Gaming the vote

A few weeks after I send in my ballot, the election commission sends me a letter asking me to update my signature. It's apparently changed from the time I registered. The only time I'd bother to update that signature is in the Nozickian situation where my vote actually did count, i.e., I am the tie-breaker.

Statistically, it's unlikely.

But is the statistical unlikelihood of being the tie-breaker a mathematically compelling argument against voting? I have my doubts. Everyone else is a potential tie-breaker and so the correct strategy is for no one to vote. But as the number of voters go down – assuming a homogeneous reduction – the likelihood of being the tie-breaker goes up.

What about a heterogeneous reduction in the numbers of voters? If it wasn't obvious, the decision of whether to vote has some Prisoner's Dilemma type aspects. Deciding to vote carries with it a burden of having to pay at least some attention to political ads, arguments, and all the other things that make the election season wearying.

Imagine two Nozickian voters on opposite sides, Red versus Blue. If Red votes but Blue does not, Red wins and vice-versa. If both vote, it's a tie but both will have wasted time and money in the process. If neither vote, neither will have wasted time and money. The stable "intelligent" choice is to not vote. But if the policy differences appear large enough, the payoff for coöperating becomes insignificant.

If this election's presidential contest were between The Apprentice Trump and First Lady Clinton, no one would vote. But when it's between Literally Hitler Trump and In Your Heart You Know She Might Clinton, the payoff is tantamount to saving the world. We saw this earlier with Brexit where I could not understand the hysteria over a largely inconsequential vote.

Although Trump is definitely the non-establishment protest figure in the election (and the candidate I would expect to win), neither offer anything radically different*. So the stable intelligent choice is still to not vote. However, if there is a meaningful difference in intelligence between Red and Blue, then the stable intelligent choice becomes unlikely because less intelligent people are less coöperative. Thus, given unequally intelligent players, the correct strategy is to vote even if the outcome is almost guaranteed to be less than optimal.

* Principled to the point of consistency. The only believable differences are a stricter immigration policy and lower corporate taxes on Trump's part.