Thursday, March 15, 2012

The Tyranny of the Majority Weak Preferences

Suppose you and a pair of friends are looking to order a pizza. You, and one friend, really like mushrooms, and prefer them over all other vegetable options, but you both also really, really like pepperoni. Your other friend also really likes mushrooms, and prefers them over all other options, but they're also vegetarian. What one topping should you get?

Clearly the answer is mushrooms, and there is no group of friends worth calling themselves such who would conclude otherwise. It's so obvious that it hardly seems worth calling attention to. So why is it, that if we put this decision up to a vote, do so many election methods, which are otherwise seen as perfectly reasonable methods, fail? Plurality, top-two runoffs, instant runoff voting, all variations of Condorcet's method, even Bucklin voting; all of them, incorrectly, choose pepperoni.

The Tyranny of the Majority

The answer is simple: All of these methods obey the majority criterion. This criterion seems so reasonable: If a majority of voters prefer one choice over all others, then that choice should be elected. And that's the case here. A majority, 2 out of 3, prefer pepperoni to all other options. Therefore, pepperoni must win. It's completely reasonable. And it means you're willing to send your friend home hungry.

If we examine the ballots these three friends would submit to the pizza-topping election, we can see the problem. Even though you and your one friend both really like mushrooms, the ballots don't show that. They only show that you like them less than pepperoni. There's no way for you to indicate the importance of that preference, and no way to mitigate it. You can't say, as you would if you and two friend were actually face-to-face and making such a decision "I like pepperoni better, but, dude, since you couldn't eat it, I'd totally be alright with eating mushrooms." Well, almost no way: You could choose to rank mushrooms above pepperoni, making a deliberate action to, after considering the thoughtful dialogue of the other voters, submerge your own narrow self-interest by voting for the choice you have determine is the one that would deliver the best result for society at-large, despite your own personal preference....

Or we could use a voting method that already knows how to do that, and lets you express your personal preferences in the same natural way that you would among your friends.

The Tyranny of Weak Preferences

The problem here is that these majoritarian methods have no way to indicate strength of preferences. Your weak preference between pepperoni and mushrooms is given as much importance as a your friend's overwhelming preference between pepperoni and mushrooms. And yet, the ability of approval voting and score voting to cleverly subvert the majority criterion in this way has been used as an argument against it. The detractors argue that it is horrible, absolutely horrible, that a candidate could be preferred by the majority of voters but that the election method would pick someone else. But is it really so horrible? After all, didn't you say you really liked mushrooms?

The truth is, under the voting methods for which I argue, voters have the power to express a willingness to compromise, and if they choose to express that desire, then these voting methods have the ability to honor it. And conversely, if the voters do not have an interest in compromising, then they can express that too.

Now, I know that, in the voting booth, we're not all friends. But that only makes it more important that we use election methods which strive for consensus, instead of divisiveness. You don't have to vote on pizza toppings with your friends, because it's a mostly unimportant decision with only a few people affected, none of which are especially invested in the outcome. You trust each other, and can quickly talk out all possible outcomes and come to a mutually-acceptable agreement. That's harder to do with 100 million angry people deciding on their government. But you still want—no, you still need—a consensus result. The majority criterion is detrimental to that goal.

Arguing Both Sides

What I find especially funny is that the other common argument used against approval and score voting is that they will degenerate to plurality voting, because voters will only vote for their single favorite choice. We know that's not true, but it's also contradicted by their arguments favoring the majority criterion. Because, for an approval or score voting election to actually exhibit majority failure, a substantial number of the voters would have to vote for multiple candidates; while, for accusations of bullet-voting to carry any weight, nearly all voters would have to vote for just one candidate. And yet, detractors argue that both of these things will happen, which is logically inconsistent.

The truth is, sometimes voters will bullet-vote, but only when it suits them to do so. And sometimes (rarely) a majority candidate won't win, but only when the voters who prefer that candidate have made the decision to express that preference as a weak preference, and defer to the whims of the minority. In other words, only when they have said "I like this other candidate better, but dude, if you really hate him, I'd totally be alright with one of these other guys."

It's called a compromise. It's how friends stay friendly, and how civilization stays civilized.


  1. This is one of the best arguments against majority-based voting that i have seen. It really needs more publicity.

  2. Thank you. Please, share it far and wide.

  3. About all I can do is post a comment on my blog, which I've done.

  4. I think that if one includes extra-political civil disobedience oriented aspects that majority rule can be made to work.

    Let's say that pepperoni or no pepperoni, along with mushrooms are initially the options. But then the vegetarians demonstrate how much they don't want to eat meat. This act moves the pepperoni lovers to accommodate them so the options become mushrooms or no mushrooms.

    The real issue, IMO, seems to be that when you relax the cardinality of utility assumption that voting patterns under approval or rank/score, even without strategic voting, are indeterminate. Politics is more complicated and not tied to something concrete. Our perceptions of our political leaders are constantly being manipulated and their fitness depends on which issues loom large.

    A majoritarian rule accepts the results from the way preferences have been shaped. I can live with that if and only if we started to have more #OWS-style civil disobedience to influence the issues and we used American forms of PR in "more local" elections to give minorities more voice.

    So to summarize, I think your concerns with IRV can be addressed in other ways than the use of Approval or Range voting for important single-member political elections. I embrace a Burkean distrust of the use of those rules in that context. I also don't trust Condorcet rules that work best when voters are well-informed and willing to rank all of the candidates. Even if they're relative simple to explain if there is a Condorcet Winner(CW), if there is both not a CW and significant spoiled ballots and/or fraud then it could get very complicated and ugly.

    So I think it comes down to realism vs idealism. IRV got rejected in Burlington because of a manipulative campaign against it that was funded by the Republican party who was fighting for its right to be among the two major parties in VT. And it was barely rejected. So this is not a smoking gun or problem that would be fixed if IRV were replaced with another better election rule. As you point out, seemingly valid, potentially persuasive args can be constructed by opponents against any rule.

    What really matters is that we go forward. IMO, with the endorsement of IRV by Barack Obama, it's now the Mitt Romney/Barack Obama of single-member election rules. So we'd be better pushing for it to be enhanced by the use of Approval Voting, not pushing a spoiler alternative alternative to FPTP.


  5. Dale, I'm sorry if I was too pushy above. peace.

  6. Technically, mushrooms are fruit because they are fruiting bodies (they release spores, so they are used for reproduction, so they are fruit). Fungus is not a plant. Since testes and ovaries are used for reproduction, they are fruit too.

    ¡I am just being silly!

    ¡Great post!

  7. This was one of the most helpful articles I've read, and I've been looking far and wide for info on voting for my app I'd like to speak with you some time about the project which intends to get alternative voting methods into the hands of a lot of people and gather data about the happiness / appropriateness of the methods chosen by the users.