What’s the Best Voting System?

Last February I highlighted a New Yorker piece about instant runoff voting (IRV) in awarding the Oscar for Best Picture. (Kudos to author Hendrik Hertzberg for correctly predicting the winner: The Hurt Locker.)

As I said at the time, I think elections to public office would benefit from IRV as well:

Why? Because it eliminates the downside of voting for a third-party candidate. In a race between D and R, you may worry that voting for third-party candidate I is “throwing your vote away.” That worry disappears with IRV. You can give I your number one vote and either D or R your number 2 vote. If I loses in the first round, you’ll be disappointed. But you won’t have wasted your vote since your second-place vote now becomes operative.

I think that would be a substantial improvement over the winner-take-all vote tallying that dominates the American political system today. But would it be the best of all possible voting systems?

In this week’s New Yorker, Anthony Gottlieb answers no, pointing to a potential flaw in IRV:

Such transferrable-vote elections can behave in topsy-turvy ways: they are what mathematicians call “non-monotonic,” which means that something can go up when it should go down, or vice versa. Whether a candidate who gets through the first round of counting will ultimately be elected may depend on which of his rivals he has to face in subsequent rounds, and some votes for a weaker challenger may do a candidate more good than a vote for that candidate himself. In short, a candidate may lose if certain voters back him, and would have won if they hadn’t.

The practical importance of this theoretical concern is a matter of heated debate, much of which has focused on a 2009 mayoral election in which Burlington, Vermont used IRV (as it had in 2006). According to IRV detractors Burlington ran right into the “non-mononicity” issue, with the “wrong” candidate winning (at least by some voting metrics). IRV supporters reject that view. (Sorry, I haven’t had time to sort this through; if you are interested, just Google “Burlington 2009 election” and have fun.)

As best I can tell, however, both sides agree that the current system is flawed. For example, many of the IRV detractors believe we should adopt a different system: range voting, which allows voters to express how much they like or dislike a candidate. Rather than just ranking Oscar movies, for example, voters would award scores: (e.g., Hurt Locker 10 points, Up in the Air 9 points, Avatar 2 points). The movie with the highest score would win.

That would also solve my primary concern about not discouraging votes for third-party candidates. But perhaps range voting has other hidden problems as well? As Gottlieb notes there is a limit to how far theorizing can take us in this debate:

Mathematics can suggest what approaches are worth trying, but it can’t reveal what will suit a particular place, and best deliver what we want from a democratic voting system: to create a government that feels legitimate to people—to reconcile people to being governed, and give them reason to feel that, win or lose (especially lose), the game is fair. The novelty of range and approval voting in modern politics is so great that we can’t know how they’ll work out without running experiments.

Let me second that recommendation: more experiments with IRV, range voting, approval voting, and other innovations would be well worth the effort.

But I think we can take a pass on the voting system of old Venice, which Gottlieb describes as follows:

Thirty electors were chosen by lot, and then a second lottery reduced them to nine, who nominated forty candidates in all, each of whom had to be approved by at least seven electors in order to pass to the next stage. The forty were pruned by lot to twelve, who nominated a total of twenty-five, who needed at least nine nominations each. The twenty-five were culled to nine, who picked an electoral college of forty-five, each with at least seven nominations. The forty-five became eleven, who chose a final college of forty-one. Each member proposed one candidate, all of whom were discussed and, if necessary, examined in person, whereupon each elector cast a vote for every candidate of whom he approved. The candidate with the most approvals was the winner, provided he had been endorsed by at least twenty-five of the forty-one.

6 thoughts on “What’s the Best Voting System?”

  1. A nifty short video describes the “topsy-turvey” ways of IRV and can be seen here:

    Instant Runoff Voting – An Informative Visual Tutorial

    Two more concerning Burlington’s election are here:

    IRV – Is it democratic? AN analysis of the Burlington, VT election

    A study performed showing IRV has problems when you vote your conscience, rather than strategically who you think will win:

    Watching these videos helped me understand IRV visually much better than reading a long report.


  2. Thoughtful post.

    The Burlington election, as in fact it was not a nonmonotonic election — e.g, no candidate lost because of winning “too many” votes. What the rankings showed is that it __could__ have been a nonmonotonic election. For that to happen, a number of the backers of the Republican candidate who finished first would have needed to switch their first choice rankings to the Progressive party incumbent — the candidate who in fact most of them saw as a last choice among the three leading candidates . If enough had done so, then the Republican would have lost enough support to fall behind the Democrat, and the Democrat was a stronger runoff candidate against the Progressive. But. hat did not happen.

    Backers of alternatives can all be passionate about their proposal, but each one has flaws – so each one can be bashed based on those flaws. It’s not particularly productive when the status quo is obviously problematic.

    But just to put it out there, among the flaws with range voting and approval voting that its advocates must accept are that it allows candidates to win against opponents who have the first support of more than 50% of voters and that your decision as a voter to indicate support for any candidate beyond his or her first choice will count against the odds of your first choice winning.

    Advocates of instant runoff voting see those as big political problems and, more importantly, problems with how they would lead to tactical voting. Some voters will bullet vote, others won’t, and results will be highly unpredictable and likely to be controversial. Indeed the article’s critique of the “Borda count” (the ranking system where getting a high ranking gives you more points) apply to range and approval voting.

    You’d think there would be some kind of Rodney King moment of “can’t we all get along,” but it hasn’t been easy. I’m sure IRV advocates are to blame for that too, but we at least are out there making change happen.

  3. Corrections of Rob Richie:

    RR: “The Burlington election, as in fact it was not a nonmonotonic election — e.g, no candidate lost because of winning “too many” votes. What the rankings showed is that it __could__ have been a nonmonotonic election.”

    Reality: RR does not know, apparently, what nonmonotonicity IS.

    FairVote’s own definition (which RR just contradicted — FairVote’s own example of a nonmonotone IRV election, corresponds exactly to what happened in Burlington, Richie apparently never read his own definition):

    RR: “among the flaws with range voting and approval voting that its advocates must accept are that it allows candidates to win against opponents who have the first support of more than 50% of voters.”

    Reality: this “flaw” is exemplified by the following election.
    51% of voters: Hitler 9, Gandhi 8, Nixon 0.
    25% of voters: Gandhi 9, Nixon 1, Hitler 0.
    24% of voters: Gandhi 9, Hitler 1, Nixon 0.
    IRV and plain plurality both elect Hitler.
    Range voting, because of its “flaw,” elects Gandhi.

    Incidentally, a considerable number of range-voting polls and elections have been carried out. I am aware of zero examples among them in which range voting even plausibly might have even come close to denying victory to a “50%+1 majority winner.” I think such examples will be extremely rare in practice. I am however aware of ONE example where range voting might have denied victory to a “Condorcet beats-all winner” (in contrast to a far larger number of examples where IRV denied that): the
    Los Angeles mayor election of 2001. You can judge for yourself
    which voting method made the right call:

    RR: “[another flaw is] your decision as a voter to indicate support for any candidate beyond his or her first choice will count against the odds of your first choice winning.”

    Reality: indeed, in the example above, the Hitler voters, by honestly saying they liked Gandhi nearly as much as Hitler, prevented Hitler’s victory.

    IRV ignores (it literally throws this information in the garbage without even looking at it) the fact the Hitler voters all like Gandhi quite a lot.

    RR: “Some voters will bullet vote, others won’t, and results will be highly unpredictable and likely to be controversial.”

    By “bullet vote” RR means range (or approval) voting in the style
    YourFavorite(max score); AllRivals(min score).
    He and others at FairVote have raised the so-called criticism that supposedly there will be lots of bullet-style range voting going on. However, an actual examination of the
    evidence finds that IRV elections, including those brought to
    us by FairVote, involve a greater percentage of bullet voting than approval. So RR really just criticized IRV. Oops:

    As for controversy, I’m surprised RR doesn’t worry about the “controversy” that arose when Burlington exhbited no-show paradox, non-monotonicity paradox, thwarted majority (Condorcet winner) paradox, and IRV spoiler, and IRV incentive-to-lie, and IRV ignoring a lot lot of what voters wrote on their ballots (without even examining it) — all in the same election.

    RR instead focuses of the horrible controversy that would arise when A gets a mean score of 75% defeating B with 67%.


  4. To add a bit more: the relative abilities of these
    flaws (and “flaws”) in range voting & IRV to cause “controversy” can perhaps be assessed by considering that the case under discussion — Burlington VT — *repealed* IRV soon after this very election!

    I don’t know about Rob Richie, but that sounds to me like a sign of worrying controversy.

    Meanwhile ancient Sparta and renaissance Venice
    employed range voting and 3-point range voting respectively
    [Gottlieb confused the issue re Venice — only the final step in Venice actually mattered, the rest was merely intended to make the voters difficult to corrupt]
    for over 1000 years between them, without, apparently,
    a “controversy” ever arising leading to any attempt to switch
    to a better voting system. Similarly academia has used range voting (GPAs) to “elect” tens of thousands of valedictorians.
    I fail to see any controversy that arose over that, nor any call
    to switch to (what would be absurd and an obvious disaster)
    instant runoff.

    Richie jibes: “We at least are out there making change happen.” Unfortunately, the main “change” RR & FairVote are making happen, is a systematic campaign to get rid of top-2-runoff (2 rounds) in the USA, and replace it with instant runoff (1 round). They did that in San Francisco, Minneapolis, Burlington VT, among others.

    Why?? The main reason they advance is “this will save money.” Unfortunately the evidence so far seems to indicate that is false — it seems to tend to increase the cost:

    OK, at least is IRV an improvement versus T2R as a voting system? Well, it is debatable, but in my opinion T2R is superior judged purely based on results as a voting system.
    [There are several web pages at rangevoting.org giving data-based analysis on this question.]

    So the “change” FairVote has accomplished unfortunately has (in my opinion) in net been
    (a) spread a lot of misinformation
    (that’s for sure – the latest baloney here from RR about monotonicity/Burlington is another example)
    and probably:
    (b) made voting systems worse,
    (c) cost more money.

    Dr.Marron has said he has not parsed though to determine who
    is right about Burlington being nonmonotonic. It might be worthwhile for him to actually do that, then come out with a clear statement saying he parsed, it indeed was nonmonotonic,
    and RR/FairVote was wrong. It helps at some point to know who is wrong.

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