Isn’t the answer easy? To vote rationally is to abstain.
But suppose that you were held at gunpoint to vote (Vote or Die bitch!), what is the most rational allocation of your resources? In other words, in which contexts should you vote?
I answer the question by making two assumptions. First, in determining what a rational allocation of resources is in the voting context, I assume that the more likely your vote would be the deciding vote, the more rational it is to vote in that context. Second, the more effective your vote is, efficiency defined as the ability of your vote to translate into policies that you want, the more rational it is to vote.
From those two premises, I generate one conclusion: the more local the election, the more rational it is to vote. Now this conclusion is not without exception, since there are structural reasons for why one should vote for Congressional elections than for the county education board. But in general, the trend holds true.
First, the probability of your vote becoming THE deciding vote. In a presidential election, your vote has a 1 in 200 million chance of being the deciding vote (in an absolute, strict, and literal majority), assuming that roughly all US population turns out, but turnout level is largely irrelevant to this discussion. However, once you get to the level of voting in Congressional districts, your vote has about a 1-in-3000 or so chance of becoming the deciding vote. If you vote at a county or a municipal level, that chance goes up even more.
Granted, none of those probabilities are very high, but since what we are talking about is strict rationality, the higher that chance, the more rational it is for you to vote.
The trend also holds for another reason: the less constituents there are under a political actor, the more responsive he becomes to the interests of his constituents. Thus, the president must respond to the interest of the country, which is inevitably inconsistent, non-uniform, all compromising each other’s effectiveness. However, a Congress man only represents a single district, so he responds to the interests of a much smaller group of people, which means that it is more likely for any given individual to voice his interest and be heard. The effectiveness increases even more at the municipal level, since a constituent can simply go see his representative in person.
As the number of constituents go down, access becomes increasingly easier, thereby increasing the chance that any given individual’s preferences will be realized.
Therefore, these two effects combine to make voting at the more local level a more rational allocation of resources.
However, this trend does not hold up linearly, since the most local elections do not affect the things that matter to the constituent. After all, municipal elections do not control welfare, health insurance, tax policy, and so forth. This is not a structural problem, but instead a historical one, since historically, the federal government has come to exercise more and more power over those of local and state governments.
But what is certain is that voting for presidential elections represents the least rational allocation of resources, for reasons mentioned above. Therefore, the rational voter must find a balance that is the most rational, given the kind of issues that he cares the most about. But I imagine for most people, the most rational way to vote is to vote for their Congressional representative, due to the historical reason just mentioned.
Therefore, it is kind of misleading on my part to say what the most rational vote is, but what I am reasonably sure of is that voting for presidential elections is the most irrational allocation of resources.