In yesterday's post How to Waste Your Vote, I said:
Your vote can’t affect the outcome of an election.
To which Bill Quick commented:
That bit about “your one single vote can’t influence an election” is a misinterpretation of the Prisoner’s Dilemma problem that gave rise to the myth.
It's a good point, but before getting into why I disagree, let's review the Prisoner's Dilemma (from Wikipedia):
The prisoner's dilemma constitutes a problem in game theory.
In its classical form, the prisoner's dilemma ("PD") is presented as follows:
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
If we assume that each player cares only about minimizing his or her own time in jail, then the prisoner's dilemma forms a non-zero-sum game in which two players may each cooperate with or defect from (betray) the other player. In this game, as in all game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution, that is, rational choice leads the two players to both play defect, even though each player's individual reward would be greater if they both played cooperatively.
In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.
The point of How to Waste Your Vote, was that you should always vote for your first preference, because your single vote can't change the outcome of the election, and voting for the "lesser evil" sends the wrong market signal which only makes things worse.
Is this a misinterpretation of the Prisoner's Dilemma and thus, a myth?
Let's go back to the2008 presidential campaign again, using Obama, McCain, and Barr as our examples.
Let's say my preference in this election are (in order), Barr, McCain, Obama. In other words, my first preference is Barr over both McCain and Obama, and my second choice is McCain over Obama, and I'd prefer Obama doesn't get elected at all.
Conventional wisdom tells us that since Barr is unlikely to win and I don't want Obama to win, I should "hedge" my vote by voting for McCain (cooperate). So voting for Barr, since he can't win, is a "wasted" vote.
In the Prisoner's Delimma, "defecting" is the dominant strategy, because it maximizes each individual players own payoff. To apply this to our presidential vote, a vote for Barr is considered a defection from McCain's voting bloc ... A betrayal that could result in Obama winning.
But considering over 130 million people voted in the election, there's no way to get everyone to cooperate with each other in the first place. This leaves defection remaining as my (or any other individual's) dominant strategy. So it still makes the most sense for me to vote for Barr.
It may seem logical that since Obama is my least preferable candidate and Barr isn't going to win, my incentive is then to vote for McCain. But this is not true. Only if I'm persuaded into making McCain my first preference, would it be in my best interest to vote for McCain. And if my preference changes to McCain, then there's no more Prisoner's Dilemma to worry about.
Game theory is based on the assumption that others see the same logic we do, and therefore act in a predictable way. So just as it's logical to think people should vote for McCain to protest Obama, it's just as logical to me that people would vote for Barr, because he's the best candidate. So again, there's no incentive for me to vote for McCain.
Continued in Rational Ignorance and Your Vote.
Prisoner’s Dilemma has nothing to do with the fact that your individual vote has no effect on the election. It’s just the outcome of the numbers involved and a basic understanding of probability (leaving aside the Presidential determination by Electoral college).
And let’s assume the improbable happens, and your vote breaks the tie (a tie between 40 million people, who exactly split down the middle). Even if that was theoretically the truth, what about in practice? All operations have an error rate, and counting votes (electronically and by hand) is no exception. Your individual vote is swallowed up by all those votes not counted, or counted improperly – even if in the perfect world your vote made the difference, in the real world the end result would be something like 240 votes in person A’s favor. But again, you can vote in a national election every day until you are 120, and never be in a position where your vote made the difference.
However, just like in religion, something doesn’t have to be true in order to give comfort to people. Voting helps some feel like a part of the democratic process, serves to protect against the fear of impotence, etc. And there’s nothing wrong with that. But in that case, one should vote their conscience; I do not understand how anyone who understands the mathematical meaninglessness of the act would waste their time trying to play pragmatic games and pick the least runt of a litter full of runts. Pick the one who you actually want to win.
Although, for a public figure looking to influence others (Buckley), it may serve a purpose to tell them to vote for the most conservative popular candidate, hoping the large number of votes makes a difference. But still, privately, that person would be foolish to vote for anyone except the best choice for them.
I voted for Perot in ’92.
To say that this vote was wasted is to say that Clinton was further left than Obama.
No, the breakdowns of the political expression matter, even though there be only one winner.