vulnerable to collusions, despite any
and all claims it is not.  The Republican majority could very simply
collude to make sure every single Democrat is eliminated, by never
repeating a name in the last-place spots.  (Do you think they are
complete idiots?)  If they did not collude, they;d be at a huge
disadvantage,
so you've created a system which essentially forces massive collusion,
like it or not.
Whoopee.

It appears that you don't understand the system.

[Warren D Smith]

--I just made a claim about this system.
(I also quoted the entire system description verbatim.) Is there
some part of my claim you dispute? If so, what?
Can you provide a counterexample?

[Toby Pereira]

I was just thinking about this again. This would go against Andy Jennings's ideas to stop a majority working together, but I think approval voting with live results and changeable votes (up to a deadline) could be a good method.

There is a set time limit (an hour, day, week or whatever), and each voter submits their approvals (presumably by computer - ignoring for now any potential fraud). At all times, the current approval totals are available to all voters so they can add or remove approvals. The winner is the candidate/voter with the most approvals at the time of the deadline.

In case there is some incentive for a group of voters to suddenly withdraw support for the leading candidate in the last minute, there could be a non-deterministic end-point. It could be that there is a set period where the election is guaranteed to be live, and then an extra period where it ends randomly according to some distribution.

On Sunday, 7 September 2014 00:10:55 UTC+1, Rob Wilson wrote:

Consider a situation in which a body has to elect a leader. This body would be educated enough to understand any voting system along with the utility of any strategy that could be used with that particular system. Each member of the body knows the ideals of each other member and has a good idea of how they would vote if they were to vote honestly. What do you think would be the best voting system to use? In this situation, I don't like score or approval because I think it might have a good chance at devolving into plurality.

For right now, I think the best method of electing a head of such a body would to be to use Black's Condorcet method (using Borda to break cycle). The winner of the election would be the elected head of the body unless members of this body could get a majority to agree on a different candidate within 24 hours.

Instead of using Black's method, maybe you could make it more range-voting like. You could maybe allow a voter to give a candidate 1 to 3 points less than the candidate ranked above him.

What do you think is the best voting system to use in this situation and what considerations do you think we'd have watch out for?

[Toby Pereira]

The median isn't meaningless in multiple dimensions. There is the geometric median - https://en.wikipedia.org/wiki/Geometric_median

[Frank Martinez]

I'm as anti-misogynistic as They come but I think it's fair to say the idea of a single elected Official being "patriarchally derived" is a stretch. Patriarchy is simply the predominant social system in early Human history and by that standard One could argue numbers are patriarchal.

As far as a committee goes, experience shows when a single Individual is responsible, accountability is easier to obtain.

On Sunday, September 7, 2014, Jim Mueller <jimmue...@gmail.com> wrote:

The question ceases to have any relevance if one dumps the archaic,  patriarchally derived, zero sum game inducing singular leader and converts to a executive council with each member having voting power equal to the number votes that the candidate received.

The council would more perfectly represent the desires of the body than would a singular leader obtained through any voting system that restricts or denies the voter's choice . The Executive Council would choose a voting system to elect a Chair or Executive Committee for the Council. 

Sent from my iPhone

On Sep 6, 2014, at 6:10 PM, Rob Wilson <blahf...@gmail.com> wrote:

Consider a situation in which a body has to elect a leader. This body would be educated enough to understand any voting system along with the utility of any strategy that could be used with that particular system. Each member of the body knows the ideals of each other member and has a good idea of how they would vote if they were to vote honestly. What do you think would be the best voting system to use? In this situation, I don't like score or approval because I think it might have a good chance at devolving into plurality.

For right now, I think the best method of electing a head of such a body would to be to use Black's Condorcet method (using Borda to break cycle). The winner of the election would be the elected head of the body unless members of this body could get a majority to agree on a different candidate within 24 hours.

Instead of using Black's method, maybe you could make it more range-voting like. You could maybe allow a voter to give a candidate 1 to 3 points less than the candidate ranked above him.

What do you think is the best voting system to use in this situation and what considerations do you think we'd have watch out for?

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[Andy Jennings]

Technically, you're right.  We can always define a norm to measure distance between candidates and then choose our speaker to be the one that minimizes the sum of the distances to the other candidates.

But the true 1D case is nice because the placement of the candidates on the spectrum doesn't matter, just the order.  And since 1D is a reasonable first approximation to current US politics, it's pretty easy to imagine.  There is research out there that actually tries to place current politicians on a 1D spectrum.

When 1D fails to be a good approximation, then choosing the distance function is a lot more important and, at the same time, more difficult.

[Brian Langstraat]

The following Approval Voting (AV) method may be a simple way to elect an acceptable moderate leader for a legislative body:

Each legislator must vote to approve more than half of the legislators.

The legislator with the the most approvals is the leader.

For example, the United States House of Representatives has 435 members with about 240 Republican and 195 Democratic representatives.

Each member must vote for at least 218 members.

All of the Ds would approve the 195 Ds, but they will need to approve at least 23 moderate Rs as well.

All of the Rs would approve at least 218 Rs, but may avoid approving the 22 most moderate R's.

Likely, the 23rd most moderate R would be approved as the Speaker of the House.

[Ted Stern]

The 22 most moderate Rs might avoid approving the 22 most conservative Rs, as well.

One problem I see with this is that the conservative to moderate to liberal spectrum is not really one dimensional.  Around the middle of the spectrum there is some squishiness where a couple of candidates could have the same approval level.

A refinement to this might be to use something similar to Jameson Quinn's 3-2-1 voting method:

Each member gives scores of A through F, with scores A-C being approved, and D-F being disapproved.  Each voter must score at least 218 candidates at C or higher.

Choose the three candidates with highest median (e.g. Majority Judgment) scores as semifinalists.

Drop the candidate with the highest disapproval to get 2 finalists.

Choose the candidate who pairwise beats the other, not counting pairwise votes below the approval threshold.  I.e., a D > F pairwise preference is not counted, but a C > D preference is.

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[parker friedland]

"In this situation, I don't like score or approval because I think it might have a good chance at devolving into plurality."

How will approval voting degrade into plurality voting in this situation?

[Andy Jennings]

On Tue, Apr 11, 2017 at 3:02 PM, Brian Langstraat <langstra...@gmail.com> wrote:

The following Approval Voting (AV) method may be a simple way to elect an acceptable moderate leader for a legislative body:

Each legislator must vote to approve more than half of the legislators.

The legislator with the the most approvals is the leader.

For example, the United States House of Representatives has 435 members with about 240 Republican and 195 Democratic representatives.

Each member must vote for at least 218 members.

All of the Ds would approve the 195 Ds, but they will need to approve at least 23 moderate Rs as well.

All of the Rs would approve at least 218 Rs, but may avoid approving the 22 most moderate R's.

Likely, the 23rd most moderate R would be approved as the Speaker of the House.

If the Rs collude, they will choose 170 of their favorite Rs who they all approve (240 approvals).  They can spread the rest of their approvals out among the rest of the legislators (265 Rs and Ds) so nobody gets more than 44.  (240 * 170 + 43.47 * 265 = 52320 = 218 * 240 = the total amount of the approvals the Rs have to give.)

170 is the critical point here.  If they go for 169, they can't do it.  (240 * 169 + 44.21 * 266 = 52320, so the Rs must give someone at least 45 votes.)  That's for an undisputed win.  If the Rs are sure they can win a tie-break vote, then they could go down to 168 but not 167.

So the Republicans (55.2% of the legislature) got to eliminate 265 or 267 people (60.9% or 61.4% of the legislature).

It's not the perfect outcome that you indicated, but it's actually not too bad.

If the Republicans are 60% of the legislature, they get to eliminate about 75% of the legislators from speaker eligibility.

If the Republicans get 66% of the legislature, they get complete control of the speaker.

Does that sound reasonable?  It's certainly simpler than the system I proposed.

Also, these "perfect balance" solutions are pretty fragile.  The defection of a couple of moderate Rs cooperating with the Ds could get practically anyone into the speakership.  So maybe they will just go with a simple strategy like you propose.

~ Andy

 

On Wednesday, July 27, 2016 at 12:16:58 AM UTC-5, Andrew Jennings wrote:

Technically, you're right.  We can always define a norm to measure distance between candidates and then choose our speaker to be the one that minimizes the sum of the distances to the other candidates.

But the true 1D case is nice because the placement of the candidates on the spectrum doesn't matter, just the order.  And since 1D is a reasonable first approximation to current US politics, it's pretty easy to imagine.  There is research out there that actually tries to place current politicians on a 1D spectrum.

When 1D fails to be a good approximation, then choosing the distance function is a lot more important and, at the same time, more difficult.

On Tue, Jul 26, 2016 at 1:52 PM, 'Toby Pereira' via The Center for Election Science <electio...@googlegroups.com> wrote:

The median isn't meaningless in multiple dimensions. There is the geometric median - https://en.wikipedia.org/wiki/Geometric_median

On Monday, 8 September 2014 20:19:02 UTC+1, Andrew Jennings wrote:

I think these are the interesting mathematical questions:

- Can we design a system that elects the median legislator as speaker even if the majority votes in lockstep for someone more extreme?

- How do you extend the concept to more than one dimension, where median is meaningless?

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[Brian Langstraat]

Dodecatheon,

My example was simplistic and I made some assumptions about strategy, so my post would be compact.

The 22 most moderate Rs might avoid approving the 22 most conservative Rs, as well.

My assumption that legislators would approve members of their own party first is fairly true, except for the rare defector (labeled RINO or DINO).

Within parties, moderate members may not be willing to vote for the most extreme members of their own party.

If the moderate members of the majority party tend to vote for the other moderate representatives, then the most approved member would tend to be even more moderate (such as the 10th most moderate R being approved as the Speaker of the House).

In a legislature dominated by moderates, a moderate member of the minority party could be the most approved.

One problem I see with this is that the conservative to moderate to liberal spectrum is not really one dimensional.  Around the middle of the spectrum there is some squishiness where a couple of candidates could have the same approval level.

I agree that the simple right/left political spectrum is too simple.

Many dimensions would need to be considered to select approvals, such as social, economic, and personal views.

Competence and experience would need to be considered, so an experienced extremist may get more approvals than a incompetent moderate.

With more than two parties (and more squishiness), this AV method would work even better to produce a consensus leader.

To deal with potential chaos/squishiness of the high approval candidates, an extra step (of plurality) could be added:

Each legislator must vote to approve more than half of the legislators.

The two legislators with the the most approvals proceed to a single-vote plurality (FPTP) election.

(In cases of ties among the most approved legislators, each legislator must vote to approve more than half of the most approved legislators.)

The legislator with the the majority of the votes is the leader.

A refinement to this might be to use something similar to Jameson Quinn's 3-2-1 voting method:

This voting method seems too complex to actually be used.

I prefer Range Voting (RV) to most single-winner voting systems, but in this case parties could manipulate the ranges to their advantage.

For example, the Rs could vote A for all non-moderate Rs and vote F for all moderate Rs and Ds.

The A votes from the majority Rs would out-number the F votes from the minority Ds for non-moderate Rs, so three non-moderate Rs with highest median scores (A) would be semifinalists.

The non-moderate R with the highest disapproval (F) would get dropped, so two non-moderate R finalists remain.

The non-moderate R whose pairwise beats the other would win.

[Brian Langstraat]

Andrew,

This is great analysis!

I was pondering a majority spread strategy as well, but had not done the calculations yet.

Also, these "perfect balance" solutions are pretty fragile.  The defection of a couple of moderate Rs cooperating with the Ds could get practically anyone into the speakership.  So maybe they will just go with a simple strategy like you propose.

Approving 170 Rs with 240 votes each (265 others with 239 votes each) would require an extreme level collusion by the majority party without at least two moderate R defectors or independents to choose a moderate R speaker, which seems unlikely considering the recent "Repeal and Replace of Obamacare" failure.

Assuming that the "perfect balance" solution occurs, we can compare center of the legislative spectrum outcomes.

The center-most legislator is the 218th from both extremes (23rd most moderate R).

Assuming that the current plurality method selects the median majority party member as the speaker,

Paul Ryan is about the 98th most center legislator for the Rs.

170 is the critical point here.

So the Republicans (55.2% of the legislature) got to eliminate 265 or 267 people (60.9% or 61.4% of the legislature)

The 170th least moderate R is the 49th most center legislator for the Rs, which is about 49 legislators more moderate than FPTP.

If the Republicans are 60% of the legislature, they get to eliminate about 75% of the legislators from speaker eligibility.

If the Rs are 60% of the legislature, about the 116th least moderate R is the 103rd most center legislator for the Rs instead of the 88th with FPTP.

If the Republicans get 66% of the legislature, they get complete control of the speaker.

If the Rs are 67% of the legislature, the least moderate R is the 218th most center legislator for the Rs instead of the 72nd with FPTP.

Does that sound reasonable?  It's certainly simpler than the system I proposed.

So this AV method could have much worse results than FPTP as the majority party increases and no moderate members defect from voting for the most extreme member(s) of their party.

With the assumption of the median majority party member as the speaker using FPTP, the least center speaker (109th most center legislator for the Rs) is when there is a 50%+1 majority.

[This partially explains why Paul Ryan seems to have so little support.]

At a 100% majority, the center-most legislator is the speaker.

The "sweet spot" where the same legislator is speaker using the AV method (w/o defections) and FPTP is around a 58% majority.

If the Rs are 58% of the legislature, about the 126th least moderate R is the 92nd most center legislator using both voting methods.

In real life when the majority reaches over 58%, at least 2 of the 125 more moderate party members would usually defect to stop an extremist majority party member from being the speaker.

When the majority reaches over 67%, at least 2 of the 290 more moderate party members would usually defect to stop the most extremist majority party member from being the speaker.

Thus, this AV method (with defective moderates) compared to FPTP would almost always elect more:

moderate leaders with a 50%-57% majority,

non-extremist leaders with a 58%-66% majority, and

anti-extremist leaders with a 67%-100% majority.

[Brian Langstraat]

Andrew,

Since the AV (approve at least half) method has a fatal flaw when parties have extreme collusion, I think that the best method is some form of the "elimination order" method copied below:

1) Every senator submits a ranking of all senators.

2) One of the senators is chosen.  The last-ranked senator on his ballot is eliminated.

3) The ballot for the senator that just got eliminated is used to determine the next senator that gets eliminated (the lowest-ranked uneliminated senator).

4) Repeat step 3 until all senators but one are eliminated.

I'm thinking this would create a back-and-forth dynamic, eliminating the most extreme senators on each side until only one remains.

The main flaw that I see is that the minority party or a vengeful loser may force the elected final speaker to be one of the least competent members.

To avoid an incompetent speaker, another voting method could be added to the beginning, middle, or end.

In the beginning, a proportional method round (such as STV or RRV) could be used to select a variety of fairly competent members (around 45) to participate in the elimination round.

This addition could result in the most competent speaker, but be the most susceptible to collusion.

In the middle (2/3 eliminated), a proportional method round could be used to select moderate fairly competent members (around 15) to participate in the final elimination round.

This addition could result in a more competent speaker, but be more susceptible to collusion.

In the end (around 5 remaining members), a range/approval method round could be used to select a competent speaker.

This addition could result in the least competent speaker, but be the least susceptible to collusion.

[Brian Langstraat]

Andrew,

There may be a simple solution to the fatal flaw when parties have extreme collusion using the AV (approve at least half) method.

Between collecting all of the ballots and counting the votes, a representative is randomly selected who automatically receives two extra votes.

(An extra 2 votes would be a drop in the bucket compared to at least 94830 approval votes.)

This would greatly increase the risk in using the majority spread strategy, since any representative could become speaker including the most extreme members of the minority party.

With an increasing 50%-66% majority, the risk that a minority speaker could be randomly selected would decrease.

With an increasing 67%-100% majority, a minority speaker could not be randomly selected, but the median majority party member (assumed speaker) would approach the median of the legislature.

Moderate majority party members would rarely risk selecting an extreme minority speaker to have an extreme majority speaker, so they would usually vote for their fellow moderates by a margin that could easily override 2 votes.

[Brian Langstraat]

For an elimination method, a good way to decrease majority collusion and increase the speaker competence may be to randomly divide the members into smaller groups that elect members to move forward in the election.

This may reduce the majority's ability to strategically pool their votes and the minority's ability to eliminate all of competent speakers.

For houses of at least 25 members:

1) Every senator submits a ranking of all senators.

2) [Senators are randomly divided into 5 groups.]

3) One of the senators [in each group] is chosen.  The last-ranked senator [in his group] on his ballot is eliminated.

4) The ballot for the senator that just got eliminated is used to determine the next senator [in the group] that gets eliminated (the lowest-ranked uneliminated senator).

5) Repeat step 4 until all senators [in each group] but one are eliminated.

6) With the group of 5 remaining senators, repeat step 3 then step 4 until all senators but one are eliminated.

[Brian Langstraat]

Andrew,

Your original solution may work well for more than two parties with some modification.

My ideal solution is to force one party to nominate 50% of the legislature and then let the other party choose among them.

The legislature is split into 2 groups, Nominators and Electors, that each consist of half (if odd, extra one to Nominators) of the representatives using the following method:

1. Each representative must choose which group to join or be randomly assigned to a group.

2. If one of the groups has more than half of the representatives, then 

random representatives are transferred to the other group until both groups contain half of the representatives.

(There are subgroups consisting of members of each party in both of the groups.)

3. The largest subgroup (ties broken randomly) in either group must trade random non-party member(s) of their group with random party member(s) in the other group until there are no non-party members in their group or no party members in the other group.

4. Step 3 is repeated with the next largest subgroup(s) (where members of larger subgroups cannot be traded) until the largest subgroup(s) are independents and single-member parties.

5. The Nominators use the AV (approve at least half) method to nominate the most approved half of the representatives.

6. The Electors use the AV (approve at least half) method to elect the most approved nominee as the speaker.

On Sunday, September 7, 2014 at 12:10:10 PM UTC-5, Andrew Jennings wrote:

I've been thinking about this same question.

In the Arizona House and Senate, the majority party meets alone (a caucus meeting) and chooses the speaker without any input from the minority.  (They do have to make it official in a floor vote later.)  The speaker chooses the chairs of all the committees and controls the legislative schedule, so the minority party is essentially shut out.

Whatever method the majority caucus uses to choose the speaker (usually plurality), we assume that a majority dominates, so a majority of the majority (as little as 26% of the legislators) can control the body.  I'm assuming this is how it is in most legislatures.

If we want a system that chooses a chair more fairly, it has to compensate for this caucus system.  A majority, voting in lockstep, should not be able to completely control the outcome.

My ideal solution is to force one party to nominate 50% of the legislature and then let the other party choose among them.  Ignoring the fact that it only works for two parties, if you wrote this into the state constitution, could the legislature subvert it?  By RRoO, can they change their speaker at any time with a majority vote?  Would the majority party try to install a non-moderate speaker?

~ Andy

====Addendum====
As an academic exercise, I've wondered if any existing voting system is robust to caucusing, choosing a compromise even if the majority votes in lockstep.

Range/approval are not.  The majority can vote one person MAX and everyone else MIN and have their way no matter how the minority votes.

Condorcet is not.  The majority can put their winner first and they will be the Condorcet winner no matter how the minority votes.

The closest I can come is Borda, if you force the majority to vote first and let the minority see the vote totals before they vote.  (Borda's biggest weakness, not being robust if candidates are added or removed, is moot if all legislators are automatically candidates.)  According to my (preliminary) calculations, in a legislature of 100 (100 candidates and 100 voters), a majority of 52 has enough power to eliminate 9 candidates from winning.  A majority of 60 could eliminate 51 candidates from winning.  And a majority of 67 could choose the winner outright.  I've been wondering if you could achieve "fairness" by adjusting the Borda points or changing the weight of each voter in the voting order.

On Sat, Sep 6, 2014 at 4:10 PM, Rob Wilson <blahf...@gmail.com> wrote:

Consider a situation in which a body has to elect a leader. This body would be educated enough to understand any voting system along with the utility of any strategy that could be used with that particular system. Each member of the body knows the ideals of each other member and has a good idea of how they would vote if they were to vote honestly. What do you think would be the best voting system to use? In this situation, I don't like score or approval because I think it might have a good chance at devolving into plurality.

For right now, I think the best method of electing a head of such a body would to be to use Black's Condorcet method (using Borda to break cycle). The winner of the election would be the elected head of the body unless members of this body could get a majority to agree on a different candidate within 24 hours.

Instead of using Black's method, maybe you could make it more range-voting like. You could maybe allow a voter to give a candidate 1 to 3 points less than the candidate ranked above him.

What do you think is the best voting system to use in this situation and what considerations do you think we'd have watch out for?

--

[Brian Langstraat]

To improve on my previous post:

The legislature is split into 2 groups, the Majority group and the Minority group, that each consist of half (if odd, extra one to the Majority group) of the representatives using the following method:

1. Each representative would be randomly assigned to a group.

(There are subgroups consisting of members of each party in both of the groups.)

2. The largest subgroup (ties broken randomly) in either group must trade random non-party member(s) of their group with random party member(s) in the other group until there are no non-party members in their group or no party members in the other group.

(This group is entitled the Majority group.)

3. Step 2 is repeated with the next largest subgroup(s) (where members of larger subgroups cannot be traded) until the largest subgroup(s) are independents and single-member parties.

4. Each group uses the AV (approve at least half) method to select the most approved half+1 of the representatives who each receive a single group approval vote.

(Ties are decided by Single Non-transferable Voting.)

5. Any representative that receives both group approval votes (one Majority and one Minority) is a potential winner.

6a. If there are at least 3 potential winners, then the elimination method is used until there are two remaining potential winners

6b. If there are 2 potential winners, then Single Non-transferable Voting is used to eliminate the loser.

6c. If there is 1 potential winner, then that representative is the speaker.

For 2 parties with high levels of collusion, this method should produce a non-incompetent speaker that is: moderate up to a 75% majority, and non-extremist up to about an 80% majority.

For 2 parties with defective moderates, this method should produce a non-incompetent speaker that is: moderate up to about an 80% majority, and non-extremist up to a 100% majority.

For more than 2 parties with no majority party, should produce a non-incompetent moderate speaker with a near majority party (1 or 2 away) and a fairly competent moderate speaker without any party near a majority.

Thus, non-incompetent moderates should be elected unless there is more than a 75% majority without defections.

The U.S. House of Representatives has had more than a 75% majority party (probably with defections): once by the Democratic, once by the Republican, and 6 times by the Democratic-Republican. https://upload.wikimedia.org/wikipedia/commons/b/bb/Political_Parties_in_the_U.S._House_of_Representatives.png

[Andy Jennings]

So all voters are divided randomly into two groups and then there's a random trading phase to consolidate parties as much as possible.

If I'm understanding correctly, at the end of that, a party that has more than 50% will fill up one of the groups and spill over into the other.  If no party has 50% then the largest party will be in one group and the next largest party will be in the other.  (I guess if no party has more than 25% then the two biggest parties could be in the same group.)

Anyways, after that, each voter has to approve half of the candidates.  The approvals are tallied in each of the groups separately and, for each group, just over half of the candidates are given "group approval points".

Thus, at least one candidate must have a "group approval point" from each of the two groups.  If only one, that candidate wins.  If not, there are elimination rules.



It seems like it might work.  But it does seem a little over-complicated at the end.  And there is quite a bit of randomness at the beginning, which might not be acceptable.

But it is an interesting direction, for sure.

~ Andy

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[Andy Jennings]

On Thu, Apr 20, 2017 at 4:24 PM, Brian Langstraat <langstra...@gmail.com> wrote:

Since the AV (approve at least half) method has a fatal flaw when parties have extreme collusion, I think that the best method is some form of the "elimination order" method copied below:

I'm not sure your "approve at least half" method has a fatal flaw.  A 55% majority eliminating 60% of the legislators from eligibility and a 60% majority eliminating 75% of them is not _that_ bad.  But I suppose we should try to do better.

I've looked at what happens if the "must-approve" fraction is higher than 0.5.  As you increase the must-approve fraction, the number of candidates a collusive majority can eliminate goes down for a while.  But once the number they can eliminate matches the number in their majority, it stops going down and stays flat.

So the best you can ever do with an "approve at least X" method is that a majority can eliminate a portion of legislators from speakership eligibility exactly equal to their proportion in the legislature.

As an extreme example, imagine a system where everyone has to approve all but one of the candidates.  That's essentially the same as everyone voting for one candidate to eliminate.  So the majority can coordinate and eliminate as many candidates as they have people.  The minority can do the same.  If we imagine that the majority keeps secret exactly which candidates they're going to leave eligible and the minority can't guess that list perfectly, then in all likelihood there will be at least one candidate not eliminated.  (There will probably be more than one non-eliminated, so we'll need a tiebreak scheme, which I'm not worrying about here.)

If you squint, it's not that different from the "elimination order" method I originally proposed.  The mechanism is similar.  The results are about the same.  The ballot is simpler, but people are going to have to collude for it to work at all.  And it can get pretty tricky if you're worried about some people from your party defecting.

~ Andy

[Brian Langstraat]

Andrew (May 9),

I appreciate your thoughtful analysis of my posts and your excellent summary of the grouping method that I suggested.

It seems like it might work.  But it does seem a little over-complicated at the end.  And there is quite a bit of randomness at the beginning, which might not be acceptable.

The random beginning, need for parties, and complicated end are the weak points of this grouping/voting method.

The random assignment (2nd draft) instead of representatives choosing (1st draft) to form the initial groups was to prevent strategic placement of representatives by the majority party.

The worst case scenario for 2 parties could be the full Majority group containing all the majority party's moderates and the Minority group containing all the majority party's extremists, so there would not be defections.

Perhaps the absolute worst case scenario would be 3 nearly equal parties with 2 that are very similar, so the lone minority party would be split between between 2 groups.

Both of these scenarios are non-fatal flaws that are possible with random assignment as well, so representatives choosing groups may not be too bad.

To eliminate the need for parties, Coalitions of representatives could be used for group assignments.

1. Each Coalition would begin as 2 similar representatives and accepts each request to join by a simple majority vote.

[Typically, casual "yeas" and "nays" would be used to accept requests with formal voting for controversial requests.]

2. Coalitions could combine with a majority vote by each Coalition to accelerate the process.

[Thus, opposition "spies" would be prevented from joining a Coalition.]

[The maximum Coalition size would be equal to the number of representatives as the Majority group.]

3. At some designated time, the largest Coalition would combine with the smallest Coalitions/independents (without a vote) progressively increasing in size (with ties determined randomly) until combining with the smallest Coalition would pass the maximum Coalition size, then the smallest Coalition would be randomly split up between the groups.

[To avoid random combining and splitting, majority and minority/minor/independent parties would tend to try to join one of the large Coalitions before the designated time.]

The complicated end (Step 6) could be simplified by repeating the AV(>1/2) method for group approvals until there are 2 potential winners, then FPTP is used to determine the winner.

For 2 parties with high levels of collusion, this method should produce a non-incompetent speaker that is moderate up to a 75% majority, but could produce an extremist beyond a 75% majority.

Another improvement may be to increase the number of groups from 2 to 3 or more.

Potential winners would need approval from every group.

With 3 groups and 2 parties with high levels of collusion, this method should produce a non-incompetent speaker that is moderate up to a 83% (5/6) majority.

With 10 groups and 2 parties with high levels of collusion, this method should produce a non-incompetent speaker that is moderate up to a 95% (19/20) majority.

Ten groups would be a reasonable amount with the U.S. House and Senate having maximum group sizes of 44 Representatives and 10 Senators.

[Brian Langstraat]

Andrew (May 10),

I described the method as "approve more than half" in my Apr 11 post, but misstated it as "approve at least half" in my Apr 20 and May 4 posts.

For shorthand, "AV(>50%)" seems appropriate.

I've looked at what happens if the "must-approve" fraction is higher than 0.5.  As you increase the must-approve fraction, the number of candidates a collusive majority can eliminate goes down for a while.  But once the number they can eliminate matches the number in their majority, it stops going down and stays flat.

I was curious about how "approve at least X" (or AV(>X)) would affect the results.

Would you be willing to share any equations or graphs that you have derived?

If a universal equation for how the mandatory number of approvals could affect election results (assuming collusion) were available, then it may be valuable for the people interested in AV and Range Voting.

As an extreme example, imagine a system where everyone has to approve all but one of the candidates.  That's essentially the same as everyone voting for one candidate to eliminate.

My problem with the list elimination method (discussed on Apr 20) and disapprove elimination method is that individual representatives may choose to eliminate competent moderates from the opposing party instead of incompetent extremists, especially in the U.S. where the Speaker of the House is third in line for leadership of the country 

Since AV(>X) = Disapprove(<=X), I guess coordinated Coalition groups could not approve competent moderates from the opposing party instead of incompetent extremists, but even this seems less nasty than eliminations.

[Jameson Quinn]

Here's an attempt at a method using a 3-2-1-like ballot and logic.

Everyone in the legislature rates each other "good", "OK", or "bad".

Find the semifinalists, the set of candidates for whom the minimum of the lowest number of people rating any them "good", and the number of candidates in the set, is highest. Break ties by the lowest "good" ratings, then by the number in the set.

Take X, the total votes minus the average "good" ratings of the semifinalists. If that is greater than or equal to the cardinality of the set, the winner is the member of the set with the fewest "bad" ratings. Otherwise, eliminate the X candidates from the semifinalists with the most "bad" ratings (breaking ties by "good" ratings) to get the set of finalists.

The winner is the ballot-based Condorcet winner among the finalists.

If one party has a majority of 50+x, and they expect the other party to give them no "good" ratings, then they can be assured of picking all the semifinalists by just making sure to each approve at least 50-x+1. Then the other side, by distinguishing between "OK" and "bad", can knock out at least 50-x. This may leave as few as 1 finalist or as many as 2x of them. Among those, it's a Condorcet election; one in which a coordinated majority would be able to dominate.

This method does not elect the median, but allows a coordinated majority to pull the winner towards their side of the median by the same amount by which they surpass 50%. I don't think that's actually a bad thing overall.

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[Brian Langstraat]

Jameson,

Dodecatheon Meadia (on Apr 11) mentioned a version of 3-2-1 voting that I replied to (on Apr 12).

How do these 3-2-1 voting methods differ other than the grading scale?

Everyone in the legislature rates each other "good", "OK", or "bad".

Does each legislator vote for all of the legislators or only one legislator?

Is the "OK" option useful in a partisan and strategic legislature?

Why wouldn't they choose only "good" (approve) or "bad" (disapprove)?

Would there be a mandatory percentage for each choice?

Could you give an example of how this 3-2-1 voting method would work?

How many semifinalists are there? 3 or more? 

What does "minimum of the lowest number" mean?

For "X", how is "total votes" defined?

How is "the cardinality of the set" defined?

If one party has a majority of 50+x, and they expect the other party to give them no "good" ratings, then they can be assured of picking all the semifinalists by just making sure to each approve at least 50-x+1.

How is "bullet" voting by a strategic majority for the non-moderate winner(s) prevented?

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[Jameson Quinn]

2017-05-19 11:33 GMT-04:00 Brian Langstraat <langstra...@gmail.com>:

Jameson,

Dodecatheon Meadia (on Apr 11) mentioned a version of 3-2-1 voting that I replied to (on Apr 12).

How do these 3-2-1 voting methods differ other than the grading scale?

Everyone in the legislature rates each other "good", "OK", or "bad".

Does each legislator vote for all of the legislators or only one legislator?

all

 

Is the "OK" option useful in a partisan and strategic legislature?

Yes. The minority uses the OK/Bad distinction to eliminate semifinalists.

 

Why wouldn't they choose only "good" (approve) or "bad" (disapprove)?

See above.

 

Would there be a mandatory percentage for each choice?

I don't understand this question 

Could you give an example of how this 3-2-1 voting method would work?

60 greens, 40 purples. The 60 all strategically rate the 43 "greenest" as "good". So if you choose those 43 as semifinalists, they have at least 60 good votes each. Min of 43 and 60 is 43, which is greater than min(40, 40) for the purples.

X is now 100-60=40. The "bad" votes, which must come from purples, eliminate 40 semifinalists. There are 3 finalists.

Use a Condorcet method on the ballots to find a winning finalist.

How many semifinalists are there? 3 or more? 

In the above example, 43.

 

What does "minimum of the lowest number" mean?

minimum across possibilities of the lowest number between {number of votes, number in set}. 

For "X", how is "total votes" defined?

Number of voters.

 

How is "the cardinality of the set" defined?

Number of candidates in set.

 

If one party has a majority of 50+x, and they expect the other party to give them no "good" ratings, then they can be assured of picking all the semifinalists by just making sure to each approve at least 50-x+1.

Yes. But then the other party knocks out 50-x, so the most moderate among the semifinalists wins.

 

How is "bullet" voting by a strategic majority for the non-moderate winner(s) prevented?

Because that would mean a set of 1, so the minority choices would win for semifinalists.

 

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[Brian Langstraat]

Jameson,

This is pretty confusing, but could work well.

So there is one set of candidates from each party, and the semifinalists are the set of candidates that have the highest value for the minimum value between the number of their candidates with "good" votes or the minimum number of "good" votes that one of their candidates received.

Would this voting method require parties?

How would independents be affected?

Would a large group of moderate independents be ignored?

[Brian Langstraat]

In a bicameral legislature, the AV(>50%) would not need to create 2 groups using Coalitions, since there are already 2 chambers such as the U.S. House and Senate.

Each chamber would have a say in the leader of the other chamber, which could be considered a "check and balance" for the chambers and may result in more cooperative moderate leaders.

1. Each chamber uses the AV(>50%) method to select the most approved half+1 of the members from each chamber who each receive a single group approval vote.

(Ties are decided by Single Non-transferable Voting.)

2. Any member that receives both chamber approval votes (one House and one Senate) is a potential winner.

3. Repeat the AV(>50%) method for chamber approvals until there are 2 potential winners from each chamber, then FPTP within each chamber is used to determine the winner.

For 2 parties with high levels of collusion and equal party proportions in each chamber, this method should produce a non-incompetent leader in both chambers that is moderate up to a 58% majority, but could produce an extremist beyond a 66% majority.

For 2 parties with high levels of collusion and the majority party controls one chamber, this method should produce a non-incompetent leader in both chambers that is moderate up to a 58% majority in the other chamber, but could produce an extremist beyond a 66% majority in the other chamber.

For 2 parties with high levels of collusion and inverse party proportions in each chamber, this method should produce a non-incompetent leader in both chambers that is moderate for any majority percentage.

For more than 2 parties, defective moderates, or sufficient independents where no party has a majority in one of the chambers, this method should produce a non-incompetent leader in both chambers that is moderate for any majority percentage.

[Brian Langstraat]

In my previous post considering a bicameral legislature, I neglected to consider Step 1 "Ties are decided by Single Non-transferable Voting."

For high levels of collusion by the majority party to be effective, many ties among the candidates at the half+1 boundary are necessary.

These ties are decided by Single Non-transferable Voting (SNTV) that will have the number of winners needed to fill the gap between non-tied AV(>50%) winners and the half+1.

SNTV with high levels of collusion would result in nearly proportional winners from each party to fill the gap, thus the majority party would give the minority party the power to select any of the tied members that were moderate or even minority extremists as winners.

A possible improvement to counter majority extremists:

3. Repeat the AV(>50%) method for chamber approvals (with only the eliminated members voting) until there are 2 potential winners from each chamber, then FPTP within each chamber is used to determine the winner.

When more minority party members are eliminated in the first round, they will have more voting strength in the second round.

For 2 parties with high levels of collusion and equal party proportions in each chamber, this method should produce a non-incompetent leader in both chambers that is moderate up to about a 66% majority, but could produce an extremist beyond about a 83% majority.

For 2 parties with high levels of collusion and the majority party controls one chamber, this method should produce a non-incompetent leader in both chambers that is moderate up to about a 66% majority in the other chamber, but could produce an extremist beyond about a 83% majority in the other chamber.

Thus, a non-incompetent leader in both chambers that is moderate will be produced unless a bicameral legislature has a majority in both chambers over 66%.

The U.S. House of Representatives and Senate have both had more than a 66% majority party (probably with defections) during 8 out of 81 sessions since 1855 where only two sessions had either chamber with more than a 83% majority during reconstruction.

[Jeremy Macaluso]

What makes voting for a speaker of the house or prime minister different from voting for any other single winner? The body can be expected to collude and be strategic, but that isn't different in general elections. If the desires of the body are completely misaligned from the desires of the population, no voting system for speaker will change that.

[Brian Langstraat]

Jeremy,

Considering how many detailed Posts are in this Topic discussion, your question may have been partially answered above.

What makes voting for a speaker of the house or prime minister different from voting for any other single winner? The body can be expected to collude and be strategic, but that isn't different in general elections.

Andrew Jennings 9/7/14:

Whatever method the majority caucus uses to choose the speaker (usually plurality), we assume that a majority dominates, so a majority of the majority (as little as 26% of the legislators) can control the body.  I'm assuming this is how it is in most legislatures.

If we want a system that chooses a chair more fairly, it has to compensate for this caucus system.  A majority, voting in lockstep, should not be able to completely control the outcome.

Legislatures are unique since they are made up of a specific number of members who are all eligible to be the leader and vote publicly for a leader.

Legislatures tend to have highly partisan members who can collude and strategize every single vote at the party level.

General election voters can be highly partisan, but usually there are significant numbers of moderates and independents with private votes.

Even with maximum partisanship, general election voters cannot collude and strategize every single vote at the party level, but parties can promote strategies for individual voters to use.

Most voting methods that work well for general elections can be exploited by a bare majority when electing a legislative leader, and most voting methods (such as Jennings's elimination order, Quinn's 3-2-1, or my AV(>50%)) that could reduce exploitation by a majority would be difficult to use for general elections.

If the desires of the body are completely misaligned from the desires of the population, no voting system for speaker will change that.

The leader of a legislature should represent the desires of the body by controlling the actions of the entire body, but a leader that is too far from the median (moderate center) of the body will misrepresent desires of the entire body.

Even legislatures that are well aligned (proportionally) to the population are susceptible to having the leader selected by the majority of the majority (26%) with most voting systems.

[Andrew Jennings]

Brian,

On May 15th, you asked for my equations or graphs.  Here is my best attempt, so far, to summarize my findings on a group of legislators choosing a speaker using approval voting where they are forced to approve a certain number.  If you can't see the image above, view it here: https://lh3.googleusercontent.com/-AxnvTGgmfHs/WTdyl_NQN0I/AAAAAAAABMk/yIUvanvb91UGI7BWoGna0hOeq2FoB-s4ACLcB/s1600/AV%2Bfor%2BSpeaker.png

Suppose there are two parties with D and R representing the number in each party.  Suppose R>D.

The vertical axis (M) represents the number of speaker candidates each legislator must approve.  The horizontal axis (C) represents the number of finalists the R party is trying to allow the D party to choose between.  We assume the R party acts in complete lockstep.  The blue area is where the Rs succeed (i.e. they can successfully force the D party to choose between C candidates).  The green area is where the Rs fail.

Obviously, the R party would try to operate as far left as they can (limit the Ds to as few choices as possible) so they are interested in the boundary between the blue and green area.  I have labeled the corners of the green area.

Most importantly, it seems impossible to force the Rs to allow more than D finalists.

~ Andy

On Monday, May 15, 2017 at 11:49:51 AM UTC-5, Brian Langstraat wrote:

[William Waugh]

I don't understand the relevance of a districting algorithm to the topic of electing a prime minister.

On Sunday, September 7, 2014 at 12:22:55 PM UTC-4, Warren D. Smith (CRV cofounder, http://RangeVoting.org) wrote:

https://www.youtube.com/watch?v=kUS9uvYyn3A

[Brian Langstraat]

The best way voting system to elect a legislative leader may be able to use the mechanisms that most legislatures already have in place.

Most legislatures have a Majority Leader and Minority Leader selected who are elected by their party caucuses.

(This could be improved by creating nonpartisan Majority and Minority Coalitions (May 3-24 Posts) and voting for both leaders using Approval Voting (more than half) "AV(>50%)".)

The Majority Leader and Minority Leader agree upon a legislative leader.

(If both are unable to agree upon a legislative leader, then AV(>50%) is used by both to determine a legislative leader.)

This voting system would be likely to result in a competent, moderate legislative leader with minimal changes to current legislative rules/laws/amendments.

[Brian Langstraat]

Below are some possible improvements to the "Majority Leader and Minority Leader both approve a Speaker" voting system.

The Majority Leader and Minority Leader nominate legislator(s) for Speaker that are not disapproved (blackballed) by either leader.

(If both are unable to agree upon at least one nominated legislator, then Disapproval Voting (less than half) "DV(<50%)" is used by both to determine a legislative leader.)

All of the legislators vote using AV(>=50%) to elect the most approved nominee as the Speaker.

The Speaker should be a competent, moderate legislator from the Majority Party/Coalition.

If the Majority Leader is not willing to blackball any members of their party, then the Speaker could be a more moderate legislator from the Majority Party (even one from the Minority Coalition).

The "Speaker approved by Legislators from nominees acceptable by the Majority and Minority Leaders" voting system (using Coalitions) would almost always elect:

moderate Speakers with about a 50%-75% majority,

non-moderate Speakers with about a 75%-83% majority, and

anti-extremist Speakers with about a 83%-100% majority.

Extremist Speakers should not occur.

[Andy Jennings]

Brian,

I like it.  Make the leaders negotiate with AV(>=50%) looming over them as a fallback.

Do you trust the process where parties form coalitions?  I know it's common in some parts of the world, but I don't have much experience with it.

~ Andy

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[Brian Langstraat]

Andy,

I realized that AV(>50%) works to elect moderates best with only 2 "votes" from partisan opponents and most legislatures have 2 Leaders that each represent about half of the opposing partisans.

Using DV(<50%) instead of AV(>=50%) to select the nominee(s) has the advantage that only one Leader needs to participate (in case the other leader is trying to obstruct).

I am from the state of Iowa in the United States, so I have do not have much experience with coalition governments either.

I think that parties forming coalitions between major and minor parties is better than just one or two major parties ignoring minor parties.

The worst case scenario (that I have heard of) is a major party and an extremist minor party form a majority coalition such that the major party is forced to endorse extremist policies, but I am not sure why a major party would not form temporary majority coalitions for each policy.

The nonpartisan "Coalitions" that I am suggesting could be temporarily used for selecting Majority and Minority Leaders.

For most legislatures, the only real change would be how the Speaker is elected.

I did a little research and found that how most Speakers are elected is pretty vague.

Constitution of the United States - Article I - Section 2 - Paragraph 5:

"The House of Representatives shall choose their Speaker and other Officers; and shall have the sole Power of Impeachment."

Wikipedia (https://en.wikipedia.org/wiki/Speaker_of_the_United_States_House_of_Representatives):

"Although no rule exists, based on tradition and practice from the earliest days of the nation, to be elected speaker a candidate must receive an absolute majority of all votes cast for individuals, i.e. excluding those who abstain."

Constitution of the State of Iowa - Article III - Section 7:

"Each house shall choose its own officers, and judge of the qualification, election, and return of its own members. A contested election shall be determined in such manner as shall be directed by law."

Iowa's Eighty-Seventh General Assembly House Rules:

No mention of how the Speaker is elected, but states many duties of the Speaker.

If there are not current legislative rules/laws/amendments for electing a Speaker (FPTP is just assumed), then a new voting system would not require a legal change.

However as Warren Smith mentioned earlier, a new voting system would be very difficult politically, since the majority party and its Speaker would need to agree to the new voting system that gives power to more moderate legislators.

The best chance for a new voting system to elect Speakers becoming law is in a moderate state with a decent proportion of moderate legislators before an election where the majority is likely to switch from one party to the other.

Iowa may be a good place to try this, since it is a "purple"/swing state with some moderate state legislators with a Republican majority but potential "Democratic wave" in 2018.

If a moderate Speaker is better at representing the whole legislature, then the majority party moderates and minority party members could resist majority party extremists from repealing a voting system for electing a moderate Speaker.

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