The Prisoner's Moderate Voter's Dilemma

If you have any familiarity with game theory—and maybe even if you don't—you've heard of the prisoner's dilemma.

The idea is simple enough: two players each have two options; cooperate or defect. If both cooperate, both do well (gain utility). But if either one defects, they do better (gain more utility), at the others' expense. And if both defect both do very poorly (lose utility). But game theory can also elegantly explains why third-party candidates, and especially moderate third-party candidates, perform so poorly.

Consider the setup: two players, although each "player" is actually a block of voters, those who prefer one of the two major parties, but would be willing to vote for the compromise candidate. Each bloc has two options; vote for their party-line candidate, or vote for the compromise (third-party, moderate) candidate (voting for the opposing party-line candidate isn't really an option.)

If both blocks choose to compromise, the compromise candidate will win, and this will usually result in the greatest net-gain for the electorate (no one gets everything they want, but most people get most of what they want). Eventually, one bloc will notice that the compromise choice isn't polling well enough to win, and neither is their preferred major-party candidate, and so they will drift back towards their party-line favorite; the opposition will then see that the compromise candidate has lost some support, but even worse, their preferred major-party candidate is now no-longer winning either, and so they will also fall back toward their own party-line candidate. As voters abandon the compromise, the balance shifts back and forth, inspiring even more voters to abandon the compromise, and so on. Rapidly, the entire compromise collapses, and one of the two major-party candidates is, once again, elected.

This is what happened to Chris Daggett in the New Jersey gubernatorial race last month, and has happened to thousands of third-party and moderate candidates in the past. Daggett polled as high as 20% just two weeks before the election, but as election day drew closer, voters began to abandon him in droves; on election day itself, he got less than 6% of the vote. If a moderate/third-party candidate isn't leading in the polls—which would only have to be around 33%—this is bound to happen. In fact, Daggett's polling plus undecideds never exceeded that critical one-third benchmark.

When a third-party candidate results in a spoiled election, that's a tragedy; but this, where the fear of a spoiled election drives out the compromise choice, is the true tyranny of the electoral system. Actually, fear isn't the right word: each voter who abandons the compromise doesn't do so out of fear, but because it is the only rational choice they have to maximize their own utility from the election. Each one comes to the rational realization that, while the compromise would be best for everyone overall, it looks like the other guy is going to win, and so they have no choice but to run to the support of their guy.

These elections are, mathematically, precisely identical to the prisoner's dilemma, and the only rational result to the prisoner's dilemma results in everyone losing.

The only solution to avoid this problem is to play a different game. That's what score voting and approval voting do. They change the rules of the game so that the strategic choice which is best for each individual player's utility more often matches the strategic choice that is best for the utility of the population as a whole. No other proposed fix—not anti-gerrymandering laws, not fairer ballot-access laws, not instant runoff voting—changes the game. Change the game. Vote with score voting.

A Majority of a Majority is a Minority

Consider an election in a swing district; one that is very nearly evenly split between voters who generally prefer Democrats over Republican and voters who generally prefer Republicans over Democrats. Consider also that, in nearly all districts, voters can vote in a primary election, but in only one of the two primaries. Unless the primaries are complete blowouts, the winner of the election can not possibly be the favorite of a majority of voters. Rather, they will be the favorite of a majority of the majority, which could be as little as 25%+1 of the voters—or less if there are more than two candidates in the primary!

Score voting is occasionally attacked because it fails the "majority criterion", which states that, if a candidate is the first-choice of a majority of the voters, that candidate should win the election. I'll provide a simple example: three candidates, A, B, and C. Three voters, two of which vote A=9, B=5, C=0, and one who votes A=0, B=9, C=9. A majority of the voters (two out of three) prefer A over B, but B wins the election, with an average score of 6.33 versus A's score of 6.00. Score voting fails the majority criteria. (This might not be a bad thing, but that's a post for another day...)

But consider this in context of the first paragraph's example: plurality elections are known to fail spectacularly when there are more than two strong candidates, which is why the system of party primaries developed. But this has the side effect of squeezing the middle out of the pool of candidates. While it's true that many primary voters will take into consideration a candidate's chances of winning the general election, the voters are still by and large trying to choose a candidate who is preferable only to the majority of the party members; then, the hope is that the party members will be a majority of the electorate. However, we must remember that this candidate was the first-preference of only a majority of a majority. And since that's the case, is it even meaningful to say that plurality elections (preceded by primaries) choose a "majority winner"?

If you were to put all the candidates from both parties' primaries up at once, how often would more than half of all the voters indicate a single one of those candidates as their favorite? Not very often! Surely, if there were such a candidate, they would win any subsequent plurality election, but when we say that plurality elects a "majority winner", we are usually not talking about such a candidate, even if the system we use obscures this fact from us.

Comics

I have two mostly-written posts waiting in the wings, but they have to take a back-burner to this.

I love the webcomic xkcd, and considering the topic of this blog, today's comic is very special to me. But then I read the hover text: "I favor approval voting or IRV chiefly because they mean we might get to bring back The Bull Moose party."

Okay; approval voting I'm in favor of. It's a minimalist form of score voting (score where the only allowed scores are 0 and 1), which is good, and since score voting is free of both candidate cloning and favorite betrayal, it could actually allow third parties, like The Bull Moose party, to have a real chance at victory.

But IRV is not good. IRV is strongly susceptible to favorite betrayal, and so is only a marginal improvement over plurality, in that all those third parties, like The Bull Moose party, will still be spoilers (yes, IRV has spoilers) before they become winners. (And that marginal improvement is before you start to account for the significant increase in complexity while counting the election, the potential cost of new machines, and non-intuitive results stemming from non-monotonicity issues.)

But, I have hope: xkcd's author and fans tend to be rather logical (you have to be in order to get all the jokes!) Hopefully this proof will convince them. And if not, this image might.

LOLotics

As you may know, the White House has its own Flickr stream. But take a look at the text bellow the images:

This official White House photograph is being made available only for publication by news organizations and/or for personal use printing by the subject(s) of the photograph. The photograph may not be manipulated in any way and may not be used in commercial or political materials, advertisements, emails, products, promotions that in any way suggests approval or endorsement of the President, the First Family, or the White House.

(Emphasis added.) As detailed in an article on Techdirt, these images, as government works, must be (and are explicitly indicated as) public domain, and you can't put restrictions such as these on items in the public domain.

So, in the name of civil disobedience, I bring you: Lolotics.

EDIT: You are welcome to join me in the virtual sit-in; pick any picture out of the White House photo stream, and manipulate away. Post links to your work in the comments. Do take note however that this is in direct violation of the legal terms presented by the White House; any who choose to do so must be aware of the potential for legal action against them, and take full responsibility for any of their own actions

Now On Twitter

You can now follow The Least of All Evils on twitter, at the very-clever name LeastOfAllEvils.

CRV On the Biggest Elections of 2009

The Center for Range Voting is putting out a press release of sorts, covering the big elections of 2009: NJ Governor, NY-23, and the Afghan presidential election.

The take away: while IRV would have fixed some of the problems in NJ, score voting would have fixed all of the problems in NJ and in NY and been significant help in Afghanistan. (The release also recommends asset voting for Afghanistan.)

Life Imitating Art: New York Edition

My last post centered around a set of example elections that serve to highlight the short-comings of instant runoff voting (IRV). Going into this Tuesday's election, we have two highly-publicized real-world elections that also perfectly highlight how IRV fails: the New Jersey governor race and special election for the US House seat for New York's 23rd district. Here, I will cover the New York race.

A lot is being made of what would, under any other circumstances, be a very minor race in upstate New York. What was expected to be a rather uninteresting race between moderate Democrat Bill Owens and equally-moderate Republican Dede Scozzafava, has been grabbing headline after headline since Conservative party candidate Doug Hoffman arrived on the scene.

I'm going to go out on a limb here and make a prediction, which I'll explain below: it will be close, but Hoffman will win. But that's not all: by a thin margin, he deserves to win.

First things first: Scozzafava's stepping out changes absolutely nothing. She was in third place under plurality, and even though she's a Republican, her and Hoffman were not about to split the (small-c) conservative vote. Hoffman's support, as 538 points out, was coming from voters who otherwise would be staying home. And even now that Sozzafava is out, her voters (at least the ones who won't now be staying home) will very nearly evenly divide between Hoffman and Owens. Which leaves Hoffman with a small, but noticeable, advantage. Were this election to be run under IRV, Scozzafava would be the first eliminated, and the results of the election would be exactly the same. IRVs results would mirror pluralities results (as is often the case.) But I'm okay with all of this because, in this case, they both agree with score voting.

I'm basing these numbers on the latest Daily Kos poll of the race (which if it can be accused of any bias, would be Democratic leaning, but meta-analysis has found them to be surprisingly honest and accurate.) To determine the score voting results of the election, I looked at the favorability scores, just like I did for the New Jersey governor race: "very favorable" = 4, "somewhat favorable" = 3; "somewhat unfavorable" = 1, and "very unfavorable" = 0. Since this poll doesn't separate "no opinion" from "haven't heard of candidate", I ran two separate sets of data; one where I treat all the "no opinion" scores as a 2, and one where I treat them all as an "X". Each candidate's real score will then be somewhere between these two values. Here's the data:

Candidate	Very Favorable	Somewhat Favorable	Somewhat Unfavorable	Very Unfavorable	No Opinion
Scozzafava	15%	17%	24%	22%	22%
Hoffman	16%	22%	12%	11%	39%
Owens	15%	21%	14%	12%	38%

Scozzafava ends up with a losing score no matter which way we count the "no opinion" column, somewhere between 1.8 and 1.7. Owens does much better, with somewhere between 2.1 and 2.2. But by a thin sliver, Hoffman takes the crown, with a low score of 2.2 and a high of 2.3. The only way Owens would win (modulo the margin of error of the poll) in a score voting adjudicated election would be if all the voters with no opinion of him voted that way because they had never heard of him and all the voters with no opinion of Hoffman voted that way because they knew him, but had a neutral opinion of him; if anything, the opposite if probably closer to the truth. Eyeballing the effect that margins of error could have on the result (which is a lot, since it's so close), I give Hoffman the advantage, 60:40, over Owens.

A lot will be made of the results of this highly-scrutinized election. But no matter how you slice the data, this is a painfully close election between the two remaining contenders. And the reason, to go back to 538's analysis, is because Hoffman has managed to excite a group of voters who otherwise wouldn't be voting.

Interestingly, the minutia of this poll doesn't fit the stereotype that most news outlets are trying to put on it: it's not a left vs. right vs. hard-right election. This is a ever-so-slightly-left vs. ever-so-slightly-right vs. I-hate-left-and-right election. Hoffman, and the voters in upstate New York, are refusing to fit the narrative. Hoffman will win (probably), but when he does, don't believe the spin you'll hear from Fox news about it: among the likely voters in NY-23, the same ones who are about to elect Hoffman to congress, Obama still has a net-positive favorability (he gets a score of 2.1.)

Update

Since posting this, Scozzafava, the Republican who suspended her campaign on Saturday, has endorsed Owens, the Democrat. Also, several new polls have come out showing Hoffman's lead has skyrocketed. So my 60:40 odds are... kinda laughable now. Looks like it'll be Hoffman in a landslide.