Alternate Voting Systems (Range, Condorcet etc)

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby achan1058 » Sat Mar 12, 2011 8:54 am UTC

Can someone with good game theory background check whether range voting avoids Arrow's impossibility theorem? The wiki article claims that it does, but the cited source doesn't necessary look credible. (If it is so, what limitations does it have?) The condorect method, from what I have seen, doesn't dodge this one at all.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby yawningdog » Sat Mar 12, 2011 2:11 pm UTC

I believe all votes should be write-ins and no candidate's name should appear anywhere on the ballot. I also believe that all votes must be spelled correctly or they don't count.

The range voting concept is just silly in my opinion. Everyone will give 100% to their favorite candidate and a big fat goose egg to all the others, effectively defeating the purpose of the system.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby achan1058 » Sat Mar 12, 2011 4:42 pm UTC

yawningdog wrote:I believe all votes should be write-ins and no candidate's name should appear anywhere on the ballot. I also believe that all votes must be spelled correctly or they don't count.
This will just be not fair. A name like John Doe ended up having a higher vote than say Sergei Vasilievich Rachmaninoff.
yawningdog wrote:The range voting concept is just silly in my opinion. Everyone will give 100% to their favorite candidate and a big fat goose egg to all the others, effectively defeating the purpose of the system.
That's not true, especially if you don't restrict it to 1 person per party. Suppose the vote is Hilary, Obama, and McCain. I would have given 100% Hilary, 80% Omaba, 0% McCain. Granted, if people do vote the way you suggested, it doesn't dodge Arrow's theorem indeed.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Indon » Sat Mar 12, 2011 6:58 pm UTC

Wow, this is a well-aged thread. Just swinging by, but I think I can contribute a bit.

achan1058 wrote:Can someone with good game theory background check whether range voting avoids Arrow's impossibility theorem? The wiki article claims that it does, but the cited source doesn't necessary look credible. (If it is so, what limitations does it have?) The condorect method, from what I have seen, doesn't dodge this one at all.


I know of no extant voting system that avoids the impossibility theorem. In fact, for that reason, I think for this reason someone needs to summarize the theorem to keep the discussion from going in circles.

Arrow's impossibility theorem states that of the following criteria for a good election, any given voting system will lack one or more, simply as a result of including all the others. (I tried as best I can to summarize the consequences of lacking each criteria, but frankly, I had a lot of difficulty trying to understand what a lack of Universality would do, and only really closely studied some of the others right before making this post, so if anyone can describe any of the below more accurately and succinctly, I'd <3 you much)

  • Non-dictatorship - Without it, your vote probably doesn't get counted.
  • Universality - Without it, the system might not be able to compile a coherent and consistent list of winners for any given election.
  • Independence of Irrelevant Alternatives - Without it, strategic voting, where you vote for candidate A to get candidate B _instead_ of A, works.
  • Monotonicity - Without it, if you give someone a higher priority in your vote, it could make them lose.
  • Non-Imposition - Without it, it might be impossible for a candidate to win even if a majority prefers them and they would be elected under a different system.
  • Unanimity - Without it, even if everyone votes for candidate A over candidate B, candidate B could still win before A would.

So rather than talking about the features you want out of a voting system, I think it best if you talked about the problem that you mind the least, and pick an appropriate system that has that problem once there's agreement, then try to see if there's any way to mitigate or remove that problem.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby achan1058 » Sat Mar 12, 2011 7:23 pm UTC

I think it also require more than 2 party as well, does it not? But even with this in, I am not sure what I want to drop out. There are advantages of having more than 2 parties.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Indon » Sat Mar 12, 2011 7:28 pm UTC

achan1058 wrote:I think it also require more than 2 party as well, does it not? But even with this in, I am not sure what I want to drop out. There are advantages of having more than 2 parties.


I think that's a part of Universality? If only because it's the concept I had the hardest time trying to convert from jargon into actual meaningful words.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Mechanicus » Sun Mar 13, 2011 2:54 am UTC

There's a referendum in May in the UK about adopting the alternative vote (also called preferential voting in Australia and instant run-off voting in the US). Anyone British have an idea of what the likely result will be?
No one knows - after the systems are explained to people, they tend to say no. When people are asked the straight question on the ballot paper with no explanation, they tend to vote yes, but the No campaign has been growing for a while now and the first poll asking the referendum question showing 'no' ahead was released today. There's still a good 30% don't knows.

Note that as people learn more about the systems involved they get more negative towards it and we've still got months ahead of campaigning, even if the large amount of public holidays and the Royal Wedding mean that debate will probably be pushed out of the public consciousness towards polling day. Ultimately, it will come down to who bothers to vote; some regional and local elections are happening on the day, but they don't get big turnouts.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby mmmcannibalism » Sun Mar 13, 2011 3:16 am UTC

Mechanicus wrote:
There's a referendum in May in the UK about adopting the alternative vote (also called preferential voting in Australia and instant run-off voting in the US). Anyone British have an idea of what the likely result will be?
No one knows - after the systems are explained to people, they tend to say no. When people are asked the straight question on the ballot paper with no explanation, they tend to vote yes, but the No campaign has been growing for a while now and the first poll asking the referendum question showing 'no' ahead was released today. There's still a good 30% don't knows.

Note that as people learn more about the systems involved they get more negative towards it and we've still got months ahead of campaigning, even if the large amount of public holidays and the Royal Wedding mean that debate will probably be pushed out of the public consciousness towards polling day. Ultimately, it will come down to who bothers to vote; some regional and local elections are happening on the day, but they don't get big turnouts.


That's odd, has anyone done research into why people tend to become opposed to it over time?
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Silas » Sun Mar 13, 2011 9:01 am UTC

achan1058 wrote:Can someone with good game theory background check whether range voting avoids Arrow's impossibility theorem? The wiki article claims that it does, but the cited source doesn't necessary look credible. (If it is so, what limitations does it have?) The condorect method, from what I have seen, doesn't dodge this one at all.

Range voting isn't covered by Arrow's theorem, because it's not in the category of voting methods covered. Arrow's theorem proves that no function from a set of ranked ballots to an outcome ranking can have all the properties Indon listed. Since range voting uses scored ballots instead of ranked, it 'escapes' the theorem.

But it's disingenuous to suggest that range voting avoids the problems Arrow's theorem illustrates. The major issue is strategic voting- in an ideal system, no matter what other votes were cast, you shouldn't have to choose between submitting a ballot that reflects your preferences and one that would result in an outcome you prefer. But it's easy to construct scenarios where distorting your own vote improves your outcome under range voting. (In the example on Wikipedia's range voting page, a coalition of voters could change the outcome by underreporting their preference for one outcome.)
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Sun Mar 13, 2011 9:02 am UTC

yawningdog wrote:The range voting concept is just silly in my opinion. Everyone will give 100% to their favorite candidate and a big fat goose egg to all the others, effectively defeating the purpose of the system.


That is utterly false. Say you believe Nader=10, Gore=7, Bush=0. If Gore and Bush appear to be the clear frontrunners, then your best strategy is to give Gore a 10, and Bush a 0. Then you can also give Nader a 10 as well. In that case, if a candidate like Nader turned out to have more sincere support than people realized he had, he could still win. By contrast, in most rank-based systems, your best bet would be to rank Gore over Nader over Bush, which would cause the appearance of weakness to become a self-fulfilling prophecy for someone like Nader. It also results in two-party duopoly and effectively two choices. (Add Gerrymandering on top of that and it's effective one choice.)

Extensive Bayesian Regret calculations show that Score Voting outperforms all commonly proposed alternatives with any mixture of sincere or strategic voters.

Here are numerous other pages that go into great detail about the game theoretical aspects of tactical voting with Score Voting and Approval Voting as compared with a variety of ranked methods.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Sun Mar 13, 2011 9:05 am UTC

achan1058 wrote:Can someone with good game theory background check whether range voting avoids Arrow's impossibility theorem? The wiki article claims that it does, but the cited source doesn't necessary look credible. (If it is so, what limitations does it have?) The condorect method, from what I have seen, doesn't dodge this one at all.


Warren D. Smith, the guy who created ScoreVoting.net, is a Princeton math Ph.D. who did his undergrad at MIT, and seems to me to be the top election methods expert on the planet, and quite possibly in all of history. He was the protagonist of the William Poundstone book Gaming the Vote. He authored this page on the subject of Arrow's Theorem.

I don't know what you mean it doesn't "look credible". It is a simple proof by example. Warren states the criteria that form Arrow's Theorem, and then demonstrates how Score Voting satisfies all of them.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Sun Mar 13, 2011 9:18 am UTC

Silas wrote:it's disingenuous to suggest that range voting avoids the problems Arrow's theorem illustrates. The major issue is strategic voting


No, that is absolutely not the issue. The issue is Independence of Irrelevant Alternatives, and the fact that any social utility function that is ordinal can contradict itself, and thus logically must occasionally pick the "wrong winner".

For instance, say we have the following ranked preferences.

35% X>Y>Z
33% Y>Z>X
32% Z>X>Y

E.g. 35% of the voters prefer X first, then Y second, then Z third.

Say for the sake of argument that X is the right winner according to these preferences. That is, "the candidate who best represents the will of the people".

Now say we eliminate Y, with no change in the voters' preferences for X or Z. Because no preferences have changed, then the electorate must still prefer X. Yet the situation now looks like this:

35% X>Z
65% Z>X

A 65% majority of voters prefers Z. Essentially any ranked voting method would elect Z here, even though X is the candidate who best represents the will of the voters.

So the problem is is not tactical voting, but rather electing the wrong candidate in at least one of the two before/after scenarios, even if voters are 100% sincere. This is the problem with any violation of a consistency-based criterion, like monotonicity as well.

This is essentially the mathematical proof that the correct social utility function must be cardinal, not ordinal.

This highlights the immense confusion Arrow's Theorem has caused in the field of social choice theory. It has done an incredible amount of damage in this way.

it's easy to construct scenarios where distorting your own vote improves your outcome under range voting.


The same goes for every deterministic voting method. But it so happens that Score Voting is astonishingly resistent to the negative impact of strategic exaggeration. It has beat out all feasible rivals in 100% of 720 different parameterizations ("knob settings") of things like "number of candidates" and "ratio of strategic voters to expressive voters", etc.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Silas » Sun Mar 13, 2011 9:47 am UTC

Range voting doesn't solve that problem, if voters adopt a realistic strategy. Look at the same scenario, with range voting, where voters (sensibly) rank their favorite candidate 1, their least favorite zero, and the intermediate candidate somewhere in between, according to how good of a second choice she is. For simplicity's sake, let's assume that all voters feel the middle candidate is exactly halfway between the best and worst.

With the same percentages you proposed in your own post, we have:
35% who feel X is a 9, Y is a 7, Z is a 5
33% who feel Y is an 8, Z is a 5, X is a 2
32% who feel Z is a 10, X is a 5, Y is a zero.

With one hundred voters, that comes down to 35 whole and 32 half votes for X (51), 33 whole and 35 half votes for Y (50.5), and 32 whole and 33 half votes for Z (48.5).

Eliminate Y from the election, and you get thirty-five votes for X and sixty-five for Z- the reverse of the outcome when there were three candidates. So with even this rudimentary strategizing on the part of voters, your system isn't independent of the irrelevant alternative. It comes down to a tricksified (though not actually in this case) Borda count.
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Re: Range voting

Postby broken lader » Sun Mar 13, 2011 11:09 am UTC

ManaUser wrote:I like the sound of ranked voting more than range voting because it's easier to understand and harder to "game".


Ludicrous. Score Voting, particularly the simplified form called Approval Voting, results in fewer spoiled ballots, whereas ranked ballots result in more spoilage (e.g. in my home of San Francisco where we use Instant Runoff Voting, there has been seven times as much spoilage.) Whereas Score Voting and Approval Voting experimentally cause ballot spoilage to go down. Using Score/Approval is empirically simpler while rankings are empirically more complicated.
http://ScoreVoting.net/SPRates.html

Further, the tabulation rules of ranked systems tend to be more complex, particularly with Instant Runoff Voting and Condorcet methods. As Warren D. Smith, a Princeton math Ph.D. and voting expert, explains:

Write a range voting computer program and an IRV computer program (preferably with error-checking of the inputted votes). The range voting program will be shorter and will run faster, assuming essentially any reasonable programmer does it. (This, called "Kolmogorov Complexity" is the standard objective metric used by scientists to assess "simplicity.")


Also, Score and Approval Voting run on all today's Plurality Voting machines without any modification (including non-computerized machines). IRV, Condorcet, and Borda (the primarily discussed ranked methods) do not.

Smith adds:

Not simple enough for you? Okay, range is a parameterized class of methods, with the parameter being the number of ratings. The simplest kind of range voting is called "approval voting." It has only two ratings, Yes and No. Approval Voting is absolutely the simplest major voting system reform possible. It requires no changes to ballot forms; all it requires is eliminating the "no-overvote" rule, thus actually simpifying the rules versus now.


Also the "harder to game" claim is based on flawed logic about what constitutes "harm" from the effect of gaming. This intuitive mistake in reasoning is epidemic. Please see this:
http://www.electology.org/tactical-voting

[Score Voting] only works if people vote their conscience, which they don't.


Utterly false. Score Voting works better than all commonly proposed alternatives, with any mixture of strategic or honest voters. In fact it's so much better than IRV, for instance, that it performs better with 100% strategic voters than IRV does with 100% expressive voters.
http://ScoreVoting.net/BayRegsFig.html

Ranked voting methods like IRV, Borda, and Condorcet, are severely susceptible to tactical voting.
http://www.electology.org/irv-plurality
http://ScoreVoting.net/DH3.html
http://ScoreVoting.net/CondBurial.html

First of all there is virtually no motivation for a voter to assign other than the highest or lowest score. So realistically most people will give their favorite candidate the highest score, whether that's "approve", 5, 99 or whatever... and then what?


The efficacy of various tactics with Score and Approval Voting is discussed here.
http://ScoreVoting.net/RVstrat3.html

You are making all of the common logical fallacies that most people (including myself) make when they first hear of Score Voting. The key is to learn the facts before forming an opinion based on your intuition.

So it looks to me like they would probably give everyone else the lowest score, unless they don't think their preferred candidate could actually win. So basically we're left with almost the same situation as plurality voting.


Ludicrous.
http://ScoreVoting.net/RVstrat6.html

Here's empirical data from real contentious elections, and some large exit polls that also utterly refutes you here.
http://www.electology.org/bullet-voting

With "Instant-runoff" ranked voting, all that is eliminated.


Wrong. You have it precisely backwards.
http://www.electology.org/irv-plurality

You simply pick your favorite candidate, your second-favorite, etc. If your preferred candidate doesn't win, your vote is not wasted as long as you marked an second choice and so on.


In the last IRV race in Burlington Vermont, a group of Republicans who preferred the Democrat to the Progressive could have gotten the Democrat instead of the Progressive if they had insincerely ranked the Democrat ahead of the Republican.

Just as importantly, selecting a second choice does not dilute your first vote, so there's no incentive to "cheat" by putting them in any order other than your real preference.


The classic "Later No Harm" fallacy. You need to focus on the Favorite Betrayal Criterion, not the Later-No-Harm Criterion.
http://www.electology.org/later-no-harm

The only problem I see with IRV is a technical one. It does require somewhat more complicated ballots than approval voting or plurality voting.


Score Voting and Approval Voting are superior to IRV in essentially every quantifiable way.
http://ScoreVoting.net/CFERlet.html
http://www.electology.org/approval-voting-vs-irv

It would have been nice if you had looked over the previously posted data massively refuting nearly everything you just posted, prior to posting.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Sun Mar 13, 2011 11:25 am UTC

Silas wrote:Range voting doesn't solve that problem, if voters adopt a realistic strategy.


Give me any set of ballots with the candidates scored in any fashion you can possibly fathom.

Now, watch as I remove any non-winning candidate I wish, and the winner does not change. It is mathematically impossible. Score Voting satisfies Independence of Irrelevant Alternatives.

What you are talking about is a situation where people re-normalize and/or re-strategize based on which candidates are in the race. And of course, no deterministic voting system can possibly prevent ideal strategy from changing based on the removal or addition of other candidates. Nor do we make any such claim about Score/Approval Voting. Score and Approval Voting do avoid an entire class of wrong-winner IIA paradoxes nevertheless. That, along with various other properties, causes those systems to outperform all commonly proposed (ranked) rivals in Bayesian Regret calculations.

It comes down to a tricksified (though not actually in this case) Borda count.


No, Score Voting certainly does not "come down" to Borda. With Borda, if I prefer X>Y>Z and Y and Z are the presumed frontrunners, I want to vote Y>X>Z, whereas with Score Voting I would vote X=10, Y=10, Z=0. Then if it turned out I was wrong about X's prospects, I could potentially be pleasantly surprised at the election outcome.
http://ScoreVoting.net/PleasantSurprise.html

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Mechanicus » Sun Mar 13, 2011 2:09 pm UTC

That's odd, has anyone done research into why people tend to become opposed to it over time?
No research as such, but at a guess, people like the idea of change to our political system because of the damage done to it by (amongst other things) the Iraq war, MPs' expenses and various lobbying scandals, but when they're told specifics of the change they get more jittery. Also, the rather unpopular Deputy Prime Minister Nick Clegg, leader of the Liberal Democrats party was behind the AV referendum and he's seen as more than a little bit of a charlatan.

The public's opinion of constitutional change is very uninformed and sketchy. Only a few years ago, there was a poll done on the House of Lords. In that poll, 75% agreed that the house should be mainly appointed to ensure its independence and 72% agreed that at least half of the members should be elected to give it democratic legitimacy.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby achan1058 » Sun Mar 13, 2011 4:41 pm UTC

broken lader wrote:Warren D. Smith, the guy who created ScoreVoting.net, is a Princeton math Ph.D. who did his undergrad at MIT, and seems to me to be the top election methods expert on the planet, and quite possibly in all of history. He was the protagonist of the William Poundstone book Gaming the Vote. He authored this page on the subject of Arrow's Theorem.

I don't know what you mean it doesn't "look credible". It is a simple proof by example. Warren states the criteria that form Arrow's Theorem, and then demonstrates how Score Voting satisfies all of them.
As in the (lack of) cited material, etc. As I don't know what the "real" technical version of Arrow's Theorem says, I cannot judge whether the claimed system really satisfies the conditions, as well as what are its limitations.
broken lader wrote:What you are talking about is a situation where people re-normalize and/or re-strategize based on which candidates are in the race. And of course, no deterministic voting system can possibly prevent ideal strategy from changing based on the removal or addition of other candidates. Nor do we make any such claim about Score/Approval Voting. Score and Approval Voting do avoid an entire class of wrong-winner IIA paradoxes nevertheless. That, along with various other properties, causes those systems to outperform all commonly proposed (ranked) rivals in Bayesian Regret calculations.
Your voting system needs to be able to deal with re-normalization, at the very least. That's the problem I would see in Range Voting, when the range is greater than 2. (ie. not Approval Voting)

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Indon » Sun Mar 13, 2011 4:58 pm UTC

broken lader wrote:I don't know what you mean it doesn't "look credible". It is a simple proof by example. Warren states the criteria that form Arrow's Theorem, and then demonstrates how Score Voting satisfies all of them.


At a glance, any system in which voters assign arbitrary measurements of 'like', or scores, to candidates violates universality.

Because there is no objective foundation to what the scores mean, any given set of preferences in a voting population can return a range of election results, based on the specific scores given.

For instance, say you have a voting population in which about 50% love Gore, hate Bush, and are fairly ambivalent about Nader, and about 50% love Bush, hate Gore, and are also fairly ambivalent about Nader.

But what does ambivalent mean in a score voting system? Is it a 50/100? Is it a 70/100, 'cause you'd rather have him over the guy you hate? Is it a 30/100, because you really want the guy you love in?

Because there is no objective meaning to what the scores are, the scores are going to vary from one election to another even if everyone's preferences remain identical - thus in my hypothetical scenario, the winner is effectively random. And the same is potentially true about any close election.

Now, admittedly, I don't think that's a serious flaw - a close election isn't going to have a mandate any way you cut it, so picking randomly isn't going to be catastrophic for democracy. Furthermore, you could probably minimize this problem with a properly written set of voter instructions. But it doesn't look like score voting evades the problem posited by Arrow's theorem, just minimizes it cleverly.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Silas » Sun Mar 13, 2011 5:15 pm UTC

broken lader wrote:Give me any set of ballots with the candidates scored in any fashion you can possibly fathom.

Now, watch as I remove any non-winning candidate I wish, and the winner does not change. It is mathematically impossible.

Yeah- if the ballots stay the same. But they won't, because voters aren't stupid. The voting method causes people to misrepresent their preferences to gain an advantage, which was the problem with IIA- and monotonicity-deficient voting systems in the first place.

The point is, range voting may escape the exact terms in Arrow's theorem, but it's misleading to point that out, because if you weaken the criteria a little bit (in a way that preserves the importance of the outcome), range voting still comes up short. The whole point of Arrow's theorem- better illustrated with the Gibbard-Satterthwaite theorem- is that the only unmanipulable decision rule is a dictatorship. Range voting isn't a dictatorship, but it's trivially easily gamed.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Sun Mar 13, 2011 7:59 pm UTC

achan1058 wrote:
broken lader wrote:Warren states the criteria that form Arrow's Theorem, and then demonstrates how Score Voting satisfies all of them.
As in the (lack of) cited material, etc. As I don't know what the "real" technical version of Arrow's Theorem says, I cannot judge whether the claimed system really satisfies the conditions, as well as what are its limitations.


You can have a brief glance at the Wikipedia entry on Arrow's Theorem, which cites original works by Arrow himself. That easily confirms that those are indeed the criteria specified by Arrow's Theorem.

achan1058 wrote:Your voting system needs to be able to deal with re-normalization, at the very least. That's the problem I would see in Range Voting, when the range is greater than 2. (ie. not Approval Voting)


Score Voting "deals with" renormalization just fine. It outperforms every other commonly proposed voting method with any mixture of strategic vs. expressive voters. It also is immune from lots of severe pathologies associated with ranked voting methods, particularly IRV.

And you are mistaken about renormalization not being an issue with Approval Voting. If my sincere normalized utilities are X=1, Y=0.2, Z=0, then a "sincere" Approval Voting ballot (approve those preferred to the average utility of all candidates) would be X=approved, Y+Z=unapproved. But if X were not running, my sincere Approval Voting ballot would be Y=approved, Z=unapproved.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby phlip » Sun Mar 13, 2011 10:04 pm UTC

broken lader wrote:By contrast, in most rank-based systems, your best bet would be to rank Gore over Nader over Bush

No, in most rank-based systems (IRV, Condorcet, etc) if it's likely to come down to Gore vs Bush, then all that matters is that you put Gore ahead of Bush. Ranking them as Nader>Gore>Bush would still count as a "Gore" vote for the two-candidate-preferred result. Borda Count is one of the exceptions here, where increasing the distance between two candidates increases the chances that the higher one will win.

broken lader wrote:Extensive Bayesian Regret calculations show that Score Voting outperforms all commonly proposed alternatives with any mixture of sincere or strategic voters.

But that isn't an argument against Condorcet methods, that's just saying that range voting is better by that particular metric. Say there's a decision to be made with two candidates and three voters - one voter strongly prefers A to B, the other two voters weakly prefer B to A. Who should win? The Condorcet opinion says B should win, as more people prefer B than prefer A - one man one vote, and all that. The "Bayesian regret" opinion says A should win, as the people who prefer B will have "less regret" if they lose. Which is right? Should my opinion be worth more than yours just because I hold it more strongly? Well, that's a matter of opinion. And to try to draw an objective line isn't going to work.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby webby » Mon Mar 14, 2011 12:21 am UTC

Mechanicus wrote:
That's odd, has anyone done research into why people tend to become opposed to it over time?
No research as such, but at a guess, people like the idea of change to our political system because of the damage done to it by (amongst other things) the Iraq war, MPs' expenses and various lobbying scandals, but when they're told specifics of the change they get more jittery. Also, the rather unpopular Deputy Prime Minister Nick Clegg, leader of the Liberal Democrats party was behind the AV referendum and he's seen as more than a little bit of a charlatan.


Yeah, it seems plausible that people believe that the system needs change, but that the specific system of Alternative Vote is less popular than the idea of change in general. The example that comes to mind immediately is the Australian referendum on whether to become a republic. There was initially clear support to become a republic, but then when it came down to things like how the president would be elected, what powers they'd have etc., the particular scheme chosen was much less popular than the idea of becoming a republic and the referendum failed.

There's also evidence in Australia to suggest that if you get different results if you ask someone about a plan in isolation than you do if you tell them that a particular political party supports/opposes the plan.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 12:26 am UTC

The whole point of Arrow's theorem- better illustrated with the Gibbard-Satterthwaite theorem- is that the only unmanipulable decision rule is a dictatorship.


That's wrong. For one thing, Arrow's theorem has nothing to do with manipulability. It has to do with getting incorrect outcomes even if the input values are correct (i.e. even with sincere individual ballots, the outcome can be wrong).

And it is also wrong that the only unmanipulable decision rule is a dictatorship. There are at least 3 strategy-immune voting methods.

1) Random Ballot - voters vote for their favorite candidate and one ballot is picked at random, and that ballot is treated as a dictator. This could also be called "random dictator", and is what you were talking about.

2) Random Pair - voters rank the candidates in order, and two candidates are picked at random and matched up head-to-head. Voters have no incentive to provide anything other than a sincere ranking.

3) Random Probability Distribution - Complicated, and only discovered a year or so ago. Voters cast Score Voting ballots. Two probability distributions are randomly created, like {X=10%, Y=25%, Z=65%} and {X=19%, Y=43%, Z=38%}. For each ballot, we compute the voter's expected value for these two utility distributions, and then count that ballot in favor of the distribution which gives the voter a higher expected value. The distribution which is preferred by a majority between the two is used to randomly elect the winner.

Range voting isn't a dictatorship, but it's trivially easily gamed.


Well, that is a ridiculous statement, since so is virtually every voting method. E.g. Condorcet, Borda, IRV.

http://ScoreVoting.net/DH3.html
http://ScoreVoting.net/CondBurial.html
http://www.electology.org/irv-plurality

And Score Voting is so much better than the alternatives, that it can outperform most of them even with differential levels of strategic voting. E.g. Score Voting with 100% strategic voters is better than IRV with 100% expressive voters.
http://ScoreVoting.net/StratHonMix.html

Silas wrote:Yeah- if the ballots stay the same. But they won't, because voters aren't stupid. The voting method causes people to misrepresent their preferences to gain an advantage, which was the problem with IIA- and monotonicity-deficient voting systems in the first place.


You're conflating two separate issues. Consistency criteria like IIA and monotonicity have nothing directly to do with strategic voting. Linking them is one of the most common fallacies that occurs in discussions on this topic.

IIA fails when a non-winning candidate who is either removed or added changes the election outcome, even though there has been no change in voter preferences for any of the candidates. The very reason that this is interesting is that it gives us a mathematical proof that the voting system has picked the wrong winner in at least one of the two before/after scenarios, even with absolutely no strategic voting.

"Pseudo-paradoxes" caused by strategic voting and/or renormalization are an entirely separate set of problems in addition to this. Score Voting avoids the former set of problems, even though you are correct that it does not avoid the latter.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 12:46 am UTC

phlip wrote:
broken lader wrote:By contrast, in most rank-based systems, your best bet would be to rank Gore over Nader over Bush

No, in most rank-based systems (IRV, Condorcet, etc) if it's likely to come down to Gore vs Bush, then all that matters is that you put Gore ahead of Bush. Ranking them as Nader>Gore>Bush would still count as a "Gore" vote for the two-candidate-preferred result.


Wrong.

In the last IRV election for mayor of Burlington Vermont, you had a situation similar to this:

% of voters - their ranking
34% X>Y>Z
29% Y>X>Z
37% Z>Y>X

X wins, even though 66% of voters prefer Y to X. If some of the voters in the last row had insincerely ranked Y ahead of Z, then Y would have won.

Since a minor party is statistically more likely to defeat one of the major parties than both of the major parties, sincerely ranking a minor party in first place is statistically more likely to hurt a voter than to help a voter, thus a voter should just always rank his favorite major party candidate in first place to be on the safe side. That strategy has a positive expected value.
http://www.electology.org/irv-plurality

Also, with Condorcet:

#voters - their Vote
8 B>C>A
6 C>A>B
5 A>B>C

Say a given Condorcet method picks B as the winner here. In that case, the 6 voters would have been better off to rank A in first place, because then A would have won instead of B.

The statistical efficacy of burial with a variety of Condorcet methods is discussed here.
http://scorevoting.net/CondBurial.html

Perhaps the more important thing than this math is simple voter psychology. If enough voters use the Naive Exaggeration Strategy, which evidence says they generally will, then any ranked voting method will tent toward two-party domination, and will be far less optimal than it would be with sincere rankings.

I pointed this all out numerous times in previous posts, but apparently you felt no need to pay attention to any of that. This pattern is extremely common.

broken lader wrote:Extensive Bayesian Regret calculations show that Score Voting outperforms all commonly proposed alternatives with any mixture of sincere or strategic voters.

But that isn't an argument against Condorcet methods, that's just saying that range voting is better by that particular metric.


Bayesian Regret is the one and only metric of voting method performance. It is the measure of average voter utility. It is mathematically proven that the socially best option is the one that maximizes the net utility of the voters.
http://ScoreVoting.net/UtilFoundns.html

Say there's a decision to be made with two candidates and three voters - one voter strongly prefers A to B, the other two voters weakly prefer B to A. Who should win? The Condorcet opinion says B should win, as more people prefer B than prefer A - one man one vote, and all that.


It is mathematically proven that the "Condorcet opinion" is wrong.
http://www.electology.org/majority-criterion

This is social choice theory 101.

The "Bayesian regret" opinion says A should win, as the people who prefer B will have "less regret" if they lose. Which is right? Should my opinion be worth more than yours just because I hold it more strongly? Well, that's a matter of opinion. And to try to draw an objective line isn't going to work.


No, it's not a matter of opinion. It's mathematically proven. It would be nice if you had researched this topic before saying such nonsense.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Indon » Mon Mar 14, 2011 12:58 am UTC

Broken, I address a post, essentially, to you six posts up regarding how the system you posit lacks Universality because, using a subjective metric, people will vary their preference reporting from election to election. Comments would be appreciated.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 1:04 am UTC

Indon wrote:At a glance, any system in which voters assign arbitrary measurements of 'like', or scores, to candidates violates universality.


No. Score Voting accounts for all individual preferences, and does so in a manner that results in a complete ranking of preferences for society, and does it deterministically, providing the same societal ranking each time voters' preferences are presented the same way.

Because there is no objective foundation to what the scores mean, any given set of preferences in a voting population can return a range of election results, based on the specific scores given.


There is indeed an objective foundation to what the scores mean. They are sincere normalized utilities.

For instance, say you have a voting population in which about 50% love Gore, hate Bush, and are fairly ambivalent about Nader, and about 50% love Bush, hate Gore, and are also fairly ambivalent about Nader.

But what does ambivalent mean in a score voting system? Is it a 50/100? Is it a 70/100, 'cause you'd rather have him over the guy you hate? Is it a 30/100, because you really want the guy you love in?


"Ambivalent" is not a number. It doesn't "mean" anything. A 50 out of 100 means a utility which is the exact average of one's utility for his favorite and least favorite candidates, and so forth.

Because there is no objective meaning to what the scores are, the scores are going to vary from one election to another even if everyone's preferences remain identical - thus in my hypothetical scenario, the winner is effectively random. And the same is potentially true about any close election.


There is an objective meaning to what the scores are. Of course there will be some loss in the translation from precise utility values to normalized scores. Our Bayesian Regret figures account for that not only by actual normalization, but by also including ignorance factors which simulate imperfect knowledge and judgement error.

Such error is no more an indictment of Score Voting than of any other system. If you actually would prefer X slightly to Y, then such ignorance and judgment error could also cause you to rank Y higher than X.

Now, admittedly, I don't think that's a serious flaw - a close election isn't going to have a mandate any way you cut it, so picking randomly isn't going to be catastrophic for democracy. Furthermore, you could probably minimize this problem with a properly written set of voter instructions. But it doesn't look like score voting evades the problem posited by Arrow's theorem, just minimizes it cleverly.


It evades the specific problem of Arrow's Theorem. The addition or elimination of non-winning candidates cannot directly affect the election outcome, meaning a particular class of paradox is eliminated.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby phlip » Mon Mar 14, 2011 1:17 am UTC

broken lader wrote:Wrong.

In the last IRV election for mayor of Burlington Vermont, you had a situation similar to this:

% of voters - their ranking
34% X>Y>Z
29% Y>X>Z
37% Z>Y>X

Well sure, if you switch the goalposts then you can prove anything. But in the post I was referring to, you specifically said
broken lader wrote:Gore and Bush appear to be the clear frontrunners
which is clearly not the case in this new dataset.

broken lader wrote:
broken lader wrote:Extensive Bayesian Regret calculations show that Score Voting outperforms all commonly proposed alternatives with any mixture of sincere or strategic voters.

But that isn't an argument against Condorcet methods, that's just saying that range voting is better by that particular metric.


Bayesian Regret is the one and only metric of voting method performance. It is the measure of average voter utility. It is mathematically proven that the socially best option is the one that maximizes the net utility of the voters.
http://ScoreVoting.net/UtilFoundns.html

Say there's a decision to be made with two candidates and three voters - one voter strongly prefers A to B, the other two voters weakly prefer B to A. Who should win? The Condorcet opinion says B should win, as more people prefer B than prefer A - one man one vote, and all that.


It is mathematically proven that the "Condorcet opinion" is wrong.
http://www.electology.org/majority-criterion

:roll:
You keep using the words "mathematically proven". I don't think they mean what you think that they mean. Your two links there are only indirectly related to what you're talking about anyway... One just explains the basics of utility theory, and the second about how there exist situations with no condorcet winner. Neither of these are relevant... the existance of utility theory doesn't "mathematically prove" that it's superior, and that people with a greater utility gain from an election should have a greater say in that election. And the scenario I posited does have a condorcet winner (as it must, because there were only two options).

So would you like to actually reply to what I said this time, and not just post more irrelevant scorevoting.net links?

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Indon » Mon Mar 14, 2011 2:43 am UTC

broken lader wrote:"Ambivalent" is not a number. It doesn't "mean" anything. A 50 out of 100 means a utility which is the exact average of one's utility for his favorite and least favorite candidates, and so forth.

Yeah, that's my point. Preferences don't exist in numerical form, and when people try to express non-numerical preferences in numerical form, the results are inconsistent. This inconsistency violates universality, straight up. It's nice to know the model integrates sophisticated mathematical tools to further reduce the problem, but the fact is that in sufficiently close elections, in any system in which each individual option (or 'point') is given a specific meaning, there will be variance and this variance, not preferences, will decide elections. This violates universality because it creates a 1:many relationship between voter preferences and election results.

broken lader wrote:No. Score Voting accounts for all individual preferences, and does so in a manner that results in a complete ranking of preferences for society, and does it deterministically, providing the same societal ranking each time voters' preferences are presented the same way.


The problem is in the method of presentation of ascribing a score gradient rather than discrete options - the preferences themselves will not be presented consistently because of that flaw.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 5:11 am UTC

Indon wrote:Preferences don't exist in numerical form


That is just not correct. Preferences are just the sum of a bunch of neurotransmitters in your brain. That is absolutely numerical.

And if you go to a store, you might notice price tags on items. You only buy them if your value for them exceeds the value of the money you have to spend to get them. Those prices are just numbers.

when people try to express non-numerical preferences in numerical form, the results are inconsistent.


So what? That in no way discounts that actual utilities are precise numerical quantities. What it shows is that people's assessment of their utilities is a lossy process, clouded by misinformation, miscalculation, and random error inherent in the neurological process.

And this also affects ranked voting methods. An error in utility assessment could cause a voter to think that Y was better for him than X, even though X was actually better for his welfare than Y. So again, this is not a differentiator between Score Voting and any other voting system.

This inconsistency violates universality, straight up.


No it doesn't. Given the same scores from the same voters, Score Voting produces the same outcome, every time. What you are talking about is the same voters with the same utilities producing different scores, because of random utility calculation/strategizing fluctuation. That's a flaw in brain function, not in the voting method.

in any system in which each individual option (or 'point') is given a specific meaning, there will be variance and this variance, not preferences, will decide elections.


Random error simulated by the "ignorance factor" model accounts for this in Bayesian Regret calculations, and Score Voting still outperforms the other systems.

This violates universality because it creates a 1:many relationship between voter preferences and election results.


Close, but not quite right. It creates a 1:many relationship between actual utilities and their transform into scores. A problem with human cognition, not with the voting method. And a problem with all voting methods, not just with Score Voting.

The problem is in the method of presentation of ascribing a score gradient rather than discrete options - the preferences themselves will not be presented consistently because of that flaw.


1) Scores are "discrete options", so I have no idea what that is supposed to mean.
2) In case you meant "ordinal options", you were still wrong, because rankings do not fix this problem by any means.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 5:53 am UTC

phlip wrote:
broken lader wrote:Wrong.

In the last IRV election for mayor of Burlington Vermont, you had a situation similar to this:

% of voters - their ranking
34% X>Y>Z
29% Y>X>Z
37% Z>Y>X

Well sure, if you switch the goalposts then you can prove anything. But in the post I was referring to, you specifically said
broken lader wrote:Gore and Bush appear to be the clear frontrunners
which is clearly not the case in this new dataset.


Yes it is the case. X and Y are the frontrunners here. Y is preferred to both other candidates by a majority. X is preferred to Z by a majority. Z is the Condorcet loser - the apparently weakest candidate. Y is actually the strongest candidate here.

The point is simply this. Say you prefer Green over Democrat over Republican. You should actually rank Democrat in first place. Why? Because Green is probably (based on historical performance) going to lose. Ranking Green in first place only helps if Green just happens, by some phenomenal fluke, to perform far better than expected, defeating BOTH major parties. But a far more likely outcome is that Green gets enough of the liberal vote to defeat Democrat, but then loses to Republican by not having enough of the center (like the scenario above, where Z=Green, Y=Dem, X=Rep). That means sincerely top-ranking a third party or independent candidate is statistically more likely to hurt than help, so you should just not do it. This is explained here in more detail.
http://www.electology.org/irv-plurality

phlip wrote:
It is mathematically proven that the "Condorcet opinion" is wrong.
http://www.electology.org/majority-criterion

:roll:
You keep using the words "mathematically proven". I don't think they mean what you think that they mean. Your two links there are only indirectly related to what you're talking about anyway... One just explains the basics of utility theory, and the second about how there exist situations with no condorcet winner.


There are important points there that you are simply missing.

The UtilFoundns link uses axiomatic logic to prove that the correct social utility function must be the sum of unbounded cardinal utilities, and cannot be an ordinal function.

In the second scenario, there IS a Condorcet winner! There are FOUR election scenarios. One of them features a Condorcet cycle, but in all the other three there is a majority/Condorcet winner. Yet we prove that it is impossible for the Condorcet winner to be the right winner in all three scenarios.

Here's how it works. Say you look at a scenario where X is the majority/Condorcet winner vs. Y. The "Condorcet opinion" says that X must be the candidate preferred by the electorate to Y. So then you add Z, creating a Condorcet cycle, with no change in voter preferences regarding X and Y. Now you know that the preferred candidate must be either X or Z. It cannot be Y, because we already said that the electorate prefers X to Y -- and the entrance of Z cannot possibly change that, because we specifically stated that the electorate's preferences for X and Y remained the same.

If you now say that the preferred candidate is X, then we simply remove Y, and see that Z is the Condorcet winner, even though X is the preferred candidate of the electorate. We see then that the Condorcet opinion is wrong, QED.

If instead we had said that the preferred candidate was Z, then we could simply remove X, and see that Y was now the Condorcet winner, even though Z was the preferred candidate of the electorate. Again, we would see that the Condorcet opinion was wrong, QED.

Neither of these are relevant... the existance of utility theory doesn't "mathematically prove" that it's superior, and that people with a greater utility gain from an election should have a greater say in that election.


Those axioms do indeed prove that the social utility function is the sum of individual voter utilities. For instance, the Transitivity Axiom proves that the votes must be cardinal, not ordinal -- which also means that the Condorcet winner is not necessarily the favorite candidate of the electorate. (This is what I proved in layman's terms at the majority-criterion page.)

=> "Transitivity Axiom: If a∼b and b∼c then a∼c."

Other axioms on that page show that the summation function must treat those utilities linearly.

And the scenario I posited does have a condorcet winner (as it must, because there were only two options).


But that Condorcet winner is not necessarily the favorite candidate of the electorate, out of those two candidates. That makes Condorcet voting methods inherently mistaken, because they are trying to maximize the wrong thing. (And due to voter tactics, Score Voting and Approval Voting are more likely to elect Condorcet winners than real Condorcet methods.)

So would you like to actually reply to what I said this time, and not just post more irrelevant scorevoting.net links?


I'm replying quite clearly, but you're misunderstanding a lot of the material I'm citing.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Indon » Mon Mar 14, 2011 8:01 pm UTC

broken lader wrote:And if you go to a store, you might notice price tags on items. You only buy them if your value for them exceeds the value of the money you have to spend to get them. Those prices are just numbers.

Buying something is a binary choice with a definitive meaning. Imagine if people set the prices for the goods they bought - it wouldn't remotely be consistent.

broken lader wrote:So what? That in no way discounts that actual utilities are precise numerical quantities. What it shows is that people's assessment of their utilities is a lossy process, clouded by misinformation, miscalculation, and random error inherent in the neurological process.

I think the assertation that 'actual' utilities are what you're trying to obtain, and that it's not the system's fault for error that exists uniquely in the system, is a facetious one.

Scored votes are affected by a form of voting error unique to scored votes, that causes a degree of randomness in reporting that does not exist in other systems, which exists in addition to all other forms of error that exist in ranked voting systems.

broken lader wrote:1) Scores are "discrete options", so I have no idea what that is supposed to mean.

Scores are not discrete, they're a gradient. Discrete options would be in which every point is assigned a specific meaning, where any given option is meaningfully different from all the others.

Giving a 71 over a 70 on a 100-point scale, for instance, does not carry a meaningful difference to a voter, even though it is meaningful to the system. This discrepancy generates that unique randomness, as voters will convey their preferences in ways that are meaningful to themselves, and the system will ascribe additional meaning that is not necessarily intended.

Now, you could, I suppose, have a scoring system where this problem is minimized - simply have a smaller range in which each option is given a description. Even then, polling studies demonstrate that when people are given choices on a continuum, the existence of that continuum can distort their choices (generally towards the middle) even when each choice is explicitly defined.

As an aside, feel free to concatenate your replies into a single post, even if it means you edit it to do so.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 8:41 pm UTC

Indon wrote:Buying something is a binary choice with a definitive meaning. Imagine if people set the prices for the goods they bought - it wouldn't remotely be consistent.


Quite right. But, again, this is proof of imperfect human assessment of actual utilities, not evidence that utilities are not precise and numeric.

I think the assertation that 'actual' utilities are what you're trying to obtain, and that it's not the system's fault for error that exists uniquely in the system, is a facetious one.


Well, there are two different systems. There is the voting method, and then there are voters' brains. To use your phrasing of "fault", I would put that as, it's not the voting method's fault that humans are not perfect and consistent at assessing their utilities.

Scored votes are affected by a form of voting error unique to scored votes, that causes a degree of randomness in reporting that does not exist in other systems, which exists in addition to all other forms of error that exist in ranked voting systems.


A) You are incorrect that this problem doesn't exist in ranked systems. An error that could cause your {X=10, Y=8} assessment to switch to {X=9,Y=10} would also cause your ranking to switch from X>Y to Y>X.

B) Bayesian Regret calculations intrinsically account for this error already. They literally measure the aggregate loss of utility from all problems like this, and all failures of all voting method criteria (even ones which have never been invented/discovered). And those figures show Score Voting beating out the commonly proposed ranked systems robustly to changes in various parameters.

broken lader wrote:1) Scores are "discrete options", so I have no idea what that is supposed to mean.

Scores are not discrete, they're a gradient. Discrete options would be in which every point is assigned a specific meaning, where any given option is meaningfully different from all the others.


No, the scores are definitely discrete. We're proposing things like "0-10 integers", not "the continuous range of express-able values". That is what discrete means. As a useful mental model, stairs are "discrete" whereas a ramp is "continuous". Discreteness has nothing to do with assigning "specific meanings" to the scores.

Moreover, the utility values do have specific meanings, based on whatever objective physical phenomena comprise utility. E.g. "a million serotonin molecules". Or to get more to root Darwinian justification for utility, "a million copies of your genome". That is the absolute, quantifiable "specific meaning" that you are after.

The scores cast on ballots are not "specific". They are, as I have explained repeatedly, lossy transforms of the specific utility values, which are distorted by normalization, random neurological error, etc.

You are quite correct that this translation from specific quantities into scores introduces noise. But the thing you seem to be blissfully unaware of, is that Bayesian Regret calculations already take this into account.

We start with actual utility values. But then we have voters cast their scores by first clouding those utilities with random ignorance, which simulates that noise. We then take those distorted utility assessments and normalize them into scores. That introduces even more noise. We then go even further, and have some fraction of the voters distort those scores even further, by tactically exaggerating.

And finally, after introducing all that noise, then running an election, we see how well the result reflected the actual undistorted utilities that we started with.

So that is how you calculate Bayesian Regret. Your alleged problem is not a problem at all. You are demanding precision on the wrong thing.

Now you may indeed be right that if we assign labels to the scores, to serve as reference points which convey an approximately equal utility to most human beings, then we could get less distortion. For instance, if we say that 0 equals "the utility of being killed right now", and 10 equals "the utility of being able to experience constant orgasm whenever you want for the rest of your life", and if lots of voters are honest, we can quite possibly reduce the normalization error (though not the random error you brought up, which has nothing to do with reference points for scaling, but with actual assessment of the utilities).

But the point is, Score Voting is already so good, that would probably have very little benefit. And it could quite conceivably cause more problems than it would solve.

And the bottom line is that this in no way counts as a differentiator between Score Voting and ranked voting methods. And even if it did, ranked methods have so many problems that Score Voting doesn't have, that Score Voting still performs better. Read the Bayesian Regret calculations and weep.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Mon Mar 14, 2011 9:04 pm UTC

I'll go a little further here.

Say Bob has utilities of: X=28, Y=18, Z=3
And Alice has utilities of: X=7, Y=14, Z=4

These are precise, inter-comparable, actual utility values, which measure neurotransmitters or whatever the material basis of utility is. (It doesn't matter what utility actually is, just as long as we know that the utility is there, and that it is quantifiable, which it must be, because the universe is just a material/physical system.)

I note that the right winner is X, as X provides a net utility of 35.

But because of ignorance, imperfect reasoning skills, random brain error, etc., their assessments of their utilities are:

Bob: X=25, Y=17, Z=5
Alice: X=6, Y=18, Z=3

Now, their sincere scores, created by normalizing these values to a 0-10 range, would be:

Bob: X=10, Y=6, Z=0
Alice: X=2, Y=10, Z=0

So the totals, with sincere voting, would be:
X=12, Y=16, Z=0

So we get Y, whose total actual utility for this 2-person electorate is 32, even though the right winner was X, whose net utility was 35. So our Bayesian regret here is 3.

That is a demonstration that Score Voting is certainly not perfect. And we didn't even add strategic voting yet.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby AvatarIII » Thu Apr 21, 2011 12:02 pm UTC

i just want to revive this thread because of the upcoming vote in the uk to decide whether or not we go over to the Australian voting system, aka Alternate Voting system aka Instant-Runoff Voting

I am still undecided however I am leaning towards the "yes, let's switch over" camp. because on first glance the IRV system looks fairer, and in a many party system like we have in the UK, it seems ideal, but i'd kind of like to hear some opinions from some of the intelligent community here, particularly people with experience with this voting system.

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Whimsical Eloquence » Thu Apr 21, 2011 1:07 pm UTC

AvatarIII wrote:i just want to revive this thread because of the upcoming vote in the uk to decide whether or not we go over to the Australian voting system, aka Alternate Voting system aka Instant-Runoff Voting

I am still undecided however I am leaning towards the "yes, let's switch over" camp. because on first glance the IRV system looks fairer, and in a many party system like we have in the UK, it seems ideal, but i'd kind of like to hear some opinions from some of the intelligent community here, particularly people with experience with this voting system.


I'm Irish and we use this but in PR (multi-seat constituencies). AV, or instant Run-Off, is used for Presidential and By-Elections. AV is indeed "a miserable little compromise" as it actually lacks that essential element of multiple seats which give representation to the minority but it's a much fairer system. Whatever the best system is, undoubtedly the worst (or at least the worst one in practice by a major democracy) is First-Past-the-Post. Take the last election in which Labour secured 29% of the vote and the Liberal Democrats secured 23%: a six point differential. This should translate to about a 38/39 seat difference [ 6x(649/100)]. Labour got 358 seats, the Liberal Democrats 57. That's an actual difference of over 46%.

Take now the Conservatives and Labour, 36% and 29% respectively, a 7% differential and yet their resulting seats were 306 and 258, an actual difference of only 3%. Opponents of A.V. tout this ridiculous myth that it will make getting rid of an unpopular Government or party harder. If anything the present does this in which the two biggest parties are protected from election losses to an almost absurd extent while parties commanding a similar amount of the vote are horribly disenfranchised. First Past the Post is the system in which the voter is most powerless, forced to hide their genuine preferences if they're for a smaller candidate and in which they have utterly no ability to affect the dominance of large parties.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby AvatarIII » Thu Apr 21, 2011 1:35 pm UTC

Whimsical Eloquence wrote:
AvatarIII wrote:i just want to revive this thread because of the upcoming vote in the uk to decide whether or not we go over to the Australian voting system, aka Alternate Voting system aka Instant-Runoff Voting

I am still undecided however I am leaning towards the "yes, let's switch over" camp. because on first glance the IRV system looks fairer, and in a many party system like we have in the UK, it seems ideal, but i'd kind of like to hear some opinions from some of the intelligent community here, particularly people with experience with this voting system.


I'm Irish and we use this but in PR (multi-seat constituencies). AV, or instant Run-Off, is used for Presidential and By-Elections. AV is indeed "a miserable little compromise" as it actually lacks that essential element of multiple seats which give representation to the minority but it's a much fairer system. Whatever the best system is, undoubtedly the worst (or at least the worst one in practice by a major democracy) is First-Past-the-Post. Take the last election in which Labour secured 29% of the vote and the Liberal Democrats secured 23%: a six point differential. This should translate to about a 38/39 seat difference [ 6x(649/100)]. Labour got 358 seats, the Liberal Democrats 57. That's an actual difference of over 46%.

Take now the Conservatives and Labour, 36% and 29% respectively, a 7% differential and yet their resulting seats were 306 and 258, an actual difference of only 3%. Opponents of A.V. tout this ridiculous myth that it will make getting rid of an unpopular Government or party harder. If anything the present does this in which the two biggest parties are protected from election losses to an almost absurd extent while parties commanding a similar amount of the vote are horribly disenfranchised. First Past the Post is the system in which the voter is most powerless, forced to hide their genuine preferences if they're for a smaller candidate and in which they have utterly no ability to affect the dominance of large parties.


thanks for your reply, on the whole you are saying that it is the lesser of two evils?

i think the way i see the system being of benefit is (if you'll excuse my random analogy):
say there is a vote for choosing which ice cream a youth club buys for their members, a vote is cast and in the lead is vanilla with 40%, however the next 2 flavours are chocolate, and "double choc chip" with 30% and 25% respectively, however everyone that voted for "double choc chip" hate vanilla, but would be perfectly happy with chocolate, because it's pretty similar,
even though 55% of people would prefer chololate, vanilla still wins because there is only vanilla, there is nothiong "like" vanilla for vanilla likers to have their vote split between.
is this a fair example of showing how IRV is better than FPPV?

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Роберт » Thu Apr 21, 2011 4:58 pm UTC

AvatarIII wrote:i just want to revive this thread because of the upcoming vote in the uk to decide whether or not we go over to the Australian voting system, aka Alternate Voting system aka Instant-Runoff Voting

I am still undecided however I am leaning towards the "yes, let's switch over" camp. because on first glance the IRV system looks fairer, and in a many party system like we have in the UK, it seems ideal, but i'd kind of like to hear some opinions from some of the intelligent community here, particularly people with experience with this voting system.

What is you're current system?
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Thu Apr 21, 2011 5:19 pm UTC

IRV does not eliminate the spoiler problem in that ice cream analogy.

www.electology.org/spoiler

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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby Aaeriele » Thu Apr 21, 2011 6:51 pm UTC

Since I don't think it's been linked yet, and it's a good summary, this table:

http://en.wikipedia.org/wiki/Voting_sys ... mary_table

Notice that there is no row with all green.
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Re: Alternate Voting Systems (Range, Condorcet etc)

Postby broken lader » Thu Apr 21, 2011 7:12 pm UTC

Aaeriele wrote:Since I don't think it's been linked yet, and it's a good summary, this table:
http://en.wikipedia.org/wiki/Voting_sys ... mary_table
Notice that there is no row with all green.


Here's another table, created by Warren D. Smith, a Princeton math Ph.D. who studies voting methods.

While it can be interesting to compare the properties of various voting methods (which criteria they pass or fail), this is generally not a good way to assess their relative quality. What matters is the combined effect of all properties. That means the statistical probabilities of the various criteria failures, times their anti-democratic effect (how much they decrease voters' utility). That latter part is important. Some criteria are more important than others. In fact, when it comes to criteria like "Later No Harm", it can actually be better for a voting method to "fail" them than to "pass" them.

The way you get this combined aggregate measure is to perform Bayesian Regret calculations, which reveal the total average performance of voting methods in objective mathematical/economic terms. Here's a crude graph of Bayesian Regrets for various voting methods from page 239 of William Poundstone's book Gaming the Vote.

Image

To make an analogy, comparing based on criteria is like comparing race cars based on engine power, aerodynamics, tire quality, lightness, etc. You can argue that one car is better than another because it has more horsepower, but it may have worse aerodynamics or tires or something else that counteracts that. So the empirical way to sum up the combined effect of all those properties is to put the cars on a race track and perform a statistically significant number of timed trials, with different drivers and weather conditions, so you cancel out "noise".

The historical problem with election theory is that people did not have an awareness of Bayesian Regret, nor the computing resources to perform Bayesian Regret simulations. Thus the issue has been incorrectly framed, and widely misunderstood, to the great detriment of humanity. People at The Center for Election Science are trying to change that.


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