I have a feeling that this is closely tied to Newcomb's paradox. It involves whether one views oneself as an independent moral agent or as one of a group of people subject to common influences.
Let us suppose that there are two influences on how I vote. The first is my position as a bearer of certain attitudes and social forces that I share with others. Call this GW (for "General Will"). The second is my own idiosyncratic individualist beliefs: call them I (for "Individual"). Suppose that G and I are independently distributed, and each has a 50% chance of being positive and a 50% chance of being negative.
If G and I are both positive, then I vote "yes". If one of G or I is positive and the other is negative, then there is a 50% chance that I vote "yes" and a 50% chance that I am too apathetic to go to the polls. If both G and I are negative, then I am too apathetic to go vote. The total vote, however, is determined by G and not by I. If G is positive, yes wins. If G is negative, it does not.
Suppose that I am--before the election--debating how to vote. I reason as follows. 75% of the time that I vote "yes" it turns out that G was positive. 75% of the time that I vote "no" it turns out that G was negative. So when I go into the polling place to punch my card, my vote makes a difference in the sense that it alters the probability that "yes" wins--raises it from 25% to 75%.
Therefore whether I vote yes matters: if I don't care enough to go to the polls, then the chance of "yes" winning falls from 75% to 25%.
There does remain the question of whether this analysis does not apply if I use this correlation between my vote and the result to argue myself into voting. I can argue either side of that question...
Brad DeLong