Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I say who wrote them.
Edlin, Gelman, and Kaplan. 2005. Voting as a rational choice: Why and how people vote to improve the well-being of others. Rationality and Society 1.
The authors want to argue that voting can be rational for people with social preferences. Their main argument is based on the idea that the extremely high stakes involved in picking one candidate over another (in terms of expected social benefits) can roughly cancel out the extremely low probability of being a pivotal voter. (Though they don't credit him, these ideas draw directly on Parfit 1994.)
Edlin et al. do away with the "selfish assumption" of earlier voting models and assume that people take into account both benefits to themselves and perceived benefits to others. As the number of people in the electorate increases, so does the magnitude of the expected social benefit--because the small average benefit received by a typical citizen is multiplied by the increasing size of the population. This counteracts the problems that a large electorate poses in terms of decreased likelihood of decisiveness.
Thus, as population grows, the probability that your vote will be decisive falls, but the benefits (to society) of getting the better candidate elected grow just as fast as decisiveness falls.
The authors note that a "feedback mechanism" keeps turnout at fairly consistent levels in their model. Basically, this is the standard idea that low turnout increases the probability of one's vote being decisive.
The model performs better than previous rational choice accounts of voting because it predicts that the size of the electorate will not substantially affect voter turnout.
This model makes sense intuitively, but there are some potential problems with it. For example, it takes for granted that people care about all recipients of social benefits. It seems plausible, however, to assume that some people care much more about the people that they interact with on a daily basis. If voter X only cares about the benefits that will accrue to people living in his small town (or county, or state, or just family), then Edlin et al.'s model falls apart: The social benefits do not rise quickly enough to offset the drop in decisiveness; actually, the benefits taper off at some point while decisiveness continues to drop.
Note something important: Their model predicts certain empirical correlates, which are observed (notably in section 3)--but this doesn't prove their model, it simply fails to reject it. There are a variety of observable implications of this model, not all of which are necessarily deduced and written out by the authors.
Research on similar subjects