Wednesday, November 10, 2010

Strategy-Free Elections, And The True Measure of a Voting System

If you get involved in the debate on voting system reform, it's never long before someone brings up the concept of "strategic voting." The idea is simple enough: we all want to be as honest as possible on our ballots, but because the voting system is imperfect, we vote otherwise. This is easy to see in plurality; lots of people who claim to really want a third-party candidate end up voting for one of the two major-party candidates on election day. But it happens, to a lesser or greater extent, under all voting methods.

Actually, that's a cleverly-constructed lie of omission.

It turns out that there are a number of voting systems which are 100% strategy-free, so your honest vote will always also be your best vote. But you're not going to like them. Here's an example: voting is performed like plurality, i.e., each voter picks a single candidate. The winner is whichever candidate is named on a ballot chosen at random. Clearly, you should always vote the one candidate you think is best for the job, because there's no reason to fear that you're "throwing your vote away" or making it easier for a candidate you dislike to win. The clever part in the constructing of the lie was omitting the word deterministic, which means "no random components". There are no strategy-free deterministic voting systems.

Constructing other (and better) strategy-free methods is easy enough. So if strategy is so vitally important that it invariably comes up in every voting-system discussion, why don't we use one of them? The answer is: average performance. Random ballot voting, as your intuition probably tells you, is an absolutely terrible system. But intuition is sometimes wrong, so it's important that we can back it up with data by running computer simulations to calculate Bayesian regret. And the data shows that, based on the number of candidates competing, random ballot is two- to four-times worse than plurality voting; which we all know from experience to be a pretty bad system.

Strategy, and a voting system's susceptibility to it, are an important thing to be aware of. But immunity to strategy, even though it sounds like a great thing to strive for, isn't the goal of a voting system; if it were, we'd have an easy answer to the problem, in the form of non-deterministic voting methods. And there are a host of other reasonable-sounding things for a voting system to accomplish, many of which have been codified as voting system criterion. But, besides many of them being mutually-exclusive (i.e., you can't meet them all), using any of them as a litmus test obscures the true objective, in the same way that focusing exclusively on being strategy-free obscures the true objective. The only true measure of a voting system is it's expected performance: how well it delivers a desirable candidate to the electorate. Average performance, as measured by Bayesian regret, smooths over all the coarse edges of criterion, implicitly assessing all of them for frequency as well as impact.

Why should it matter that, for instance, approval voting fails the majority criteria, if the failure rate is vanishingly-infrequent and has minimal impact? When it performs significantly better than a host of other systems that do meet this criteria, but fail some other, equally-reasonable criteria? It shouldn't. Holding the percentage of strategic voters constant, approval voting has significantly better performance than just about any other voting method. Range voting (AKA score voting) can be even better. Which criteria are passed are secondary to that fact.

8 comments:

  1. I can just hear the dissent now:

    "But the rate of strategic voting isn't constant!"

    ;)

    Good post, Dale.

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  2. Thanks, BL. It's good to be able to get back into writing here, now that the election isn't stealing all my thoughts.

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  3. There's no modelling of how the threat of voting strategically, or alternatively "spoiling" an election, can make a major candidate reposition themselves.

    In BR-speak, if a candidate changed their views on an important issue, it would result in changes in voter preferences. But this makes into a "dependent variable" that which is taken as a given for voters in BR models.

    And so, your conclusion that all strategic voting is bad (and must be eradicated for the sake of democracy via the use of AV or SV for all elections) stems from how you are modelling only part of "reality". You are denying candidates the ability to strategically take on new issues or to "flip-flop" to reposition themselves in order to improve their chances to get elected.

    Third parties in an elections with an FPP election rule have succeeded in forcing the major parties to accommodate them so as to induce their supporters to vote strategically for the least evil of the major party candidates.

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  4. This comment has been removed by a blog administrator.

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  5. DLW,

    As I have told you numerous times before, the BR calculations incorporate something called ignorance factors, which account for the disparity between voters' assessments of the candidates, and the actual performance of the candidates once they serve.

    We never said that "all strategic voting is bad". However, in every voting method I've ever seen, the rate of strategic voting is
    inversely proportional to the representativeness of the outcomes.

    More importantly though, we NEVER claimed that SV/AV "eradicate" strategic voting. ScoreVoting.net actually has tens of pages that talk about the ways that you can be strategic with these methods.

    As far as I am concerned, your comment is worthy of deletion. It's one thing to raise legitimate points of disagreement, but it's quite another when you repeatedly make preposterous claims like this, with absolutely no evidence.

    I'll justify that by reiterating what I said above. You assert that we've somehow proposed SV/AV as a way to "eradicate" strategic voting. Here are just some of our pages which specifically acknowledge that voters CAN be strategic with these systems:

    http://scorevoting.net/StratHonMix.html
    http://scorevoting.net/PleasantSurprise.html
    http://scorevoting.net/RVstrat1.html
    http://scorevoting.net/RVstrat2.html
    http://scorevoting.net/RVstrat3.html
    http://scorevoting.net/RVstrat4.html
    http://scorevoting.net/RVstrat5.html
    http://scorevoting.net/RVstrat6.html
    http://scorevoting.net/RVstrat7.html
    http://scorevoting.net/HonStrat.html
    http://scorevoting.net/ShExpRes.html
    http://scorevoting.net/Honesty.html

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  6. BL,
    I'm talking about the endogeneity of candidates' positions prior to the election in early November, not how they do not always do what they said they'd do after the election.

    As for the inverse ratio between representativeness and strategic voting, since we don't observe either of these two variables in real life, it seems you're still conflating BR-world with "reality", which doesn't negate my basic point that the BR model takes as exogenous what is in fact endogenous in "reality".

    As for me saying, "proposed SV/AV as a way to "eradicate" strategic voting", I overstated things for rhetorical purposes.
    dlw

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  7. I'm talking about the endogeneity of candidates' positions prior to the election in early November, not how they do not always do what they said they'd do after the election.

    That makes no difference. On election day, at the time a voter casts his ballot, he has some estimate of his utility for the candidates. Then later there is the actual utility the voter got from what that candidate did in office. The BR calculations include a disparity between those two values.

    As for the inverse ratio between representativeness and strategic voting, since we don't observe either of these two variables in real life, it seems you're still conflating BR-world with "reality", which doesn't negate my basic point that the BR model takes as exogenous what is in fact endogenous in "reality".

    Okay, I challenge you to fire up a Bayesian regret simulation and find any even vaguely realistic parameter tunings which cause any of the common methods to do better with more strategic voting. I'll bet that you cannot.

    There, your point is negated.

    As for me saying, "proposed SV/AV as a way to "eradicate" strategic voting", I overstated things for rhetorical purposes.

    You mean, you lied to make a point.

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  8. dlw1:I'm talking about the endogeneity of candidates' positions prior to the election in early November, not how they do not always do what they said they'd do after the election.

    BL:That makes no difference. On election day, at the time a voter casts his ballot, he has some estimate of his utility for the candidates. Then later there is the actual utility the voter got from what that candidate did in office. The BR calculations include a disparity between those two values.

    dlw2:It does make a difference. I'm saying that the estimate a voter has of the candidates is determined by positions that the candidates take prior to election day. The potential of voters to vote strategically can move candidates to take positions that they wouldn't have otherwise. This then affects the relative "utilities" of all the voters for the candidates.

    dlw1:As for the inverse ratio between representativeness and strategic voting, since we don't observe either of these two variables in real life, it seems you're still conflating BR-world with "reality", which doesn't negate my basic point that the BR model takes as exogenous what is in fact endogenous in "reality".

    bl:Okay, I challenge you to fire up a Bayesian regret simulation and find any even vaguely realistic parameter tunings which cause any of the common methods to do better with more strategic voting. I'll bet that you cannot.

    There, your point is negated.

    dlw2: Urgh, it's not a matter of "parameters" but the endogeneity of variables.... I'm not contesting that BR model makes strategic voting into an unadulterated "bad", I'm simply contesting that the BR-model captures all of the relevant aspects of "reality" that make strategic voting more of a mixed bag.

    And hyperbolic exaggeration is a common form of rhetoric, the point being that in real life strategic voting is more of a mixed bag.

    In my 3-seated Hare LR election rule, the incentive to vote strategically is reversed away from the biggest party towards the biggest of the third parties... This is like "karma" ;0. Rather than end the incentive to vote strategically, Strategic Election Reform changes the incentives so that it works in different directions.

    dlw

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