Approval plus top 2 runoff and real-world examples

[Warren D Smith]

On 5/21/13, Warren D Smith <warre...@gmail.com> wrote:
> http://RangeVoting.org/RangePolls.html
>
> (and pages linked from there) collects
> much about real-world elections under different voting systems.
> (The more recent elections usually have more data about more systems.)

--
http://rangevoting.org/FunnyElections.html

also collects more real-world election stories. (More contributions please?)

Also, for those interested in the approval-plus-top-2-runoff system
proposed for Arizona,
see

http://rangevoting.org/France2002.html

for a real-world example where this likely would have changed the winner.

[Thomas Ruen]

The 2002 French election is definitely one that Approval would make a difference, but its not clear to me that "unlimited approval" is necessary or helpful. What is needed is a PRIMARY to reduce the field!

 

So my (smaller step towards approval) alternative might be a 2-vote limit, top-4 winner primary (like the plurality-at-large primary rules for a 2 seat election). This would help reduce the field without enabling a united plurality of voters to pick all the primary winners.

A top-4 primary maintains the "plurality" spoiler-disincentive, so like-minded candidates who work together before the election can improve their odds, without the harsh cliff of top-two cutoff among so many choices.

 

With 4 candidates, in the general election, a THIRD election, a top-two runoff might still be good if there's no majority winner and you require it. Alternately an unlimited approval vote could pick a winner immediately, if you skip the majority requirement.

 

I'm not saying this suggestion is BEST, only showing the NEED for primary process to reduce the field AND I continue to assert that an unlimited Approval vote primary (like Arizona's bill) gives too much power for manipulating the field.

 

Tom Ruen

 

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[Warren D Smith]

However, computer studies by Fishburn, as well as by myself,
show that with first round electing M, who then proceed to round two electing 1,
the best value of M is 2.

In this particular French 2002 election, with Thomas Ruen's suggestion M=4,
it would have been Chirac, Jospin, Bayrou & Le Pen. I'm not sure who would
have won that.

Also, Ruen should note that many (all?) French parties already hold
primaries prior to
the first round election. For example, in the 2012 election, Hollande won, and
had previously won his party's primary versus Aubry (who therefore did not run
in the official election). Polls indicated that Aubry would also have won the
presidency if she'd run instead of Hollande. Had, however, BOTH run,
they would have
split the official vote (presumably) whereupon the top-2 runoff would
have been Sarkozy vs Le Pen, to the detriment of France. If this
vote had been approval, or better score, then that vote-splitting
effect would have been reduced or eliminated and hence H or A still
would have won in the end (probably) and indeed the final round would
with score likely have been H vs A. If that indeed happened, then
the net effect would be that the whole of France would et to choose
between H & A, instead of what happened, which was only the members of
their party got to choose. This would have been better
for France.

Also, about this kind of cloning, it should be noted that in France
2007, two candidates
looked to be having difficulty meeting petition requirements to get on ballot:
Besancenot and Le Pen.
Sarkozy publicly announced he would HELP them obtain the necessary
signatures, as a "service to democracy." Hmmm.
Approval and score voting are immune to cloning, and so is IRV with
full rank orderings (but not, e.g. rank-top-3-only IRV).



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

[Dale Sheldon-Hess]

On Tue, May 21, 2013 at 1:44 PM, Thomas Ruen <tom...@yahoo.com> wrote:
> The 2002 French election is definitely one that Approval would make a
> difference, but its not clear to me that "unlimited approval" is necessary
> or helpful. What is needed is a PRIMARY to reduce the field!
>
> So my (smaller step towards approval) alternative might be a 2-vote limit,
> top-4 winner primary (like the plurality-at-large primary rules for a 2 seat
> election).

Primaries are certainly useful. I think I'd rather see closed (or at
least not-jungle) primaries, followed by (unlimited) approval with a
runoff. Three reasons:

* Parties are still going to want to focus their efforts; we've
already seen that determined parties will try to create pre-primaries
in the face of jungle primaries. Just don't bother. With a better
voting system, the problem in many lop-sidedly partisan districts of
"the primary IS the election" is much less of a problem. (Basically:
Parties happen. Don't fight it, accept it.)

* Limiting the number of approvals doesn't help. It's a common
suggestion, but I'm not really sure what logic motivates people to
keep bringing it up. (I feel it's related to liking jungle primaries;
I think the same logical error is buried at the bottom of both of
these, but I can't quite put my finger on it.) The problem of
plurality is that it's "approval, limit 1". Raising the limit higher
is always better, so just forget having a limit at all. People will
approve candidates when they judge that it's in their interest. If you
give them a limit, they'll feel they're "wasting" something if they
don't approve a number equal to the limit, and they'll be angry (and
potentially overvote and invalidate their ballot) if they want to vote
for more than the limit.

* Why top 4? Yes, top 2 could always, potentially, have issues. There
could always be a case where #3 before the runoff "should" win. But
it's also going to be possible that the winner from a 3- or 4-way
runoff isn't going to be right either. Or that #5 before the top-4
runoff would be. What, and how much, do you actually gain here? One of
the motivations for top 2 is to bring back majority rule, and anything
more than 2 imperils that. (And if write-ins/none-of-the-above are
allowed, it's even possible to fail it with two.) But 4 seems entirely
arbitrary (especially since it's the lowest number where strategy (as
we were discussing the other day, by its original definition) could
possibly be necessary).

Some clarifications inline:

> This would help reduce the field without enabling a united
> plurality of voters to pick all the primary winners.

This is also true for unlimited approvals and top-2. The only time you
can't stop them is when a united MAJORITY picks both members of the
runoff. And we should be so lucky!

> A top-4 primary maintains the "plurality" spoiler-disincentive, so
> like-minded candidates who work together before the election can improve
> their odds, without the harsh cliff of top-two cutoff among so many choices.

Better done with party primaries. If anything, cases where top-2
jungle primaries have had two members of the same party go to the
general, should be a warning against expecting such candidates would
work together.

> With 4 candidates, in the general election, a THIRD election

...and now the voters throw their hands up in disgust :)
A runoff? Sure. A runoff-runoff? Hmm.

Let me share a little tip from computer programming: Never do anything
three times. Once? Of course. Twice? Sure, sometimes. Three? No; you
should have redesigned your system to handle an infinite number
instead. And, as Abd is fond of saying, infinite elections--with no
eliminations--can be really great and is in fact recommended by
Robert's Rules. But there are (obvious) downsides.

> Alternately an unlimited approval vote could pick a winner immediately, if
> you skip the majority requirement.

...or keep majority and do unlimited with top-2 runoff? :)

> I'm not saying this suggestion is BEST, only showing the NEED for primary
> process to reduce the field AND I continue to assert that an unlimited
> Approval vote primary (like Arizona's bill) gives too much power for
> manipulating the field.

Too much power to who? Voters? Because the alternative--again, as seen
in top-2-jungle-primary elections already--is to have party leaders
hold secret pre-primaries. Is that better?

--
Dale Sheldon-Hess

[Warren D Smith]

French elections reviewed:
http://RangeVoting.org/France2002.html
http://RangeVoting.org/France2007.html
http://RangeVoting.org/France2012.html

Approval with top-2 runoff always succeeded in electing best winner.
Approval with top-4 runoff would not have done better and perhaps did worse.
Approval without runoff elected best in 2007 and 2012, but in 2002 it
elected Chirac
who with about 50% chance was worse than Jospin (said pairwise polls
which were basically tied between C & J). The quality difference
between C & J as perceived by France was very small.

IRV failed in 2007, succeeded in 2012.
In 2002 with 50% chance would have done better than
plain approval (and IRV and top-2 approval runoff would have been equivalent).
If so this superiority was tiny.

So among all the systems just discussed, approval with top-2 runoff
(as proposed Arizona) would have been best-possible for France 2002,
2007, 2012 and as good or
better than every alternative just discussed. In particular superior to IRV.

[Leon Smith]

On Tue, May 21, 2013 at 5:07 PM, Warren D Smith <warre...@gmail.com> wrote:

http://rangevoting.org/FunnyElections.html

Thanks Warren.   Looking at this,  and our work on http://rangevoting.org/BBCaltVote.html,  I'm reminded that I deeply regret not taking some Statistics courses for my math major,  actually in retrospect I probably would have really enjoyed making stats at least a third of my major,  supplemented with some high-quality Machine Learning classes.  (However,  I'm not sure if my University offered _good_ ML classes.  I do know their stats department was quite good.)    In any case,  it's a hole in my knowledge that I'm trying to fill via Coursera.   

It would be nice to write each one of these elections up,  providing a computer file (e.g. a spreadsheet or say an R program) showing the precise calculations used,  and to make the methodology as regular and statistically rigorous as possible.   Perhaps someday we might even get to the point that we would produce a reasonably good library for making these types of calculations,  which could very well lead to fewer mistakes,  more regularity,  and better statistical methods.

Of course at this point my knowledge of stats is atrocious,  so it's just a dream at the moment.

Best,

Leon

[Abd ul-Rahman Lomax]

At 04:44 PM 5/21/2013, Thomas Ruen wrote:
>The 2002 French election is definitely one that Approval would make
>a difference, but its not clear to me that "unlimited approval" is
>necessary or helpful. What is needed is a PRIMARY to reduce the field!

There is a primary. The election is a primary! The problem is the
specific election method used, including the rules for determining
who goes to a runoff, should one be required. As has been pointed out
subsequently, the candidates in the primary are themselves chosen
through party process, which includes party primaries. The field has
already been reduced.

The election has as many candidates as it has because France has a
very healthy multiparty system. However, voters have little
difficulty choosing from among the candidates, if they have a party
affiliation, a party whose goals and process they adequately trust.

Partisan elections behave *very differently* from nonpartisan ones.

>So my (smaller step towards approval) alternative might be a 2-vote
>limit, top-4 winner primary (like the plurality-at-large primary
>rules for a 2 seat election). This would help reduce the field
>without enabling a united plurality of voters to pick all the primary winners.
>A top-4 primary maintains the "plurality" spoiler-disincentive, so
>like-minded candidates who work together before the election can
>improve their odds, without the harsh cliff of top-two cutoff among
>so many choices.

Why limit it to two votes? But I would *not* suggest, for France, a
pure approval primary. I'd suggest a Bucklin primary, or whatever
they call it in France. (We also call it Majority Judgment or
Graduated Majority Judgment or median Range. Sum-of-votes Range could
also be fine.

A top-four primary could then lead to difficulties in the runoff.
With a Range ballot (which can be used for Bucklin or MJ), it's
possible to test for a winner who would beat the other runoff
candidates pairwise. If there are normally two candidates (top-two
range), then, a candidate who beats both of them, it could be argued,
should be in the runoff. Rare, probably, but possible. So the runoff
method should be able to handle three candidates. That's easy.
Bucklin allows specifying preference, still, but amalgamating
approvals, and it would be very simple to vote in a three candidate
elections (It need only be two-rating, but three-rating allows better
expression of preference strength. If there are three candidates,
then, a few voters might rate all three, thereby accepting all three.
It's purely symbolic in a three-candidate election. However, some
voters would defer the second preference to the third rank, and that
has more meaning and can affect the outcome.

It's what I have called "limited later-no-harm protection." That this
can be done with Bucklin has been missed by many analysts, who have
treated Bucklin as if it were a pure ranked voting system.

>With 4 candidates, in the general election, a THIRD election, a
>top-two runoff might still be good if there's no majority winner and
>you require it. Alternately an unlimited approval vote could pick a
>winner immediately, if you skip the majority requirement.

There are already three elections: party primaries, general election,
runoff if needed.

>I'm not saying this suggestion is BEST, only showing the NEED for
>primary process to reduce the field AND I continue to assert that an
>unlimited Approval vote primary (like Arizona's bill) gives too much
>power for manipulating the field.

A critical factor has been missed; the Arizona bill covers only
municipal elections, and is optional for municipalities. There is
only one municipality in Arizona that has partisan elections, that's
Tucson, which, then, has party primaries. Tucson is heavily
Democratic, it's rare for any Republican to get elected to anything
there. Tucson could use approval for the party primaries, if they
wished, it would be a *slight* improvement at *very low cost.* They
could safely use approval in the general election, as well. Approval
can really be used anywhere, with appropriate rules. Approval in the
general election would allow supporting a minor party or candidate
*and* supporting a frontrunner. But Bucklin would make that even
easier as a decision for voters.

The Arizona bill is a giant leap forward, in fact, in context. What I
had never considered even possible was the effect of an open approval
primary with nonpartisan elections, where the primary does *not*
determine the winner. In these elections, it is quite unlikely that
the best winner of the primary would not be among the top two in the
primary. It's possible, then, later, to tweak the primary to improve
it even further; but meanwhile, if there are any implementations, we
will get real election data. At very low cost. After all, Approval is
merely Count All the Votes.

[Abd ul-Rahman Lomax]

At 05:17 PM 5/21/2013, Warren D Smith wrote:
>However, computer studies by Fishburn, as well as by myself,
>show that with first round electing M, who then proceed to round two
>electing 1,
>the best value of M is 2.

There are some unstated assumptions here. How are the M selected, and
what method is used for Round 2?

>In this particular French 2002 election, with Thomas Ruen's suggestion M=4,
>it would have been Chirac, Jospin, Bayrou & Le Pen. I'm not sure who would
>have won that.

Pretty obviously, it depends on the second round method.

>Also, Ruen should note that many (all?) French parties already hold
>primaries prior to
>the first round election.

This is a *crucial* distinction to note. Parties must have a process
for determining their candidates (which, by the way, is ignored in
some U.S. "jungle primary" implementations, a serious problem where
the party system breaks down and becomes not only useless but
harmful. It's been tested: can a candidate use a label of choice? No,
they must choose an "eligible party" label, or they will be labelled,
say, "Independent" or "Unaffiliated." The party label, however, could
be totally deceptive, indicating no party endorsement whatever.)

> For example, in the 2012 election, Hollande won, and
>had previously won his party's primary versus Aubry (who therefore did not run
>in the official election). Polls indicated that Aubry would also have won the
>presidency if she'd run instead of Hollande. Had, however, BOTH run,
>they would have
>split the official vote (presumably) whereupon the top-2 runoff would
>have been Sarkozy vs Le Pen, to the detriment of France.

Right. The French system already has vote-splitting problems,
constantly. They do need a better general election method. Since they
are clearly willing to hold two rounds, they can, by using better
methods in the two rounds, set up a practically ideal voting system.
They can eat their majority, Condorcet winner cake and keep the
tested social utility winner at the same time.

> If this
>vote had been approval, or better score, then that vote-splitting
>effect would have been reduced or eliminated and hence H or A still
>would have won in the end (probably) and indeed the final round would
>with score likely have been H vs A. If that indeed happened, then
>the net effect would be that the whole of France would et to choose
>between H & A, instead of what happened, which was only the members of
>their party got to choose. This would have been better
>for France.

And not bad for the party. However, the question is *how much.*? This
is crucial to understand about a party system: voters know what party
they support. They often know much less about individual candidates,
they trust their preferred party to make a decent choice.

Very bad idea: combining a jungle primary with a party system. Either
the general election process is nonpartisan, *or* only pre-chosen
candidates, by party process, are allowed on the ballot, identified
as such. France clearly wants their parties!

And that addresses the old problem Dodgson identified, voter
ignorance of more than their favorite.

An interesting solution for a vote-for-one primary: Asset. If the
primary finds a majority, great. If not, multiwinner Asset chooses
the top two (for a vote-for-one runoff) or top three (for a more
sophisticated runoff system). This would work fine with a party
system. The party is, then, choosing their best representative in the
election process. It *could* be that this round could complete, if
some threshhold of support is crossed, which might be *higher than
majority*. Those are all details for the future....

>Also, about this kind of cloning, it should be noted that in France
>2007, two candidates
>looked to be having difficulty meeting petition requirements to get on ballot:
>Besancenot and Le Pen.
>Sarkozy publicly announced he would HELP them obtain the necessary
>signatures, as a "service to democracy." Hmmm.

Yeah. Great. Nice framing, though. Skillful on Sarkozy's part. This
has happened in the U.S., with Republicans helping Nader to get on
the ballot. Service to democracy, my rump. Legal, though.

>Approval and score voting are immune to cloning, and so is IRV with
>full rank orderings (but not, e.g. rank-top-3-only IRV).

IRV would be ridiculous if just dumped into that French election.
However, multiwinner STV, and especially with an Asset tweak, could
be quite good, with a runoff when needed.

[Abd ul-Rahman Lomax]

At 05:33 PM 5/21/2013, Dale Sheldon-Hess wrote:

> > With 4 candidates, in the general election, a THIRD election
>
>...and now the voters throw their hands up in disgust :)
>A runoff? Sure. A runoff-runoff? Hmm.
>
>Let me share a little tip from computer programming: Never do anything
>three times. Once? Of course. Twice? Sure, sometimes. Three? No; you
>should have redesigned your system to handle an infinite number
>instead. And, as Abd is fond of saying, infinite elections--with no
>eliminations--can be really great and is in fact recommended by
>Robert's Rules. But there are (obvious) downsides.

Call it a "cost." That's accurate.

It is not "infinite elections," the probability of that reduces to
zero. I.e., it's infinitesimal. I raise the default Robert's Rules
procedure because this is what people, in fact, do, when holding a
new poll is really easy.

My sense is that with sensible voting system design in a primary and
runoff, further improvement by holding a third election would be very
small, so small that we don't need it.

But that takes more sophisticated voting systems in the primary and
runoff. That is also a cost.

Hence the ultimate solution is Asset, with a *single election* to
choose an body of public voters who then can do whatever it takes to
find either a majority (single winner election) or fully-accurate
proportional representation (multiwinner election). This *could* be
used to choose an optimal two candidates for a final public election.
I just don't know how necessary that might be. It's not necessarily
an improvement. It would only look like one to those who don't trust
the person they voted for in the first election. That's an artifact
of the existing system, where most voters really know very little, on
a personal level, about candidates who could possibly win.

> > Alternately an unlimited approval vote could pick a winner immediately, if
> > you skip the majority requirement.

It could. Better than Plurality, basically. But ... not much better.
Just a little better, well worth the cost of counting all the votes.
The Arizona system is much cooler than we realized at first. The
final decision is made in the general election, so the primary is
really more like a party primary, i.e., the Party of the People,
those who care to vote in that election.

I still don't have a definitive answer to my question about write-in
votes in the general election. If they are allowed, it would be
better if that election was *also* approval. Certainly harmless if it
were. Bucklin, even better, but ... more complex ballot.

>...or keep majority and do unlimited with top-2 runoff? :)
>
> > I'm not saying this suggestion is BEST, only showing the NEED for primary
> > process to reduce the field AND I continue to assert that an unlimited
> > Approval vote primary (like Arizona's bill) gives too much power for
> > manipulating the field.
>
>Too much power to who? Voters? Because the alternative--again, as seen
>in top-2-jungle-primary elections already--is to have party leaders
>hold secret pre-primaries. Is that better?

The analysis assumes partisan elections. Probably won't happen in
Arizona, unless Tucson decides to use approval *in their party
primaries.* Not a bad idea, in fact, but, then, top-two primary?
Contradiction with a party system.

"Jungle primaries" are primaries which are partisan, but which lump
together candidates from different parties. Horrible idea (unless the
voting system is much better than vote-for-one, and raw approval is
not good enough). The Arizona proposal is *not* a jungle primary, but
some observers treated it as if it were.

[Warren D Smith]

Peter C Fishburn & William V Gehrlein:
Majority efficiencies for simple voting procedures: Summary and interpretation
Theory and Decision 14,2 (June 1982) 141-153
DOI: 10.1007/BF00133974
Abstract:
Several studies published during the past five years have attempted to
assess the propensities of different voting procedures to elect the
simple majority candidate [Condorcet winner] when one exists in a
multicandidate election. The present paper provides a summary of what
we believe to be the most salient results of this research. The data
are first discussed within the context of the assumptions used in our
simulations. We then extend our interpretations to account for
potential political realities that were not incorporated in the
simulations.



Peter C Fishburn & William V Gehrlein:
An analysis of simple two-stage voting systems,
Behavioral Science 21,1 (Jan .1976) 1-12
Abstract:
This paper examines two-stage voting procedures [x,k,y] at the level
either of a local governmental organization or of a national
governmental system in which x is the number of candidates a voter is
to vote for on the first ballot, k is the number of candidates to be
placed on the second ballot according to the greatest vote totals from
the first ballot, and y is the number of the k candidates on the
second ballot that a voter is to vote for on the second ballot. The
winner is the candidate with the most votes on the second ballot.
These systems are practical in many situations and correspond to many
two-stage voting systems in current use. The main purpose of the paper
is to assess the propensities of alternative two-stage systems to
elect the candidate which would be elected by a theoretically more
sophisticated but less practical norm procedure such as simple
majority [Condorcet] or the Borda sum-of-ranks method. Extensive
computer simulation, restricted to three to ten candidates but
allowing a variety of methods by which voter preferences are randomly
generated, reveals that the best propensity maximizing two-stage
system has the form [x,2,1] in which exactly two candidates appear on
the second ballot. Under the [plurality] restriction that a voter is
to vote for only one candidate on each ballot, the best system is
common double plurality [1,2,1]. Without this restriction the best
system usually has x = 2, with x approximately equal to the optimal
number of candidates to vote for on the single ballot in a one-stage
election in which the winner is determined by the greatest number of
votes from the single ballot.

[Abd ul-Rahman Lomax]

Very interesting. Here is a problem: simulating a two-stage system is
often done by assuming the same electorate. Further, informed by the
results of the first election, entirely aside from what candidates
are selected for the runoff, the voters now have a kind of reliable
poll data on which to make strategic decisions in the second election.

Suppose the system is (1,3,1) -- their notation from the abstract for
the second paper.

Voters in the second election will know the relative popularity of
the 3 candidates, and will know if the 3rd candidate, the one who was
not included in the first two, were those the choices, could win.

I very much doubt that the simulations performed then would be
capable of understanding differential turnout, which is rooted in
preference strength, because their method of study did not even
consider preference strength.

(But there is a hint in the first paper that they looked at
"Potential political realities." If simulations have not considered
political realities, they were poor or primitive simulations!)

This work would need to be redone using utility profiles and Bayesian
Regret as a measure of performance, and voter strategy must be
realistic, and any two-stage system must consider the effects of
voter turnout, which will vary with preference strength and expected
election utility.

The possibility of hybrid systems wasn't even on their radar, beyond
considering two-stage systems at all.

Even much later than this, simulations of runoff voting were naive
and highly inaccurate, as to what really happens in runoff voting.

There is a lot of work to do! These are opportunities for new
students of voting systems to make substantial contributions.

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