Will Baude:

Voting instrumentally (in presidential elections, at least) is quite irrational, except to the extent that voters enjoy doing it. The probability of any single voter changing the outcome of a presidential election is 0.

Tell that to a voter in Florida in 2000 (his probability was about .002, which isn’t great, but beats the heck out of the lottery). Because of the electoral college, the probability of any single voter changing the outcome of a presidential election varies from state to state, and is a function of the competitiveness of the election in that state. But you don’t have to believe me; instead, believe, er, Chris Lawrence:

For [supporters of third party candidates], the strategic/sincere choice rests on whether their vote is likely to be pivotal. Although Downs (1957) argues that casting a non-strategic vote is irrational, that is only the case if the vote has a non-negligible chance of affecting the outcome of the election. Sincere voting for minor candidates is irrational in the sense that elections are not normally thought of as a forum for expressing general preferences, but rather as a “selection process”; however, if political actors respond to election results as if they are referenda on particular policies espoused by candidates, sincere voting for minor candidates may be rational in certain circumstances. If a citizen’s vote is almost certainly not pivotal, it may be rational for voters to show their public policy preferences by supporting a minor candidate. ...

Thus, voters may be considered rational if they express a preference, rather than merely taking part in a “selection process,” in states where their vote is highly unlikely to make a difference in the outcome. For example, according to CNN (2000), only 20 of the 51 elections for electors in 2000 were in so-called “battleground” states that were expected to be close. Thus, a voter in one of the other 30 states or the District of Columbia could presumably vote for a third-party candidate and thus have virtually no expectation of affecting the presidential contest, as their vote would be highly unlikely to affect the disposition of their state’s electors. (103–04)

Unfortunately, the astounding finding that the variation in “pivotalness” of an individual’s vote varied in 2000 by a factor of nearly 1000 between the most competitive and least competitive state didn’t make it into then-Mr. Lawrence’s dissertation, although it has made it into at least one presentation of the findings of this chapter.