I just finished reading and reviewing The Myth of the Rational Voter. Most of classic Public Choice theory assumes that voters vote in their self interest, in his book, Caplan explains why voters vote altruistically:

Consider. First, altruism and morality are consumption goods like any other, so we should expect people to buy more altruism when the price is low. Second, due to the low probability of decisiveness, the price of altruism is drastically cheaper in politics than in markets. voting to raise your taxes by a thousand dollar when your probability of decisiveness is 1 in 100,000 has an expected cost of less than a penny.

I find this logic convincing, but it brings up another question: why does the plurality electoral formula generate only two political parties? Does voting altruistically for a candidate who has a chance to win feel better than voting for one that does not?

In classic Public Choice theory, assuming self interested voting, this result is fairly easy to explain; the expected benefits from voting for a particular candidate are proportional to benefits from policies the candidate will implement as well as the expected probability that the candidate will win because the probability that the voter is decisive goes up as their chances of winning go up. As time goes on, a reputation for winning elections gives two parties much better chances of winning than 3rd parties, because their percieved chances of winning rise. Reputation is self reinforcing because it attracts votes, so the equilibrium is stable. This process stops at two parties because 50% of the vote is the maximum ever needed to win an election, so getting above 50% of the vote does not improve winning reputation.

Public Choice theory using a rationally irrational voter assumption explains this in a similar but slightly different way. I think the answer is that the feeling of altruism is proportional to the expected social benefits from voting for a particular candidate. The expected social benefit from voting for a particular candidate is proportional to the percieved external social benefits from the policies the candidate will implement as well as the expected probability that the candidate will win because the probability that the voter is decisive goes up as their chances of winning go up. Then, the same thing happens as in classic Public Choice; a reputation for winning elections gives two parties much better chances of winning than 3rd parties, because their percieved chances of winning rise. Reputation is self reinforcing because it attracts votes, so the equilibrium is stable.