"the core principle of democracy"

[Brian Olson]

"If more people want A than B, A should win"

This is the simplest, most concise statement of the Condorcet criterion that I think I've heard yet. And I think it's worth rebranding 'the Condorcet criterion' away from abstract mathiness and the mathematician and towards something for general advocacy. I'm leaning towards naming this "the core principle of democracy". If someone has a better way to phrase that, or some phrase in common use elsewhere I'm not aware of, I'd love to hear it.

"If more people want A than B, A should win"

Instant Runoff Voting can fail this.

Isn't that a punchy little statement? IRV fails the core principle of democracy. IRV can give the win to B when more people would rather have A. (Of course, our current pick-one voting does this too, it just doesn't even measure this. Sometimes we get it in statistical surveys.) And of course this has actually happened in Burlington, VT in 2009.

Happy advocacy workshoping,

/Brian

[Lonán Dubh]

I'd be nervous about calling the Condorcet Criterion the "core principle of democracy," if only because score/approval voting also fail that criterion, and so if we run with that, the same can be said of us.

Further, I'm not certain that being a Condorcet complaint is actually a desirable trait; it brings up the old saw about democracy being 3 wolves and 2 sheep voting on what's for dinner...

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[Brian Olson]

Wolves vs sheep is a parallel concern of whether we want our government to be absolute or limited and constitutional, whether it be monarchy or democracy or anything else. A constitutional democracy says that at least in some ways the majority can't vote to eat the minority. Even if things are going badly and the constitution just slows down a hell bent majority that's worth having. No system of government is so good that it doesn't require the participants to be good. Shrug?

So, on any reasonable question, "if more people want A than B, A should win".

[Lonán Dubh]

Again, I disagree. The fact that you can't immediately think of a scenario where not selecting the Condorcet winner is reasonable, possibly even preferable, does not mean no such scenario exists.

http://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html

[Warren D Smith]

http://rangevoting.org/CondorcetCycles.html

even contends that what Olson wants to call "the core
principle of democracy" (aka "majoritarianism")
is self-contradictory and hence cannot be correct.

Olson can try (and has tried) to wriggle out
of it by saying is only is true for "reasonable questions"
but that is a sleazy wriggle attempting to ignore
the contradictions by pretending they do not matter much
and are not very severe... without presenting evidence.
Well, when one does try to get evidence one finds Olson's
wriggle seems to be approximately ok in some circumstances, but wrong
in others. In particular Condorcet cycles are quite common
in legislative votes because of the intentional
introduction of "poison pills' into bills being common, which
causes them to be what Olson would call "unreasonable questions."

A better solution is (?) to formulate a different "core principle" which is
contradiction-free. In a nutshell:
"utilitarianism" is a better philosophy than "majoritarianism."



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

[Brian Olson]

I don't think a Condorcet cycle-resolution rule is inconsistent with what I said. It's just saying that of "A>B", "B>C", "C>A" some of those are better or worse than the others by some measure. For the 'best' A>B, A should win.

To make a parallel analogy, I might formulate social utilitarianism as, "If the net benefit across all people of A is higher than B; A should win" (for options A and B, where we're going to do exactly one of them)

Versus my statement of democracy, "If more people want A than B, A should win"

Warren, do you dislike 'majoritarianism' because of bogus IRV rhetoric about their constructed 'majority'? I will counter that with case studies of "more people wanted A than B; IRV gives the election to B".

Lonán

​, I agree that it's possible to better consider what people want given more information. I may have dug myself into a hole similar to Arrow's work that considers only rankings ballots but neglects more flexible score ballots.​

​I guess the fusion of these two points is that if a score ballot is a person's estimate of the utility they would derive from a candidate winning, then if everyone votes honestly we can do better than Condorcet by simply summing up all those score votes and sometimes we'll have a more utilitarian result that isn't a Condorcet winner.​

​

​Perhaps I should claim my statement to be relatively true at a certain level of detail. Good enough for the general population; more refined versions will exist for us elections nerds and philosophers.

Also, it is about democracy and making the best democracy is be a different question than making something better than democracy.

​

​

[Warren D Smith]

On 12/31/17, Brian Olson <b...@bolson.org> wrote:
> I don't think a Condorcet cycle-resolution rule is inconsistent with what I
> said. It's just saying that of "A>B", "B>C", "C>A" some of those are better
> or worse than the others by some measure. For the 'best' A>B, A should win.
>
> To make a parallel analogy, I might formulate social utilitarianism as, "If
> the net benefit across all people of A is higher than B; A should win" (for
> options A and B, where we're going to do exactly one of them)
> Versus my statement of democracy, "If more people want A than B, A should
> win"

--well, the wording difference may sound subtle, but it makes the difference
between a statement which is inherently self-contradictory, versus
a statement which is self-consistent.

You here are trying to wriggle out of it by adding to your original
statement "well, I meant
only for the 'best' A and B, not all the other A and B" where you
refuse to define what
'best' means. Well, if you have to keep modifying your original
statement in ways you cannot even define, then something was wrong
with that original statement.
The cure for this wrongness is not to retreat into ever-more obscurity
about what you are trying to say, so that nobody can accuse you of a
contradiction because nobody even knows what the hell you are saying.

The real cure is, to advance into being precise, and to make a
statement which actually
is not self-contradictory.

And it is not an equivalent statement to yours.

1: "the best candidate is the one with greatest summed utility."
Utility is a real number,
for each person for each possible event. Real numbers are ordered.
Self-consistently. Without any cycles.

2: Something unclear about being wanted by the most voters.

1 is not equivalent to 2. Certainly 1 and 2 are correlated, but not the same.
And 2 is just wrong since it is self-contradictory. And that kind of matters if
you want to have a logico-moral foundation for everything.

And further, 1 has consequences. For example, consider the case where
a Condorcet winner exists. That is a highly favorable case for
supporters of (2). But a believer in (1), such as me, would contend
that, even then, this Condorcet winner is NOT necessarily the best
candidate.

> Warren, do you dislike 'majoritarianism' because of bogus IRV rhetoric
> about their constructed 'majority'?

--no, I dislike it because it is self-contradictory and a bad
foundation to rest on.
If people, such as IRV propagandists, or you, or Condorcet,
then construct bogus rhetoric about it, that does not help.
But it is not the underlying problem. It is a second-level
problem. The underlying problem is the wrong foundation.

> ​Perhaps I should claim my statement to be *relatively true at a certain
> level of detail.* Good enough for the general population; more refined

> versions will exist for us elections nerds and philosophers.

--sigh. You keep trying to retreat into vague bullshit, thinking that
is a cure for your problems. It is not a cure. It IS the problem.

An analogy:
When self-declared supporters of the Christian God figured the best cure for
Charles Darwin was to retreat into vagueness about what exactly James
Ussher's deduction was about how the first day of creation fell upon
23 October 4004 BC -- maybe the Bible really meant something a bit
vaguer, e.g.
maybe the first few days really were extra-long days.
Well, no. That was not the cure. And actually, earlier days were
shorter, not longer.
The problem was the Bible was just wrong, and was simply not a good
foundation to base the entire system of science and natural philosophy
upon. And no, the Bible was not
a good enough foundation for the general population with only a few
nerds needing something better. That was not the right view either.
Sorry. And the problem here was not the annoying rhetoric of some.
The problem was: the actual truth.

[NoIRV]

Then there is that classic paradox-like thing where there are two independent referenda, X and Y.
1/3 of the population hates X (e.g. -200 utility) but likes Y (e.g. +100). 1/3 hate Y but likes X. 1/3 like both (say, +50 each). Is it even possible to define a "majority winner" here? The questions would both pass with a 2/3 majority voting for each... but then groups 1 and 2 both regret their choices and band together to try and repeal both. And then group 1 teams up with 3 to get Y passed... trying to "always do what the majority wants" here leads to an absolute mess.

This is actually like a prisoner's dilemma... for each individual in classes 1 and 2, it is better to vote yes on their preferred issue. But if at least 1/4 of classes 1 and 2 do that, they all get their second worst choice!

---------

I find it interesting that Warren just put Brian, Condorcet, and the IRV propagandists in the same boat there.

[Warren D Smith]

> I find it interesting that Warren just put Brian, Condorcet, and the IRV
> propagandists in the same boat there.

--let's not further muddle things...

[Lonán Dubh]

​I guess the fusion of these two points is that if a score ballot is a person's estimate of the utility they would derive from a candidate winning, then if everyone votes honestly we can do better than Condorcet by simply summing up all those score votes and sometimes we'll have a more utilitarian result that isn't a Condorcet winner.​

That was largely my point: that satisfying the Condorcet Winner criterion is not an unqualified good; when the Condorcet Winner is the Utilitarian winner, then sure, but otherwise, it brings us back to the idea of a majority winning (which I have no problem with, in a vacuum or as a fallback) at the expense of the complement losing.  

That, fundamentally, is the problem I, personally, have with majoritarianism, in contrast to utilitarianism: majoritarianism it means the minority loses more than they need to.  Some candidates must lose (otherwise there would be no need for an election), but when sections of the electorate lose, they want to win, so that they can make the previous winners lose.

​

Also, it is about democracy and making the best democracy is be a different question than making something better than democracy.

You seem to be dismissing my concerns as looking for something "better than" democracy. 

How is it not Rule of The People for them to vote in a more expressive manner? 

Is optimizing the coordinated group decision (voting method) for group benefit rather than subgroup benefit really less democratic?  If making decisions based on the desires of the people is democratic, is not listening to the desires of more of the people more democratic?

How do you justify the Democracy/"Better Than Democracy" distinction when you had a few hours earlier defended against the wolf/sheep/dinner question with Constitutional Restrictions that improve democracy?

 

[Warren D Smith]

>> Also, it is about *democracy* and making the best democracy is be a
>> different question than making something *better than* democracy.

--also, I did not like that sentence.
The word "democracy" arose from the Greek
Demos=People, and Kratos=Power.
Democracy, it seems to me, is the people getting what they want, i.e.
getting what benefits them the most, by being somehow
empowered by some system of rules, to get it or
some approximation of it.

If you think what democracy means is "a particular system of voting"
and therefore some other system would not be democracy
(maybe something "better than" democracy, but not democracy) then we
have a disagreement.
You if you have that view would be trapped in shallowthink
and missing the bigger picture, which is: democracy is simply a way to
get the people what benefits them most.

Better democracy is just a better system which works better, i.e.
yields greater benefits. This can be objectively measured,
at least in some settings, which is what "Bayesian Regret" was about...
as I think Brian Olson already knows.

[Clay Shentrup]

On Sunday, December 31, 2017 at 9:19:00 AM UTC-8, Brian Olson wrote:

"If more people want A than B, A should win"

This is mathematically proven to be false, e.g. via Condorcet cycle + IoIA.

http://scorevoting.net/CondorcetCycles

Or here's arguably a more blistering refutation.

http://scorevoting.net/XYvote.html

The one and only social welfare function that can possibly be correct is just pure utilitarianism.

http://scorevoting.net/UtilFoundns.html

[William Waugh]

I submit that if anything deserves to be called the core principle of democracy, it is the principle that every citizen is entitled to equal political power to every other. This has been expressed with "one person, one vote", but not perfectly well expressed, because in theory that one vote might not necessarily be equal in power to another vote and the semantics of the phrase would still be satisfied, from the viewpoint of a linguist treating the semantics in a very strict and literal way. But courts have held that "one person, one vote" isn't fully realized if those votes are not equal. And if for example your vote is a thousand times as powerful as mine, the situation clearly makes a mockery of "one person, one vote"; with such a small vote, I might as well not have a vote at all.

IRV fails the principle of equal power, although it can be hard to convince a listener that this is true. I think the difficulty of convincing comes from the complexity of IRV. When an IRV advocate thinks about how IRV works, it looks to them like such a knot of complexity that if they mentally start with an assumption that it does give equality of power, they can't see from an understanding of it that it does not.

On Sunday, December 31, 2017 at 12:19:00 PM UTC-5, Brian Olson wrote https://groups.google.com/forum/?fromgroups#!topic/electionscience/ra_civPA4fU

[Steve Cobb]

>"If more people want A than B, A should win"

Cool, as long as I get to control the nominations.

[Steve Cobb]

>I submit that if anything deserves to be called the core principle of democracy, it is the principle that every citizen is entitled to equal political power to every other. 

"Every citizen is entitled to equal political power." I rather like that, but what then would a stake-based system be?

Both could be considered fair, as long as things were clear. The problem with IRV and choose-one plurality voting is that the inequality is hidden.

[Ciaran Dougherty]

William made a very interesting point, here.  I have to wonder if IRV (and other Dictatorship methods) aren't unconstitutional.

If you have the extreme scenario cited on a RangeVoting page (IIRC), of numerous candidates and  very close pairings at every runoff step, you have an insane disproportionality of power among voters.

1 Z
1 Y>Z
2 X>Y>Z
4 W>X>Y>Z
8 V>W>X>Y>Z
16 U>V>W>X>Y>Z
...
16,777,216 A>B>C>...>X>Y>Z

If you have one more voter, that voter dictates the election.  If they vote for Z, Z wins. If they vote for A, A wins.  If they vote for any candidate from B to Y, that candidate wins.  That is a failure of IRV/STV, but not of Cardinal voting systems.   Indeed, there are even a number of Ordinal methods that don't fail this (at least, not as spectacularly).

Bringing up constitutionality is a nuclear option, but I would argue that the Dictatorship aspect is rather damning even independent of that, even without getting the courts involved.

[parker friedland]

Although I tend to lean towards utilitarianism, the utilitarianism vs majoritarianism debate is an interesting discussion.

However no matter which way you lean, there are some basic facts that both sides cannot deny.

Even if you lean towards majoritarianism, you cannot deny that DH3 pathology (http://scorevoting.net/DH3.html), which is a huge flaw that every Condorcet method exhibits. It is also important to note that while rated methods do not exhibit DH3 pathology, they may be even more Condorcet then Condorcet methods: http://scorevoting.net/StratHonMix.html

Even if you lean towards utilitarianism, you cannot deny that the ranked pairs Condorcet method scored extremely well on Jameson's utilitarian VSE simulation when voters were 100% honest, and if you are one of the score voting advocates who do not believe that score voting will degenerate into approval voting because of an impulse for honesty, the same logic would imply that in Condorcet voting methods, voters would be fairly honest. I however am not of this opinion of score voting, and believe that how the voting systems behave when voters are much more strategic is a much more relevant test, I just want to warn anybody in the impulse for honesty camp against being a hypocrite. However it is important to note that warren's VSE sim had very different results, (http://electology.org/sites/default/files/comparing_voting_methods_simplicity_group_satisfaction.png), so much more experiments should be conducted in the future regarding VSE.

On Sunday, December 31, 2017 at 9:19:00 AM UTC-8, Brian Olson wrote:

[Toby Pereira]

I don't think these necessarily present problems for the positions though. For example, someone who leans towards utilitarianism could still declare a Condorcet method to be the best, even if it is at heart "majoritiarian", if they think that it will produce the most utilitarian results. A majoritarian might similarly decide on score voting - unlikely but logically possible. See this - http://rangevoting.org/AppCW.html

[NoIRV]

On Monday, January 1, 2018 at 1:32:15 PM UTC-5, Ciaran Dougherty wrote:
> William made a very interesting point, here.  I have to wonder if IRV (and other Dictatorship methods) aren't unconstitutional.
>
> If you have the extreme scenario cited on a RangeVoting page (IIRC), of numerous candidates and  very close pairings at every runoff step, you have an insane disproportionality of power among voters.
>
> 1 Z
> 1 Y>Z
> 2 X>Y>Z
> 4 W>X>Y>Z
> 8 V>W>X>Y>Z
> 16 U>V>W>X>Y>Z
> ...
> 16,777,216 A>B>C>...>X>Y>Z
>
> If you have one more voter, that voter dictates the election.  If they vote for Z, Z wins. If they vote for A, A wins.  If they vote for any candidate from B to Y, that candidate wins.  That is a failure of IRV/STV, but not of Cardinal voting systems.   Indeed, there are even a number of Ordinal methods that don't fail this (at least, not as spectacularly).
>
> Bringing up constitutionality is a nuclear option, but I would argue that the Dictatorship aspect is rather damning even independent of that, even without getting the courts involved.

Then FPTP (and Score) have cases where 1 voter dictates the election..
10 A=1 (B=0.5) others=0
10 B=1 (C=0.5) others=0
10 C=1 (D=0.5) others=0
...
10 Z=1 (A=0.5) others=0
1 <whatever> = 1 others=0
Next voter dictates the result. (We also have a Condorcet cycle, and I think most Condorcet systems would give the election to the next voter's first choice.)

I understand this is different from your example (which had 16 million votes for A, and 8 million for B, and no one else comes close). But I wanted to point this out.

------

I do not believe that score will degenerate completely into approval, but it will for SOME voters. But UnfairVote's "score => approval => honest FPTP => strategic FPTP" chain is definitely false in the aggregate.

[Warren D Smith]

Re "equal power" as a core principle, it does not (at least not by itself)
take us very far.

There are many voting systems all of which obey "equal power" symmetries.
But many of them are poor.
If all you had to work with was a desire for equal power, then
you'd be unable to discriminate among them.

Utilitarianism, on the other hand, has the ability to discriminate
between systems.

Further, equal power or something pretty close to it presumably is a
LOGICAL CONSEQUENCE of utilitarianism, in which case we would not need
to explicitly assume it as an axiom at all.
Similarly, majoritarianism is an approximate consequence.

[Brian Olson]

I think ideal utilitarianism is inaccessible. We can't practically make such a system. People won't perfectly introspect their utility payoffs, or we can't measure it, or people will vote strategically instead of honestly. (I get one million utility points from electing my candidate, right?)

So 'equal power' is necessary. I think the 'XY' examples are less good for not normalizing voter utility. ( http://scorevoting.net/XYvote.html )

When I do election algorithm simulations, I work with pure utility because it is knowable in simulation. But I want to design for the messy real world where that isn't accessible.

Score ballots are absolutely more expressive (better) than rankings ballots. More information is available. A clever election algorithm can use that to get a better result.

Our descriptions of this math and science must have multiple levels of detail as part of practical outreach. Newtonian Physics isn't the best model we have, but it's good enough for 95% of engineering that doesn't need relativity or quantum effects. Pre-calculus newtonian physics is more than enough for for people not doing engineering. Sometimes you just want intuitive physics so you can throw a ball around. We should be speaking at all those levels when we present to the world; and lead with the simplest version first and let people dive as deep as they want to. Several sources tell me that this sort of structure is good information design.

I also want to pick something 'good enough' and get it enacted. Sadly some people rushed that and decided IRV was 'good enough' and I think we all here agree that IRV sucks. For me Condorcet is good enough (with pretty much any cycle resolution rule (is there consensus on a favorite? I know there were big debates about that in this group a few years back)). But hey, maybe we should go all in on 1..5 score ballots instead of ranking ballots.

But maybe I should run simulations about how different election algorithms fare when losing information due to quantization error, in other words: how many score steps do we need to get good results? Hunches: 5 is pretty good; but possibly with large numbers of candidates we should have more score steps.

[Jan Kok]

> 1 Z

> 1 Y>Z
> 2 X>Y>Z
> 4 W>X>Y>Z
> 8 V>W>X>Y>Z
> 16 U>V>W>X>Y>Z
> ...
> 16,777,216 A>B>C>...>X>Y>Z

>

> If you have one more voter, that voter dictates the election.

That's not a fair argument against IRV because one can construct scenarios with ANY voting method where "one more voter dictates the election." For example, with 0-100 Score Voting:

100 A=100 B=99

1 A=0 B=100

It's tied, and one more voter can dictate the election. (Rob Richie once used an example like this to ridicule Score Voting, saying how could B win when so many more voters prefer A over B? The answer is: those 100 voters have only a very slight preference for A over B, while for that other voter, A is completely unacceptable and B is fine. One would hope that the 100 voters would not make a fuss if B wins in this situation. If any of the 100 really cared that much for A over B, they were free to rate B lower.)

The thing that seems outrageous about the IRV example you showed is that Z can win despite being voted in last place on all but two ballots. But wait a minute... is Z really in last place on all those ballots? No! A is in last place on 16,777,217 ballots because A is unranked on those ballots. Thus, Z wins by one ballot.

The IRV example is a red herring. It diverts discussion into such issues as: what is the voters intent when they don't rate or rank all the candidates? How should the voting method handle such ballots? It's also a near-tie situation, in that there are reasonable arguments for any of several outcomes.

I think it's a better use of our time to critique voting methods when they can make unambiguously poor choices of winners based on whatever ballot data is available. With Plurality voting, you can get poor choices of winners because the ballots don't collect enough data. With IRV, you can fail to choose the Condorcet winner when one exists. Burlington, VT is a great example of that. More people preferred Montroll over Kiss, according to the ballots, but Kiss won. http://scorevoting.net/Burlington.html

--

[Warren D Smith]

On 1/1/18, Brian Olson <b...@bolson.org> wrote:
> I think ideal utilitarianism is inaccessible. We can't practically make
> such a system.

--agree.

> People won't perfectly introspect their utility payoffs, or
> we can't measure it, or people will vote strategically instead of honestly.

> (I get *one million* utility points from electing my candidate, right?)

> So 'equal power' is necessary. I think the 'XY' examples are less good for
> not normalizing voter utility. ( http://scorevoting.net/XYvote.html )

--yes, i.e. truncating the range of allowed scores here being
what you here seem to mean by "equal power."

Ideas about unequal power (which all have been tried)
would be that, for example, mentally
defective people, or felons, or insufficiently rich people, are not
allowed to vote. Unfortunately all those ideas have been abused
to try to bias elections. Very heavily abused.
Based on that history it seems likely that
the risks of unequal power voting exceed its benefits,
in the real world. In an idealized world it could help.

> When I do election algorithm simulations, I work with pure utility because
> it is knowable in simulation. But I want to design for the messy real world
> where that isn't accessible.
>
> Score ballots are absolutely more expressive (better) than rankings
> ballots. More information is available. A clever election algorithm can use
> that to get a better result.
>
> Our descriptions of this math and science must have multiple levels of
> detail as part of practical outreach. Newtonian Physics isn't the best
> model we have, but it's good enough for 95% of engineering that doesn't
> need relativity or quantum effects. Pre-calculus newtonian physics is more
> than enough for for people not doing engineering. Sometimes you just want
> intuitive physics so you can throw a ball around. We should be speaking at
> all those levels when we present to the world; and lead with the simplest
> version first and let people dive as deep as they want to. Several sources
> tell me that this sort of structure is good information design.
>
> I also want to pick something 'good enough' and get it enacted. Sadly some
> people rushed that and decided IRV was 'good enough' and I think we all
> here agree that IRV sucks. For me Condorcet is good enough (with pretty
> much any cycle resolution rule (is there consensus on a favorite? I know
> there were big debates about that in this group a few years back)). But
> hey, maybe we should go all in on 1..5 score ballots instead of ranking
> ballots.

--condorcet is probably sufficiently complicated as to face severe
enactment hurdles.

> But maybe I should run simulations about how different election algorithms
> fare when losing information due to quantization error, in other words: how
> many score steps do we need to get good results? Hunches: 5 is pretty good;
> but possibly with large numbers of candidates we should have more score
> steps.

--I've done those. More accuracy (as one would expect) helps, but
with diminishing returns, e.g. 100 scale levels does not help terribly much
more than 20...

I've also done sims where voters do not know their own utility numbers,
they only know noise-contaminated versions of them. The results seem
to be pretty
much the same as for full-knowledge voters, except less dramatic (the noise kind
of scales down the advantage of better voting systems).

Re quantization, see
http://rangevoting.org/RateScaleResearch.html

[Clay Shentrup]

On Monday, January 1, 2018 at 2:13:35 PM UTC-8, Brian Olson wrote:

I think ideal utilitarianism is inaccessible. We can't practically make such a system. People won't perfectly introspect their utility payoffs, or we can't measure it, or people will vote strategically instead of honestly.

Warren's BR sims account for that, with "ignorance factors", and the normalization that occurs when utilities are translated to scores on a ballot, and strategic voting.

Checkmate.

[Clay Shentrup]

> So 'equal power' is necessary.

Not "necessary". Logically disproven. Like, the exact opposite of necessary.

[Brian Olson]

Clay, we might be talking about different things here.

If I'm designing a practical real world election system, I want either the ballot to constrain people to casting equal power votes, or I want the back end system to normalize votes to be equal power. Maybe the ballot constrains the upper limit of vote power cast but allows people to vote less; like only ranking a few choices or not allocating all their points if it's some kind of point-allocation ballot.

I think this is necessary for dealing with real world humans.

Right?

On Mon, Jan 1, 2018 at 10:40 PM, Clay Shentrup <cshe...@gmail.com> wrote:

> So 'equal power' is necessary.

Not "necessary". Logically disproven. Like, the exact opposite of necessary.

--

[Clay Shentrup]

On Monday, January 1, 2018 at 9:30:22 PM UTC-8, Brian Olson wrote:

If I'm designing a practical real world election system, I want either the ballot to constrain people to casting equal power votes, or I want the back end system to normalize votes to be equal power.

There's no need for a voting system to normalize Score Voting ballots. If voters don't want to use the extrema, I don't see what benefit you get from complicating the procedures to normalize their ballots.

Maybe the ballot constrains the upper limit of vote power cast but allows people to vote less; like only ranking a few choices or not allocating all their points if it's some kind of point-allocation ballot.

The amount of voting power is primarily a function of the circumstances. If there are 20 candidates and you bullet vote for one of the frontrunners, whereas I assign scores to all 20 candidates, but score the frontrunners equally, then your ballot technically has more power than mine. So I see no way for a ballot to constrain vote power, beyond the obvious sense of just giving everyone the same scale to vote with.

Limiting people is exactly what you don't want, because that creates scarcity which is how you get favorite betrayal.

I think this is necessary for dealing with real world humans.

Right?

No.

[Warren D Smith]

--huh?

[Warren D Smith]

Ok... since some people do not realize it...

WHY does "equal power" follow as a logical consequence of "utilitarianism"?

Well, suppose we had a voting system with unequal power for two classes
of people. For example "Jews" and "Palestinians" -- or fill in
the blanks some other way. In that case the powerful class would be able to
exploit the unpowerful class. If by so doing they tend to
cause a transfer T of wealth between what otherwise would have been
equally-wealthy people, then letting U(w) denote the typical utility enjoyed
by a wealth=w person, we get
U(W+T) + U(W-T)
instead of
U(W) + U(W).
The former quantity is smaller if U(w) is a concave-down function, such
as U(w)=log(w). And I happen to believe it is such a function.
[And there is evidence for that. E.g. billionaires are not 1000 times
happier than millionaires. Maybe they are 2 times happier, but not 1000x.
In other words U(w) grows very sublinearly at least in that range of w's.]
In the presence of concave-down U(w), the unequal system thus
tends to yield a smaller total utility for
all of society.

Now perhaps that could be outweighed by other things. For example,
suppose we said you had to pass a literacy test in order to vote. You
might argue, or hope, that society would benefit (greater utility)
from the better decisions made by literate voters, and that would outweigh
the utility-loss from the literates exploiting the illiterates.
It makes sense.

Unfortunately, that experiment has been tried. The "literacy tests"
in the USA were not really about literacy, they were about whether you
were black. In short, the system was, or quickly became, almost entirely
about exploitation and almost entirely not about improving
utility with more literate voters.

How about refusing to permit felons and/or imprisoned criminals from voting?
That also has been tried. In fact in all or almost all the USA right now,
imprisoned criminals cannot vote; and felons are disenfranchised for life
in some states (such as Florida). Well, in case you have not noticed,
prisoners in the USA are exploited and mistreated, and the system often
seems almost designed to create lifetime criminals and lifetime prisoners.
It seems clear to me that a lot of social utility could be gained in
the USA if prisoners
were treated better, and it also seems to me that the prisoners
themselves are more capable of understanding and judging what that means,
than the rest of us. We, because of our bad, unequal voting system,
are sacrificing that.
And this may be you: the USA has the highest incarceration rate, usually
by far, of any remotely comparable country, including many non-democracies.

How about only permitting people of the right religious or racial type to vote?
After all, those other religions are clearly inferior and/or wrongheaded.
Well, this experiment also has been tried. In case you have not noticed,
whenever that happens, the rest of the world denounces and is disgusted by
that country, and virtually the only supporters of the system are found
to be members of the uber-class in that country (and/or occasionally those
of the same or highly related race/religion outside it).

And how about geography? For example, Puerto Ricans cannot vote
since they are not a US state. Well, look how well that worked out.

And in the USA right now other unequal voting ploys are being and have been
pushed. For example "voter ID" laws with very carefully chosen kinds
of ID being permitted and not, such as in Texas today, gun permits are
a permitted form of ID while college ID cards are forbidden -- sort
of a reverse literacy test.
And the fact that election day is a Tuesday, which tends to
discriminate against those people who have to work on tuesdays. Has
this, over time, led to exploitation and
buildup of unnecessary inequality, and thus loss of utility?

Gerrymandering is another kind of intentionally-designed unequal power ploy.
It is virtually universally denounced, except by those in charge of it.

How about women not being allowed to vote? Oddly enough, women tended to
be treated (socially and/or legally) rather more differently than men, versus
in times & places they did vote; and the net result seems to have been
decreased total
utility.

BUT there are possible ways to design unequal-power voting systems
that are immune
to utility-reducing problems. For example, suppose people were
randomly selected
each election (the "red" people, say 1% of the population) and forced to vote,
while all the other people could not vote. If this selection truly
were random, then
this in my opinion would produce good results, essentially indistinguishable
from a "good democracy," even though the red and non-red people are
entirely unequal.
The key is that the true randomness makes exploitation of the non-reds
impossible.

You might complain that "1% vote" system would suffer more "noise" --
but it also
would be cheaper and less time-consuming for society as a whole which might
be more than enough to compensate.

Mind you, if we had such a system it would be very important to make
that selection truly be random. Some forces would try to cheat to bias
the randomness.

In view of that, I am not opposed, or anyhow not very much, to unequal
voting systems,
as a matter of principle. This all makes it clear the true core principle is
utilitarianism. Equality of voting is a CONSEQUENCE of that core principle, and
thus not really ITSELF a core principle -- and furthermore there are
kinds of inequality in voting which should be permitted --
to those of us not hamstrung by stupid and wrong "core principles"
and thus unable to see that.

So it is important not to bullshit about core principles. If you want
to have some, and if you want to force all of society to be built around them
forever, then get them right.

[Jon Roberts]

Has anyone tried to quantify the benefits of more expressive votes? I'm interested in relating voting power as a function of the voting method. I'd define voting power as the probability that a given vote can change the election outcome, assuming a uniform distribution of all the other voters' votes. I'd define the election outcome as the group's aggregate rank order preferences of the candidates after applying the voting method and its algorithm. Can we compare voting methods by the amount of voting power they convey to each voter? Does score voting convey higher vote power to each voter than IRV?

[Andy Jennings]

Jon,

In my thesis, I did simulations of what I called "random manipulability", which is, from a uniform distribution, the probability that a voter who randomly changes their vote will change the election outcome to one they like better.

I also did simulations of "voter manipulability", which is (also from a uniform distribution) if a voter could try changing their vote to every other possible vote, the probability that they would find at least one that changed the election outcome to one they like better.

http://ajennings.net/dissertation.pdf

See Chapter 3 and Section 8.2 and 8.3.

It sounds like the same thing that I considered negatively (manipulability), you're considering positively (voting power).  Interesting.

~ Andy

--

[Phil Uhrich]

Possibly more in depth than you are looking for but I like Jamison's Voter Satisfaction Efficiency. You could consider the 100% honest voter scenario as how expressive the voting system is. The more expressive the voting method, the more satisfied the voters should be.
http://electology.github.io/vse-sim/VSE/

[Jon Roberts]

Thanks Andy! Your thesis looks quite useful for quantifying voting power. I'll study it further.

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[Jon Roberts]

Phil I appreciate your pointing out Jameson's VSE, but this seems not quite the same as voting power. Let me try to explain why I'm asking for this. We're searching for criteria ("core democratic principles") to inform our choice of single-winner voting method. Methods that fail to support core tenets are ruled out, and so we have an argument we can make when advocating for election reform. William Waugh proposed "equal power" as being core (one person, one vote), certainly that's about fairness, but I'd like to formally define and quantify voting power with mathematical rigor. Here are 3 possible notions of equality:

1. each person has the same right to cast one and only one ballot, and both the ballots and the rules for filling them out are the same for all

2. the election outcome is independent of which voter casts which ballot; if the voters interchange their filled-out ballots before they're cast then the election outcome remains unchanged

3. each voter's influence is the same, in that everyone has the same ability to cast a vote which changes the outcome

I doubt "equality" as a criterion will help our election reform advocacy because I suspect that most voting methods will satisfy it, even plurality. For advocacy it's better to point out the evils stemming from plurality's suppression of expressiveness, which is censorship and in my view is a violation of our voting rights. I think the amount of power of one's vote is exactly the measure of one's voting right. If we can measure how much plurality infringes our voting rights then we can use this in advocating for reforms. I suspect plurality grants us all equal voting rights, but there are better methods that grant each of us much greater voting rights than plurality (in an absolute sense) while still maintaining equality (in a relative sense). Quantifying voting power will make people become aware of the massive amount of plurality's disenfranchisement of the electorate, and urgently push for reform.

I don't think utilitarianism should be a core tenet of democracy. In Warren's example of unequal voting rights - nobody can vote except for a random sample of the electorate - he says imposing utilitarianism will eventually lead to equality anyway: equality of wealth. Many people would disagree with an imposition of utilitarianism in a manner that enforces equality of wealth or outcomes. We should therefore propose tenets that are nonpartisan such as equality of voting rights, and apply utilitarianism to determine society's choices, and not dictate that society's choices must all maximize utility.

[William Waugh]

On Monday, February 5, 2018 at 1:39:22 AM UTC-5, Jon Roberts wrote https://groups.google.com/d/msg/electionscience/ra_civPA4fU/jhqgWNXZAgAJ and so this is my reply.

I don't see a need to use a model that turns on probability to understand equal power. Analysis suffices, focusing on theoretical scenarios where a single vote can swing the outcome.

Plurality/antiplurality is more equal than IRV. In Plurality/antiplurality, every vote has an antivote, which IRV advocates have not proven is the case for IRV, and cannot prove.

Approval is more equal than plurality/antiplurality. Although both of these systems have an antivote for every vote, there are some valuations that voters might occupy that Approval lets them express exactly in their vote but plurality/antiplurality excludes. Other things equal, a voter who is blocked from expressing her position is denied the same power that is permitted to a voter who is allowed the exact expression of his position. For example, in a four-candidate election, a voter who likes two of the candidates can express her position exactly in Approval but not in p/ap.

In summary, I point out two levels of equality. The first is formal equality or Frohnmayer balance, characterized by the balance between every possible vote and its antivote, which must be also be allowed in the system. Plurality/antiplurality exhibits this level of equality. But the case of plurality/antiplurality shows that formal equality does not go as far as other and deeper forms of equality that we can imagine. If two systems A and B exhibit formal equality, B is more equal than A if it allows expressions that A prevents.

Waugh

[William Waugh]

<< There are many voting systems all of which obey "equal power" symmetries. 

But many of them are poor. >> also sprach Warren D. Smith.

Please cite an example.

<< Further, equal power or something pretty close to it presumably is a 

LOGICAL CONSEQUENCE of utilitarianism >>

Maybe that is so, but equality is easier to test for and explain than utilitarianism. That makes equality valuable as a principle.

Moreover, you yourself present the argument, which I have been citing all over the place, that [to be continued]...

[Jon Roberts]

How is equality guaranteed by the existence of antivotes for each vote? With an electorate of 4 people {A,B,C,D} and a voting method where, before tallying, the votes are weighted {10,10,1,1} respectively, each vote has an antivote, but this method has huge inequality because each of A and B have 10 times the voting power of C and D. For me equality is proven by equating the amounts of everyone's voting power (using a model or analysis of theoretical scenarios or any other way are all acceptable). Equality is a relation, a relative concept; I don't follow your use of it in an absolute sense when you say one method is more equal than another. Voting power, on the other hand, might be measured in an absolute sense, and then we could say one method conveys more power than another. Regardless, you're saying plurality satisfies equality anyway, which to me means we can't use equality as a criterion in our reform efforts: if our current voting method is already equal then we don't need to change it.

[Warren D Smith]

The problem raised by Jon Roberts (which I answered, or started to, in
another thread)
was not to assure "equal power" for different voters (W.Waugh seemed
to think it was); it was to ASSESS the power each voter had, versus if
it were some other voting system.

Some voting systems give voters relatively more or less power than if
they were using
other voting systems. I now give some extreme examples:

1. the "random winner" voting system,
where the votes are ignored and a random candidate wins, is "fair"
in the sense all voters are treated equally -- but gives each voter zero power!

2. the "random ballot" system where a random ballot is selected &
whoever it names wins.
In this system each of the N voters has power=1/N (i.e. that is the
chance their
vote is capable of changing the winner). This is very tiny by comparison
with all the "additive" systems I treated in my other post, for which
voting power behaves like Q/squareroot(N) for large N, where the constant Q
depends on the system and #candidates, and was what I was discussing
in that other post.

So Jon Roberts' measure succeeds in those 2 cases in arguing those 2 voting
systems are undesirable.

3. The "random pair" system where a pair of candidates is elected at
random, then
all the ballots (which each are rank orderings) are examined to find out
which member of that pair is preferred vs the other, then he wins.
In this system the usual sort of Q/squareroot(N) power behavior happens
and this Q should be the same as for plurality with 2 candidates.

[Jon Roberts]

Thanks Warren for these examples. I'm trying to learn something from this antivote existence property, which I see Equal.vote calls the "Equality Criterion". As I explained I think this guarantees only pairwise equality, not necessarily equality among all voters. But this Equality Criterion may actually be more useful for assessing absolute voting power than relative equality.

Under plurality with C candidates, to fully offset a vote you need C-1 other votes (each for a different candidate), but with any cardinal method you can fully offset a vote with only one other vote (as long as the allowable ratings can be paired up where each pair has the same total rating). So passing the Equality Criterion in some sense means the voting method is sufficiently expressive on all the candidates.

Can Information Theory and entropy be applied to make voting rights a function of the amount of information that a voter can communicate to be used by the voting method?

[Warren D Smith]

> Can Information Theory and entropy be applied to make voting rights a
> function of the amount of information that a voter can communicate to be
> used by the voting method?

--certainly your "voting power" measure is not a function of that ALONE,
(since the random winner method yields a disproof).

I like this whole voting power idea, and a good next step would be to consider
IRV (instant runoff) via computer sims of random elections.
I would guess that in an IRV C-candidate election the voting power is
proportional to
C^a * (logC)^b
asymptotically for large C, for some constants a and b, which the
computer sim could try to estimate... with considerable difficulty.
It is possible this estimation task will be so difficult the computer
will not be able to figure out a and b to decent accuracy.

Presumably IRV gives voters more power than a 2-candidate plain plurality
election because just consider the last IRV round alone. That is a LOWER
bound.

Voters can affect any of the C-1 rounds, but if they affect some round
that might
not alter the election result in which case the "effect" of some vote was
illusory. If no illusions happened, then one might imagine IRV gave power
equal to the sum of the power of a voter in a K-candidate
plurality election, summed from K=2 to C-1. To the extent such illusions do
happen, presumably that sum therefore provides an UPPER bound.

My personal guess is that in the limit of large C,
almost all changes in the winner of a single round are indeed going to
be illusory, i.e. will not affect ultimate IRV winner, so I'm guessing
that upper
bound is going to be very weak. But quite likely that lower bound is
also weak.

So that immediately gives you a very crude notion of the power measure for IRV.

I do not think the view mentioned by Jennings that this whole concept
instead should be called "manipulability" and viewed as bad, has much merit.
I think this has little to do with how manipulation in the real world
actually works,
and I also think it is much more good than bad.

And I also think, if you really DID want to think about this kind of
manipulability,
then you'd want to estimate the chance your dishonest vote could change
the winner in a direction you favor, minus the chance your honest vote could
(if this difference positive). That would have been a better quantity
for that purpose,
than the one Jennings considered.

[Jon Roberts]

There is zero amount of information that a voter can communicate to be used by the random winner method, because random winner does not use any of the information communicated, and so voting power should rightfully be measured as zero for all. I think this is all about information and information alone: both the amount of information allowed to be communicated as well as how the information is processed (used) by the voting method or algorithm. I don't see any other independent variables, except perhaps election fraud or error (to the extent those may vary based on the voting method). That's why I thought information entropy could be useful, although I know nothing about it.

Regarding the illusory effects of IRV, would it help if we defined a change in election outcome as any change to the final rank ordering of the entire slate? I think right now you're only considering vote influence as the ability to change the (first place) winner. However, 2nd and 3rd place do matter (albeit diminishingly so) in terms of accurately reflecting the their support, which can impact how much money these candidates and their parties can raise for future elections. So in some sense the ability to change anything in the final ranking is a power. Does that make the analysis easier?

To simplify things, maybe the vote power calculation should assume voters know nothing about how others are voting (uniform distribution, so that's why I'm interested in Andy's thesis). It also makes sense that your power should be the chance that your vote makes a favorable change minus the chance it makes a change you deem unfavorable.

[Warren D Smith]

On 2/5/18, Jon Roberts <zyr...@gmail.com> wrote:
> There is zero amount of information that a voter can communicate to be used
>
> by the random winner method, because random winner does not use any of the
> information communicated,

--yes, but: how much "use" a voting method makes of information
is hard or maybe even impossible to define.
I agree in this particular artificial example, "zero use" is made of
it, but in, say, IRV, one can argue that the vast majority of the
marks the voters write on their ballot are never examined by my IRV
algorithm. (In fact, I can and have proven, asymptotically 100%
of it is not "used" when the #candidates becomes large.)
But wait, maybe somebody else's IRV algorithm looks at them all!
But then I'd argue that algorithm and mine are equivalent (i.e. always produce
same winner from any set of election data)
so their algorithm is "equivalent to not looking" even
though it does look.

Yuk. Pretty soon, with arbitrary voting methods,
it becomes as clear as mud. I think you are going to be
in big trouble if you try to base anything quantitative on
information "that gets used" and weigh "how much & how well"
it is "used."

But your "voting power" concept can be made into precise
definitions, and then you can just try to evaluate that measure one
voting system at a time.

[Andy Jennings]

Yes.  I was taking a definition of manipulability in a paper by E. Friedgut, G. Kalai, and N. Nisan (called "Elections Can be Manipulated Often") and doing simulations to calculate that quantity.  It was only concerned with "profitable" manipulations.  (Starting from a collection of votes, from the uniform distribution, assumed to be honest, if one voter changes his vote randomly, what is the probability that will change the election winner to someone he liked better in his original ranking?)  It seems that this is related to manipulability and is probably a quantity that you would want to minimize.

After further thinking about Jon's comment it seems that is not what he's really after.  "Voting power" would be more like whether a voter can change the election outcome at all, without distinguishing whether the change is profitable or unprofitable to that voter.

Not that it's something you want to maximize blindly.  I can make up degenerate systems that maximize it.  Suppose voters submit 0-9 scores for each candidate.  Scores are summed for each candidate, and we only keep the remainder modulo 10.  Each voter has maximum power to affect the election, but it's still essentially random-winner.  (Unless some voter knows how everyone else is going to vote, then they can change the election outcome to whatever they want.)

But this concept may still be a helpful yardstick for analyzing methods that are otherwise sensible.

~ Andy

 

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

[Jon Roberts]

Good point Andy. High voting power is not the sole criterion for picking a voting method. Maximizing VSE is key, for example.

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[William Waugh]

Jon Roberts << Regardless, you're saying plurality satisfies equality anyway, which to me means we can't use equality as a criterion in our reform efforts: if our current voting method is already equal then we don't need to change it. >>

That's not what I meant. Where I wrote "plurality/antiplurality", I was not referring to plurality, but to a system different from it. In plurality/antiplurality, the tallying is done like Approval, but the ballots are restricted to either support one candidate and oppose the rest, or oppose one candidate and support the rest.

(Tien Shang Chang has been arguing very earnestly for a system that is very like plurality/antiplurality. His only tweak to it creates a possibility of the election being thrown out and new candidates sought. He agrees with me that Approval is more expressive but says that his system will be easier to get people to accept because of the common understanding of "one vote". A voter has one vote for someone or one vote against someone.)

[Jon Roberts]

Sorry I misunderstood, and thank you for teaching me a new method (plurality/antiplurality). My two main points are that:

1. The "equality" criterion (or Frohnmayer balance) has very little to do with equality. There are methods with huge and flagrant inequality that pass this "equality" criterion with flying colors, and there are methods that fail this formal "equality" criterion while conveying truly equal voting power to each and every voter.

2. Plurality should pass any true test of equality a priori, because plurality treats all voters equally. This renders any notion of equality practically useless in pushing for voting reforms for single-winner elections. Inequality is not the problem right now; the problem is plurality's suppression of freedom of expression. Plurality disenfranchises all voters equally. Our fight is about suffrage and censorship, not inequality.

[Warren D Smith]

I think Jon's "voting power" measure is sort of like measuring
voter expressiveness, but captures something more like
"EFFECTIVE expressiveness."
Effective meaning winner-altering.

Andy's "plurality mod 10" example is a good illustration of the
difference between
Jon's voting power concept if you ("the" voter) knew everything about
all the other voters, exactly, versus if you did not. In the latter case,
you;d be unable to take advantage of your so-called voting power
and would be effectively powerless; in the former case, you'd have at
least 90% of the power you'd have with plain plurality, and actually I think
a lot more. In my post on other thread I looked at both flavors of the
concept and I think the one that assumes you are ignorant of
the other voters' behaviors, is the flavor I prefer.

[Phil Uhrich]

My first thought is to try to quantify the ability of a voter to express their honest preference for all candidates on the ballot. unfortunately the best idea I have for that is a check list of sorts. Something like this...... This is just a rough start

https://docs.google.com/spreadsheets/d/1eJWZ8m-LOBLzBNssFxihlOeEvGq-ZYABcdnO0Sv7alE/edit?usp=sharing

Step 2 would be determine the likelihood that each voting system will incorporate that data.

[Clay Shentrup]

To maximize voting power, you could just make the winner be a hash of all voters' votes. Then there's nearly a guarantee that your vote changes the outcome.

Hmm, maybe voting power is not what we want.

[Jon Roberts]

Yes Clay, Andy Jennings made this point yesterday with his "score modulo 10" example, although your hash example takes it to the extreme! As I said to Andy, maximizing voting power cannot be the sole criterion for picking a voting method. But the ability to change the outcome in an unknown direction is not true power. Voting power should be defined as being able to change the outcome in a particular desired direction. It should measure the responsiveness of the method's algorithm to a voter's honest vote, like a partial derivative, being the marginal change in the election outcome for a marginal additional honest vote, but where outcome changes favorable to the marginal voter are positive and unfavorable changes are negative. So this way Clay's hash method and Andy's mod 10 method would both convey zero voting power because the favorable and unfavorable changes, while each very high in likelihood, offset each other. On the other hand, Warren's random winner method also conveys zero voting power but for a different reason: there's zero likelihood of any change in outcome, favorable or unfavorable.

[Clay Shentrup]

Ah, Andy beat me to the punch.

> Voting power should be defined as being able to change the outcome in a particular desired direction.

Thing is, if that applies to you then it applies to me too. So this seems paradoxical.

I would come back again to the idea that voting isn't about power, it's about utility. For instance, suppose tomorrow your city adopted Score Voting but also disenfranchised you. Well, you'd have zero power. But you'd still be better off, statistically more happy with election outcomes.

> Warren's random winner method also conveys zero voting power but for a different reason: there's zero likelihood of any change in outcome, favorable or unfavorable.

The probability isn't zero.

[Jon Roberts]

Different voting methods have varying degrees to which an individual can impact social choices. Each individual's voting power is higher under plurality than their power under random winner, yet both methods convey equal power to all. I hope that resolves your paradox. I disagree with your claim that voting is about utility, not power. Voting is each individual's right or power. It's about the right to have all our voices heard and incorporated into collective decisions. A benevolent dictator might maximize society's utility, but this is a thread about democracy.

Under random winner, where ballots are ignored and the winner is chosen randomly, each voter has zero probability of making even the smallest change to the outcome.

[Warren D Smith]

On 2/7/18, Jon Roberts <zyr...@gmail.com> wrote:
> Yes Clay, Andy Jennings made this point yesterday with his "score modulo
> 10" example, although your hash example takes it to the extreme! As I said
> to Andy, maximizing voting power cannot be the sole criterion for picking a
>
> voting method. But the ability to change the outcome in an unknown
> direction is not true power. Voting power should be defined as being able
> to change the outcome in a particular desired direction.

--well, in the hash and mod 10 examples,
it is a KNOWN direction, IF you knew all the other voters' votes.

If not, however, then pretty unknown.

[Warren D Smith]

More interestingly, in the hash & mod 10 examples,
you have to know ALL other votes to be able to
effectively use your voting power; merely knowing 99% of
them would be useless.

But for (say) plain plurality,
if you knew 99%, but not all, the other votes, that would be
almost as useful as knowing them all, and would greatly enhance
your voting power versus if you knew none, by about a factor C/2
in a C-candidate election.

For approval, knowing 99% of the other votes would enhance
your voting power almost as much as knowing 100% -- but
only by about a factor of 2 versus knowing none.

Hence there are at least 3 flavors of the voting power concept
to consider.

In real life elections I vote in, I normally either know a good guess
about the other votes based on pre-election polls, or know essentially nothing
because there were no polls about that race (or anyhow none that
I knew about).

[Jon Roberts]

Yes and I too am starting to prefer a definition of power where the voter votes honestly and does not know anything about any of the other votes, i.e. a uniform probability distribution of all the other votes. Maybe that would be a simple first step and then we can add some complexity later (i.e strategic vote based on some knowledge of the other votes)

[Jon Roberts]

Would your 3 flavors be?:

1. Honest vote and uniform distribution of other votes

2. Strategic vote based on a distribution of other votes that has less variance than uniform

3. Strategic vote based on a point distribution (zero variance) perfect knowledge of every other vote

I think it's simplest to start with #1. The complexities of #2 seems hard to explain to the public. For example do we assume a difference between the marginal voter's perception of the distribution of other votes and the actual distribution of other votes? Maybe we just use only flavor #1.

[Warren D Smith]

On 2/7/18, Jon Roberts <zyr...@gmail.com> wrote:

> Would your 3 flavors be?:
>
> 1. Honest vote and uniform distribution of other votes
> 2. Strategic vote based on a distribution of other votes that has less
> variance than uniform
> 3. Strategic vote based on a point distribution (zero variance) perfect
> knowledge of every other vote

--no: mine would be
uniform others, yours is credited if you have the power to cause
one of at least two election results, and the credit is:
the chance you will be able to be able to succeed in causing the best one.
1. if you know all other votes
2. if you know 99% of all other votes
3. if you do not know any other votes

I do not say anything about "honesty" since defining what it means for
a vote to be
"honest" is in general difficult or impossible (i.e. consider that
hash-based system)

Of those I like #3 the best but somehow feel that something somehow
somewhere between 2 & 3 is what is wanted (but if so then I do not know what).

[Jon Roberts]

Warren when you say "causing one of at least two election results", what do you mean by an "election result"? Why not measure the chance that the winner is changed to someone preferred more by the marginal vote, minus the chance that the winner is changed to someone preferred less by the marginal vote?

The set up so far is:

1. assume a uniform distribution of everyone else's vote (every other vote assigns a random score or ranking to each candidate from the set of all scores and rankings allowed by the voting method)

2. the marginal voter knows absolutely nothing about any of the other votes (i.e. the marginal voter's perceived distribution of other votes coincides with the actual distribution of other votes).

[Warren D Smith]

On 2/13/18, Jon Roberts <zyr...@gmail.com> wrote:
> Warren when you say "causing one of at least two election results", what do
> you mean by an "election result"?

--the name of the winner.

> Why not measure the chance that the
> winner is changed to someone preferred more by the marginal vote, minus the
> chance that the winner is changed to someone preferred less by the marginal
> vote?

--because that notion is not defined in a maximally-general setup where "votes"
are just "arbitrary bitstrings." I submit the vote 1000101010101101.
Tell me: did that vote "prefer" Joe over Mary?

I like notions which actually are clearly defined, always.
If we are going to use them as a foundation of something of general
theoretical importance.

[Mark Frohnmayer]

Tl;dr: the core principle of democracy is equality.

[Jon Roberts]

The core principle of democracy is the right to vote!

The right to vote is the extent to which people can influence collective decisions.

North Korea has equality. Dictatorships grant equal voting rights (namely zero).

Plurality grants equality. Equality should not be our rallying cry.

[Clay Shentrup]

I contend the core principle of democracy is utilitarianism.

[Warren D Smith]

On 2/15/18, Jon Roberts <zyr...@gmail.com> wrote:
> The core principle of democracy is the right to vote!
> The right to vote is the extent to which people can influence collective
> decisions.
> North Korea has equality. Dictatorships grant equal voting rights (namely
> zero).
> Plurality grants equality. Equality should not be our rallying cry.

--well, a bit exaggerated: in N.Korea, there is one person with a
vote, unequal to the others.

But the trouble with "equality" is it does not get you very far at all.
Essentially all seriously-proposed voting systems satisfy "equality" including
ones that are clearly absurdly bad like "random winner," so if that is
all you had to go on, you'd have no way to distinguish among them.

Jon's proposed principle of "maximum voting power" is much more consequential
and therefore actually useful. I doubt we should call it "the sole core
principle of democracy" but it sure seems far better than merely
mouthing the word "equality." And it conceivably might even be
possible to prove it is strictly stronger in the sense that it IMPLIES
equality. I.e.

QUESTION: Does any voting system maximizing my
version of Jon's measure, automatically satisfy some equality test?

Try to find a proof or counterexample system...
To prove it, some symmetrizing argument might work, e.g. given some unequal
voting system with V voters, you can apply it V! times on each of the possible
orderings of the V voters, then somehow combine all the V! results,
to create a symmetrized version of the system which treats all voters equally.
If you can then prove Jon's measure gets larger whenever one symmetrizes,
then success. One way to combine the V! results is simply to choose
one of the V! at random and use its election-winner. With that combining method
it is obvious that Jon's measure is unaltered by the symmetrization.
So we have a THEOREM that "maximizing Jon's measure" and "voter equality"
at least are not logically incompatible (at least if we permit nondeterministic
voting systems).

[Mark Frohnmayer]

Equality does not simply mean equal access to the franchise (i.e. everyone gets to vote). It means that the weight and worth of the vote, as nearly as is practicable, must be equal between the voters.

Democracy is literally Demos (the people) kratia (have the power). The equal sharing of that political power is core to the principle.

[Jon Roberts]

I agree we want voting methods that maximize utility. Voting power measures the amount of data communicated by voters and how that data is used by the method. These are likely related and perhaps we can prove that greater social utility is a consequence of more expressive ballots.

[Jon Roberts]

It's pointless to demand equality when seeking voting method reform because we already have equality right now. Far more fundamental to democracy is that the Demos must have the Kratia in the first place. Only then can we require that such power be shared equally.

[Phil Uhrich]

IMO democracy is being able to have a say in your government. Finding out the consensus pick would clearly be the most democratic. Obviously the more expressive the ballot and the more honest the voters will be the better at finding the consensus pick.

[Warren D Smith]

On 2/15/18, Jon Roberts <zyr...@gmail.com> wrote:
> It's pointless to demand equality when seeking voting method reform because
>
> we already have equality right now. Far more fundamental to democracy is
> that the Demos must have the Kratia in the first place. Only then can we
> require that such power be shared equally.

--agreed, and Jon's idea (or some version of it) encapsulates the "kratia"
and as a side-effect addresses (slightly indirectly)
a lot of other things such as voter
expressiveness, information content, utility.
I think it is fairly near to the "right thing."

As far as my QUESTION of whether it also induces equality as another
side-effect is concerned...

...In math, one often has optimization problems
that obey some symmetry, and then in some cases the optimum solutions of
those problems, are symmetric. But in other cases, you can get a better optimum
by being unsymmetric ("symmetry breaking").
My demonstration with that V! random choice lottery trick, shows that
symmetry breaking cannot improve over the best symmetric (i.e. "equal")
voting systems under the Jon-measure... but perhaps it might be able to do
equally well. If a different combining method could be invented and
used which acted
"concave down" then that quibble would go away.

[Mark Frohnmayer]

Obviously we at the Equal Vote Coalition beg to differ about whether our current voting method provides an equal weight vote to the voters. See http://equal.vote/theequalvote 

[Jon Roberts]

I agree. Plurality fails this test miserably.

[Mark Frohnmayer]

Whoah, that was an easier argument than I was expecting! Glad we wrote it down :-).

--

[Jon Roberts]

How would you calculate the weight of a vote under STAR? Your formula for plurality is 1/(number you like), so how you would generalize this formula to other voting methods? More generally if you define vote weight as dependent on voter preferences then wouldn't different preferences produce different vote weights regardless of the voting method? In other words even STAR would have inequality by your logic. What am I missing?

[Jon Roberts]

Sorry it takes me so long to digest your comments. Given a marginal vote (e.g. your arbitrary bitstring), let's define that this vote "prefers" Joe over Mary if and only if the voting method's algorithm would determine Joe the winner under the assumption that this marginal vote is the only vote cast (no other votes) and the only candidates are restricted to just Joe and Mary. Now we can calculate the probability that casting the marginal vote changes the winner to someone preferred MINUS the probability that such winner becomes someone less preferred. 

[Jon Roberts]

Warren this is creative but a bit unclear to me. I think you may be conflating (i) the power of an individual voter under a given method, with (ii) some measure of a method's aggregate voting power. I'm still trying to figure out (i) whereas you seem to have jumped ahead to trying to maximize (ii) and showing that such optimal methods have equality under (i). That's fine, but how would you clearly define (ii) presumably as a function of the (i)'s for each voter?

[Warren D Smith]

On 2/15/18, Mark Frohnmayer <mark.fr...@gmail.com> wrote:
> Obviously we at the Equal Vote Coalition beg to differ about whether our
> current voting method provides an equal weight vote to the voters. See
> http://equal.vote/theequalvote

--I do not recall anybody "differing" with the contention star voting
provided "equal weight votes." But it seems possible to me that you
(MF) are trying
to create the false illusion that star voting somehow does that while
other rival systems
do not, and are trying to create the false illusion others are somehow
against equality
or others are contending star is not symmetric. I.e. both by this
quoted email and also by using the deceptive name "equal vote
coalition."

This is just one example of your rather disgusting propaganda-driven approach,
as opposed to a truth-driven approach. That approach was in fact the
whole reason you
initially invented star voting, and it turned me off it, probably to a
greater extent than if you had invented the exact same system driven
solely by the quest for truth.

In other words, you think propagandistic BS will cause greater success
at winning hearts, but in fact, at least in my case, that backfired.

[Mark Frohnmayer]

We do not at all try to create the "false illusion" that STAR voting is alone in meeting the Equality Criterion: all of the scoring methods do, and for ranked systems, Borda without ballot truncation also does.

I honestly don't look to you for marketing advice for obvious reasons.

[Warren D Smith]

On 2/16/18, Jon Roberts <zyr...@gmail.com> wrote:
> Sorry it takes me so long to digest your comments. Given a marginal vote
> (e.g. your arbitrary bitstring), let's define that this vote "prefers" Joe
> over Mary if and only if the voting method's algorithm would determine Joe
> the winner under the assumption that this marginal vote is the only vote
> cast (no other votes) and the only candidates are restricted to just Joe
> and Mary.

--well, first of all, that is not necessarily even possible. I.e. if the

"only candidates are restricted to just Joe

and Mary" then probably the bitstring 10010001010100101011
would have been an "illegal vote."

Second, it might also just be misleading. Such as in systems like IRV with
nonmonotonic phenomena.

I could raise other objections too, but you've got the wrong attitude.
The right attitude
in math is to cook up definitions that are generally applicable.
Not to keep on trying to restrict voting systems to a small somewhat
arbitrary subclass, forbidding all the voting systems not in your
class, and then pretending you did not do that
(or not even realizing you did it) which is just lame.

In fact, exactly that wrong attitude in the
past led the political science literature to focus on systems with
rank-order ballots ONLY, arbitrarily forbidding other possibilities.
This misdirected all of political science for 50 years.
Purely because they had not learned this
(already well known to mathematicians)
lesson about how to behave. Why try to repeat that mistake?

[Jon Roberts]

Then I'd define a vote prefers Joe over Mary if and only if either (i) Joe would be ranked above Mary if such vote were the only vote, or (ii) if the algorithm only determines a winner and does not allow for Joe and Mary to be compared, then Joe must be that winner, again assuming such vote is the only vote. No restrictions on the slate of candidates. What voting methods would be excluded by that definition?

[Jon Roberts]

Warren I think by "our current voting method" Mark meant plurality voting, not STAR voting (i.e. by "our" he meant "society's", not "the Equal Vote Coalition's").

[Jon Roberts]

Mark, I don't think all scoring methods satisfy the "Equality" Criterion. For example for 3 candidates where the only permissible scores are {0,2,3}, what single vote fully offsets the vote [0,2,3]? Yet wouldn't this be a valid cardinal method? If so, then STAR itself (using this kind of scoring in the first round) fails the "Equality" Criterion. Regardless, STAR and all such cardinal methods are truly equal in my mind because all voters have the same power. I actually like STAR voting. My counterexample (if it is one) shows that by suppressing expressiveness (preventing a score of {1}), we violate the "Equality" Criterion. It seems the "Equality" Criterion has nothing to do with "one person, one vote" but rather is about symmetric information. For example Plurality/Anti-Plurality is perhaps one of the least expressive voting methods that satisfy this criterion.

[Warren D Smith]

The quote was

"Obviously we at the Equal Vote Coalition beg to differ about whether
our current voting method provides an equal weight vote to the voters.

See http://equal.vote/theequalvote ."

I interpreted it as a claim that Frohnmayer objected to
somebody disputing that Frohnmayer's
current voting method was providing an equal vote. The reason I interpreted
it that way is, that is what he said. Note that "our" obviously refers to "we."
I also object to the very NAME "equal vote coalition."
Obviously this name is an attempt to mislead people into thinking
his voting method has something more to do with equality
than other methods. It does not.

Frohnmayer then claimed he was not going to take public relations
advice from me, i.e. he likes lying and misleading people, and I
advise the opposite.

Well, exactly. That is exactly what Frohnmayer's problem is, that has
turned me off him,
and ditto Rob Richie who is even worse (or maybe RR is not "worse,"
but merely has been "doing it longer.")
And the fact Frohnmayer continues to advocate that approach, continues
to turn me off him. He just seems to have this weird idea that
somehow he is going to impress me by acting that way, then doubling
down on it whenever anybody objects.
What he does not get:
people are the opposite of impressed by that sort of bullshit-first approach.

[Warren D Smith]

On 2/16/18, Jon Roberts <zyr...@gmail.com> wrote:
> Then I'd define a vote prefers Joe over Mary if and only if either (i) Joe
> would be ranked above Mary if such vote were the only vote, or (ii) if the
> algorithm only determines a winner and does not allow for Joe and Mary to
> be compared, then Joe must be that winner, again assuming such vote is the
> only vote. No restrictions on the slate of candidates. What voting methods
> would be excluded by that definition?

NO NO NO.

Look. I point out you are doing it wrong, You then find a new way to do
it wrong. Cycle repeats. Stop. Think before you speak.

Can you not see, immediately, that you are simply making the exact
same error over again in a new guise??

Define property in such a way that you do not restrict your class of
voting systems.
That is a worthwhile goal if you are defining a property of voting systems.
It usually is not hard. But it is hard if you try really really
really hard to keep failing at it
over and over.

[Mark Frohnmayer]

“Our current voting method” was a reference to plurality voting.

You don’t have to be in the Equal Vote Coalition if you don’t want to be, but you’ve yet to provide a credible critique of the equal weight argument. So all the swearing and name calling just comes across as silly nonsense. Just FYI.

[Warren D Smith]

On 2/16/18, Mark Frohnmayer <mark.fr...@gmail.com> wrote:
> “Our current voting method” was a reference to plurality voting.

--You might want to learn about "pronouns" then.
In case you want to "communicate."

> You don’t have to be in the Equal Vote Coalition if you don’t want to be,

--well, if your very first move is to mislead the public via your very
name, then, no, joining does not seem appealing.

> but you’ve yet to provide a credible critique of the equal weight argument.

--what "argument"?

[Warren D Smith]

On 2/16/18, Mark Frohnmayer <mark.fr...@gmail.com> wrote:

[Warren D Smith]

On 2/16/18, Jon Roberts <zyr...@gmail.com> wrote:
> Then I'd define a vote prefers Joe over Mary if and only if either (i) Joe
> would be ranked above Mary if such vote were the only vote, or (ii) if the
> algorithm only determines a winner and does not allow for Joe and Mary to
> be compared, then Joe must be that winner, again assuming such vote is the
> only vote. No restrictions on the slate of candidates. What voting methods
> would be excluded by that definition?

--let me try again.

Why do mathematicians try to make foundational definitions have
maximally general
applicability? Is it just to be anal and annoy you?
Or might there be another reason? Well, there are many freaking
reasons. But...

Your goal with this definition is to start a subfield of research.
The ultimate goal of that field of research would be to find a voting method X,
such that X is the best possible voting method measured by your yardstick.
Will humans ever be smart enough to identify X and to prove it best? I
do not know.
It might be quite easy or impossibly hard. But that surely is a top,
if not the ultimate, goal.

Now to prove X is the best, you have to prove every other voting
method Y, is worse than X on your yardstick. Now to do that, EVERY
voting method Y has to be MEASURABLE AT ALL on your yardstick. If
you, as your first move, make a definition of the yardstick
that EXCLUDES some Y, then you have slit your own throat as your very
first move.
You have forever prevented achievement of your ultimate goal, as your
very first move
in life!

Whyever would you ever want to be that stupid?

Whenever, historically, mathematicians, physicists, etc HAVE ever been
that stupid, their names are usually in some footnote about how,
stupidly, some idiot began this field of research by making a stupid
definition which wasted 5 decades.

Why join that club? You don't want to enter the hall of negative fame.
This simply is not how to behave as a mathematician.
It should go against every fibre.

[Jon Roberts]

So what is the definition of a voting system? I thought it's any arbitrary function from a set of allowable inputs from voters to the set of candidates; a winning candidate would be the output from a particular array of inputs (votes) from voters. Is there a more general definition?

[Warren D Smith]

On 2/16/18, Jon Roberts <zyr...@gmail.com> wrote:
> So what is the definition of a voting system? I thought it's any arbitrary
> function from a set of allowable inputs from voters to the set of
> candidates; a winning candidate would be the output from a particular array
>
> of inputs (votes) from voters.

--sure, and the "inputs from voters" could be any information, which
most generally is a bitstring.

[Andy Jennings]

I, for one, dislike the "every vote must have an anti-vote" argument.  I believe that every vote having an anti-vote is not necessary or sufficient for a good voting system.

Insufficient: Mod10 score voting.  Every vote has an a priori anti-vote, but the system is worthless.

Unnecessary: Median.  For an odd number of people trying to decide on a single number (or a value in any ordinal scale), the median is an excellent aggregator.  It finds the value that a majority would say is not too high and a majority would say is not too low.  Also, exaggerating your vote does no good, so every voter should vote honestly.

With the median, however, only MAX and MIN have anti-votes.  All other score submissions have no a priori anti-vote.  If someone submits a 5 (on a scale of 1-10), their vote would pull the societal value higher if it were below 5 and lower if it were above 5.  There's no vote I can submit to "push it away" from 5.  I can only submit my own honest vote and pull it toward some other number.

Because of this, any system based on the median (MJ, GMJ, MCA, Bucklin-ER, etc.) fails the equality criterion.  When Jameson was designing his 3-2-1 system, he thought about adding a vote that didn't make any sense (an "anti-2" which supports a candidate in the second round but not the first) just so every vote would have an anti-vote.  I recommended against it.


I see how this "equality criterion" argument is good rhetoric.  It sounds good.  It feels good.  Unlike Warren, I don't really resent you for making it.  But I think there are some good systems that fail it, so it annoys me as a bedrock criterion.

~ Andy

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[Warren D Smith]

While sleeping I was thinking about the "ultimate goal" of finding
"the best voting system" by Jon's "voting power" measure, and the good
news is, I pretty much solved
that ultimate problem. The bad news is, the answer is silly and reveals
the whole idea was flawed. Furthermore the flaw is not easy to repair and
it is possible that there is no repair that we would consider nice enough
(there might be some repair one would consider too
"disgusting"/"ugly"/"complicated" to want to go with)...

Specifically I am speaking of this flavor I advanced of Jon's measure:
1. all voters other than you vote randomly (all legal votes equally likely,
or all "non-silly" ones)
2. you do not know how they voted (although actually my example will
also work in the flavors where you know 100%, or where you know 90%, of the
other votes)
3. you then vote in a manner most likely to
alter election winner in a direction you favor
4. measure is the probability your vote alters election winner
in a direction you favor.
("Better" voting systems have higher probability.)

Now here is a voting system, or rather, a limit case of a voting system,
"best" by this measure.
It is kind of like range voting, only the set of allowed scores is
"geometrically fine in the middle" such as
{000, 333, 444, 481, 494, 498, 499, ... ,501, 502, 506, 519, 555, 666, 999}.
The "..." denotes a large number of scores which I have not written down,
and we are interested in the LIMIT as that large number approaches infinity.

In this system, the random voters with probability->1 will use scores
arbitrarily
close to midrange, causing a near-tie, which you then break with your vote.

This is best possible since probability approaches 1, which is as
large as a probability can be.
QED.

But it probably seems to you (certainly it does to me)
that this voting system is silly and it really is merely
exploiting the flaws in the measure to "look good,"
as opposed to genuinely being a good voting system.

[Mark Frohnmayer]

Andy, to be clear, the equality criterion as we have articulated it -

"A voting method passes the Equality Criterion if every possible vote expression has a counter-balancing vote expression and if the counting system produces the same election outcome when any pairing of a vote expression and its counter-balancing vote expression are added to the tally." 

- is only meant to definitively show that such systems positively provide an equal weight vote. There may be other valid systems that don't pass that criterion but still "as nearly as practicable" provide equality. For example adding any multi-seat re-weighting formula would make such a system fail the test, but still may be valid from a representational accuracy point of view.

And I'm glad you don't mind the rhetoric, since you can thank the Center For Election Science for the foundation of our argument -- it was this FAQ entry on the web site that led to the eventual a ha moment:

"Does approval voting violate one person, one vote?

No. The term “one person one vote” refers to the weight of votes, not to how votes are expressed.

The U.S. Supreme Court made the “one person one vote” rule explicit in Reynolds v. Sims (377 U.S. 533). The rule stated that no vote should count more than any other so that it has unequal weight. This unequal weight would violate the Equal Protection Clause of the Constitution. And it was Baker v. Carr (369 U.S. 186) that extended the Equal Protection Clause to districting issues. In Reynolds, the state of Alabama set up its districts so that they varied wildly in population. The districting was so bad that it gave some voters’ ballots as much as 41 times more weight than others. Because the weights of the ballots were different between districts, that violated the “one person one vote” rule.

A common misconception is that Approval Voting gives more weight to voters who vote for more candidates. To see why this isn’t the case, imagine a tied election between a liberal and two conservatives. Bob casts a vote for the liberal, while Alice casts an opposing vote for the two conservatives. After Bob and Alice have voted, the election is still tied. Bob and Alice have an opposite but equal effect on the election. Another way to think of it is that if you vote for all candidates, that has the same effect as not voting at all. The key here is that no voter has an unfair advantage. Effectively, every voter casts an “aye” or “nay” vote for every candidate."

We just took that and ran with it. Because if Approval Voting provides an equal weight vote according to the logic above, Plurality Voting most certainly does not.

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[Jon Roberts]

Very enlightening example! So far I see two possible paths of resolution. First, observe that under such a system these theoretical other voters should not cast votes that are concentrated towards the middle. Assuming a uniform distribution of voter preferences (not votes!), those preferences would be expressed in votes giving higher probability to the extreme scores (towards 000 and 999) and decline to a valley of low probabilities in the middle, simply because this system's ballot has too many options in the middle compared to the extremes. Here I'm assuming if a voter's actual score (reflecting preference) for a candidate is X (on a scale including all reals in the closed interval [0 to 999]) then such voter on the ballot will score the candidate at the score closest to X from the set of all scores allowed by the system. Note this represents a departure from our assumption that the other voters' VOTES be uniformly distributed, and modified with the assumption that the other voters' PREFERENCES are unknown and uniformly distributed.

Another possible resolution is to require voting systems not to be "silly" in this way. In other words we require that voting systems must offer choices of scores on the ballot that are themselves uniformly distributed (equally spaced). This approach avoids making an assumption regarding how preferences are expressed in the votes cast (in the above approach we assumed votes would be as close as possible to preferences).

[Warren D Smith]

> So far I see two possible paths of resolution.
> First, observe that under such a system these theoretical other voters

> should not cast votes that are concentrated towards the middle. Note this represents a departure from our

> assumption that the other voters' VOTES be uniformly distributed, and
> modified with the assumption that the other voters' PREFERENCES are unknown
> and uniformly distributed.


> Another possible resolution is to require voting systems not to be "silly"
> in this way. In other words we require that voting systems must offer
> choices of scores on the ballot that are themselves uniformly distributed
> (equally spaced).

--well, ok ideas in spirit, but, major suckitude.
Your second idea restricts the class of allowed voting systems, which
sucks -- and in a vague, hard to make clear exactly which are ok way, which
sucks even harder.

Your first idea basically is that the other V-1 voters are not going
to be "random" they are going to be "smart." Actually somewhat random
but in smart ways.
True, but finding a good way to try to define what that even means for
a fully general voting system, is going to get you into deep muddy
waters. Probably not going to be sweet and simple anymore. Going to
be disgusting and hard to work with if you can do it at all.

I could be wrong, but suspect this kind of idea is busted so hard it
will never recover
good health...

[Jon Roberts]

Mark, in Reynolds the offending part of the voting system that failed "one person, one vote" was the malapportionment of the electorate into districts of unequal numbers of eligible voters. This created inequality between districts. I find a more relevant (intra-district equality) court opinion in Stephenson v. Ann Arbor from 1975 where IRV was successfully defended as satisfying "one person, one vote." The same logic would show plurality as inherently equal. The following are excerpts, and notice that this court did not test equality/"one person, one vote" after the ballots are cast, or in a manner dependent on voter preferences, how they voted, or the ideology of the candidates!:

"There is no deliberate scheme or practice that classifies voters under this system of voting. Each voter has the same right at the time he casts his or her ballot. Each voter has his or her ballot counted once in any count that determines whether one candidate has a majority of the votes. Each voter has the same opportunity as the next voter in deciding whether or not to list numerical preferences for his or her candidate and has the same equality of opportunity as any other voter if his or her candidate is eliminated as the lowest vote-getter, and his or her second choice preference becomes the viable vote. ... The fact that each person voting lists different orders of preference does not mean that some voters have greater rights than others. Each voter is on an equal footing with the next voter as to whether his first preference, second preference etc. will remain in the "elimination process". It is the equal right to list preferences and the equal opportunity to be eliminated or to stay in the running that accords each voter the same rights, not the possibilities of whose first or second preference may or may not stay in the counting. Each voter is given the same rights at the same time, that is, the time of casting his or her ballot. ... no one person or voter has more than one effective vote for one office. No voter's vote can be counted more than once for the same candidate. ... no voter is given greater weight in his or her vote over the vote of another voter ... The form of majority preferential voting employed in the City of Ann Arbor's election of its Mayor does not violate the one-man, one-vote mandate nor does it deprive anyone of equal protection rights under the Michigan or United States Constitutions."

[Warren D Smith]

yah well, be careful about court decisions about voting methods. My
experience is
the courts are highly inconsistent, contradicting each
other/themselves, plus do not know what they are talking about. As a
result the very next court decision can be quite opposite to whatever
you think it will be.

[Mark Frohnmayer]

The State of Michigan Circuit Court is not the arbiter of the U.S. Constitution.

We rely on the opinions expressed by the  Supreme Court in construction of our argument.

[Jon Roberts]

That court opined on the U.S. Constitution. Which Supreme Court opinions are you relying on that relate to voting methods (as opposed to redistricting)? Have you found any court opinions (US Supreme or otherwise) that support your contention that plurality does not provide an equal weight vote?

[Jon Roberts]

Your first idea basically is that the other V-1 voters are not going
to be "random" they are going to be "smart."  Actually somewhat random
but in smart ways.
True, but finding a good way to try to define what that even means for
a fully general voting system, is going to get you into deep muddy
waters.

It may be difficult to define this in a way that would allow us to find the optimal voting system from all possible voting systems, or solve for the system with the most voting power from all possible systems. That might be too much. But I think it's feasible to define a measure of voting power that would allow us to compare and rank specific voting systems.

[Mark Frohnmayer]

To my knowledge, we are the first to make this argument in federal court (Amicus filing in the 2014 NJ primary case). Not aware of the supremes looking inside the voting method... yet.

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[Mark Frohnmayer]

Recent court cases on partisan redistricting ought to provide some new ammo re: vote splitting and partisan factions, but haven’t done the spelunking on that front yet.