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.
Feddersen. 2004. Rational choice theory and the paradox of not voting. Journal of Economic Perspectives.
A review of the rational paradox of not voting. For a more recent and slightly more complete review, see Geys (2006). Relative to Geys, the strengths of this review are its more detailed discussions of game theoretic and information-based approaches to the paradox (and their shortcomings). Since Feddersen is writing in an economic journal, he is able to treat these models more mathematically than Geys.
Feddersen argues that recent group-based explanations of turnout are most promising. He subdivides these explanations into two approaches: group-based mobilization, and group-based ethical voter models.
Ideologically similar voters are mobilized by their leaders. These leaders incur some positive cost in order to mobilize their followers. In a sense, this has the effect of reducing the voting game to a handful of players (group leaders) rather than millions of potential voters, making the paradox of not voting evaporate. Each leader decides how many of his resources to expend on mobilization. Morton (1991) finds that there is an equilibrium with positive turnout if at least one leader has a strict preference for a single candidate. Later authors have extended this model to capture the mechanics of the US electoral college.
This model has all the right comparative statics. It predicts well turnout levels and other observed patterns. It has difficulty, however, with micro dynamics. Why do people join groups? Why do people listen to the leaders? Although some vote-buying surely takes place, it cannot explain the large levels of turnout that we observe. Perhaps leaders use social pressures to get group members to pressure one another; even still, if exerting this pressure is costly, why do group members incur the cost of sanction one another?
More generally, why do people join groups? If it is to act collectively toward a political end, then mobilization is epiphenomenal.
Ethical voters might be conceived of as those using a Kantian rule--these "rule utilitarians" receive a payoff (in addition to their policy-contingent payoffs) if they use a decision profile that satisfies the golden rule (i.e. social welfare is maximized). Thus, if some group of voters supports a candidate who will not maximize social welfare, these rule utilitarians will turn out knowing that if all the other rule utilitarians turn out, social welfare will be maximized (i.e. the bad guy loses).
Of course, we ought to allow that not everybody will agree as to who will maximize social welfare. This leads us to a more complicated model (from Feddersen and Sandroni 2002), which determines cost cutpoints. As long as voting costs are below a certain cutpoint, a type of voter with that cutpoint will turn out.
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