Thursday, May 7, 2009


I got into a bit of an argument discussion in the comments of this article about instant runoff voting over at Independent Political Report. I hope I was able to provide some compelling arguments to the folks there, but I stopped myself short of getting down into the weeds about strategy in different systems, and which ones are more susceptible to strategic manipulations. But I did promise to talk about it here.

One of the commenters at IPR asked the following:

Wouldn’t a 100% strategic vote be identical for all voting systems? With range voting, you could just give someone a 10 out of 10 and everyone else a 0 out of 10 or not vote for them.
The short answer to the first question is "no", they're not all the same, and to the second, while you could vote that way (often called "bullet voting"), it's usually not going to be your best strategy. But these questions (well, one question and one statement) are blind to another strategic consideration, one that takes place outside the voting both and long before the election. We'll cover that at the end.

Strategy for Score Voters

While the strategy for different voting methods are different, they do all share some similarities. Most of them involve first figuring out who the two front-runners are, since that's the "real" fight and each voter is going to want to maximize the effect their vote will have on its outcome. You do that by reading the polls. Polling, and the feed-back effect polls have on opinion and voter turnout, is a whole other subject, but for now, let's assume that polls will nearly, but not perfectly reflect voter's opinions (after all, if they were perfect, we could just skip the vote entirely.) Additionally, there's a chance that there may not be two clear front runners; there may be a three-or-more-way tie for first, or a clear front runner and tie for second. We'll discuss that complication later too; for now, assume we can determine two clear front runners.

For score voting, once you've figured out who the front runners are, you vote like this: Give your most-preferred candidate among the two front runners the maximum score. If there are any candidates you prefer more than that candidate, give them the maximum score too. To the other front-running candidate, give the minimum score. If there are any candidates you prefer less than that candidate, give them the minimum score too. If there are any candidates between these extremes, give them a score scaled linearly between them. Most of the time this means that most voters will give most candidates one of the two extreme scores. In other words, highly-strategic score voters look a lot like voters in approval voting elections, but not exactly; we'll come back to that.

The practical upshot of this is, you can always give your honestly-most-preferred candidate the maximum possible score, while still having the greatest possible effect on the "real" fight between the two front-runners. This may not seem important right now, but keep it in mind, because we'll come back to it too, soon.

Strategy for Plurality Voters

Strategy under plurality should be familiar to everyone. Like score, you determine who the two front-runners are. You vote for whichever of the two you prefer. If there's another candidate you prefer more, then too bad; if you vote for them, you might accidentally give the election to your least-preferred candidate.

Theoretically, if the spread between the two front-runners is wide enough, you could throw away the tiny effect you could have on that contest, and toss your vote to your honest-favorite as a show of moral support. It's strategically not the best plan, but in that situation even the best plan isn't very good for you (no one you like has a chance to win!), so maybe you don't care, maybe communicating your dissatisfaction with both likely winners is more important to you; but this line of thinking feeds into the outside-the-ballot-box strategies which we'll discuss later. So keep it in mind (I know, it's a lot to keep in mind; stay with me!)

Strategy for Instant Runoff Voters

Again, determine the top-two. Among those two, rank your favorite first, and your least favorite last. Rank all the others in between those two. You will note that, in contrast to what IRV advocacy groups claim, it is not in your best interest to rank your honest-favorite first (unless they are in the top two), but rather to rank them second. This is because (again, in contrast to advocates claims) it is possible that your honest favorite could be a spoiler for your preferred top-two candidate, an issue I discussed at length in my posts on non-monotonicity (part I and part II).

Now, if the spread between the top-two candidates is large, or if support for your honest-favorite candidate is low (less than 25% if there are three candidates in the race, and progressively less and less if there are more candidates), you can safely communicate your dissatisfaction with both likely winners buy ranking your honest-favorite first. The percentage values are different, but the logic is the same as under plurality: if your honest vote doesn't really matter, you can afford to be honest. But if the "real" contest is close, your best bet is to betray your favorite, and rank them lower. In this way, highly-strategic instant-runoff voters look very similar to plurality voters.

Instant Runoff is to Plurality as Score is to Approval

Strategic IRV looks like plurality, and strategic score looks like approval; it's an interesting result, and one that is well supported by Warren Smith's Bayesian regret study (representative result graphic). And the values aren't just close, they are exactly the same; a surprising result that Smith went on to prove mathematically.

I want to reiterate this: the correct strategy for IRV gives identical results to plurality voting when all voters follow it. So the only potential improvements we could see under IRV would come from voters choosing to vote honestly instead of strategically. At this point, IRV advocates claim that voters will be more honest; but there's no evidence to support that. Indeed, since this strategic favorite-betrayal is the leading reason for two-party dominance in a government, and all nations that have used IRV have seen their elections stay two-party dominated, we can presume that favorite-betrayal is, in real life, common. And that honesty is relatively rare.

Thinking Outside the (Voting) Box

Voter strategy is just part of the equation though; candidates and political parties have strategies too, under the umbrella of "strategic nomination". Under plurality, for instance, parties absolutely must make sure that they have only one candidate in the race: if they run more than one, the candidates will likely split the vote, and so neither will win. This is why we have party-primaries. In addition, recently parties have realized that they can support candidates who are similar to their opponents, in order to split their vote and ensure their own success (for instance, Republicans buying ads for Green party candidates to defeat their Democratic rival), a tactic so underhanded that even some politicians find it despicable!

IRV fares better, but only slightly better: if there's only one strong opposition party, then running two or more identical candidates can't cause the party any problems. However, since under our current system there is only one strong opposition party, and since all the candidates from the same party are quite similar, IRV advocates have stretched this truth to claim that, under IRV, any number of parties can run as many candidates as they want, without suffering any repercussions, and therefore third parties should help them get IRV enacted. But this claim isn't true; it only seems true given the context of our current two-party environment, and a false appeal that what's true for two must be true for three or more. The truth is, IRV will continue to keep us locked in to a two-party system; although you may be allowed to vote for your favorite among a large homogeneous selection of Democratic and Republican clones. Anything riskier, and they would find themselves in the same vote-splitting catastrophes that plurality suffers from.

There's also consideration of the "nursery effect". Political parties, as a general rule, don't spring up over-night; they grow slowly over several election cycles. Under plurality, they grow and grow until they spoil an election by splitting a vote, and then voters abandon them in droves (the Green Party received 4% as many votes in 2004 as they did in 2000, for instance). Under IRV, the pattern will be the same. Parties will grow, they will spoil elections, and they will be abandoned. The only difference is that they will grow larger before they spoil an election (at least 25% rather than Nader's paltry 2.7%.)

It's that critical point, where a party has grown large enough to be a spoiler, that we must focus on. How well an election method performs in "run of the mill" elections is completely unimportant; in such elections, any method that's ever been seriously proposed will work as well as any other. It's performance in messy, close, near-tie elections that matters; these are the times when polling will flounder, and determining the top-two contenders will be hard. And at these critical points, plurality and IRV will often punish honest voting, electing the wrong candidate because of a spoiler, and pushing voters back towards the two well-known parties.

But what about score and approval voting? Under these methods, any number of parties actually could run any number of candidates without fear; no need for primaries. There can't be any spoilers, and so nothing will force a "lesser of two evils" decision and keep us locked in to a two-party system. Instead, third parties would grow, and grow, until they... win. And in those messy, close, near-tie elections, your best strategy is... honesty.

Strategy Strategy

So which method is "most prone to strategic manipulation"? You've read the strategies, judge for yourself. But know that there's no objective data to back up claims one way or the other, and intelligent people on both sides have written similar descriptions and they all still disagree about what it means. But here's the thing: It doesn't matter. That question is a mere distraction, taking attention away from the actual important question: which method gives us the best results? If you think two-party domination is definitively bad then the answer is clear: score voting or approval voting. If you examine the only marginally objective measure of effectiveness, Bayesian regret, then the answer is clear: even if you cling to the (unsubstantiated) claim that IRV encourages more honesty than score or approval, score and approval still perform better (likely because they avoid two-party domination). This is the only way that new parties (and the fresh ideas they represent) can grow without being cut-off at a critical point; so that they can continue to grow, get elected, and put their ideas into practice. IRV can't do that. (In fact it's been proven that no rank-order method can.)


Strategy is the wrong question. It leads to pointless, subjective, and unsubstantiated arguments. Effectiveness is what matters. An end to two-party dominance is what matters. And score voting is the only logical answer.


  1. You assume that voters will know who the strongest candidates are and can give one of them maximum support and the others minimum support, then vote sincerely for the "sure losers."

    But what if you're not sure where people stand -- or support your favorite may have a chance to win, but probably will lose. You're going to want to give maximum support to your favorite and no support to others.

    This will be a much more normal situation than the one you lay out.

  2. Yes, I do assume that, as I stated in the third paragraph. The stratgy sections are how to maximize your expected utility under that assumption. And at the end I briefly cover the messy case where that's not a good assumption at the end. To recap for you:

    When it's hard to determine the front-two, then plurality and IRV force you to choose: play it safe, and vote for the lesser of two evils, or play it honest, and risk electing the "greatest evil".

    Approval and range don't force that choice; you can put your honest favorite on top AND have maximum effect on the front-two's fight; at worst, you get your second choice rather than your first.

  3. This page is not very helpful:
    The optimum value of T is presumably roughly 50% of the size of the largest set of fanatics anybody can organize to support them while at the same time staying unknown to the rest of society, or at least inspiring no interest. (It is very hard both to organize your fanatics and stay unknown at the same time, so I do not expect this number will be very large, percentagewise.) (...)
    That may not even be
    the worst part. The whole entry doesn't inspire a lot of confidence since it's about the difficulty(but apparent necessity) of providing a solution for a problem that the author claims doesn't exist.

  4. I'll admit, a lot of Dr. Smith's writing isn't what you could call "good marketing." He's a scientist, not a salesman, so he always give the honest results of his work, not the spun-up version.

    The quorum rule was developed because other people were afraid of an unknown group of fanatics; in practice, most people who aren't familiar with a candidate give them a zero score. So yes, the author doesn't think it would really be necessary; but if someone were afraid of that scenario, the quorum rule is there.

    Typically, the quorum would account for fewer votes than the number of signatures needed to get on the ballot in most jurisdictions, so it's almost redundant.