One votes from self-interest or from a sense of duty. Voting from self-interest requires there to be some chance, however small, that one's vote swings the outcome of an election from one political party to another. This paper is a discussion of three models of what that chance might be: the...

A duty to vote may be many things. It may be no more than an obligation to cast one's ballot as self-interestedly or as altruistically as one pleases. It may a requirement to vote for the political party most likely to yield the highest social welfare. It may be a requirement to choose between...