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.
Grafstein. 1991. An evidential decision theory of turnout. American Journal of Political Science 35 (November): 989-1010.
"Causal" decision theory--i.e. the standard calculus of voting--runs into problems by wanting an individual's actions to have a causal effect on the outcome (i.e. by including the p term). Grafstein advocates a switch to "evidential" decision theory, which involves choosing the action with the highest expected utility. Although causal and evidential decision theory usually lead to the same conclusions, they do not in the case of turnout; this is Grafstein's.
If I wished to intercept my colleague on his way to work, and I had preferences very similar (nearly identical) to my colleague's, then the best way to intercept him would be to ask myself, "If I were walking from his home to the office, which route would I take?" Since we are so similar, I would know where to go to find him.
Grafstein cites this as an analogy to explain voting. Suppose there are two political groups. I know that members of my group have much in common with me. As such, I know that my group is more likely to turn out at the polls if I am more likely to turn out at the polls myself.
Thus, my decision to turn out is rational; the conditional expected utility of voting is higher than the conditional expected utility of not voting, since my decision to vote reflects my group's decision to vote, and my group is certainly large enough to affect the outcome.
The remainder of the article is devoted to a formal proof that these premises lead to equilibria predictions in line with the turnout levels we actually observe. Unlike "causal" decision theory, in which I vote only if my personal vote will be decisive, this correlation between my behavior and the behavior of others in my group makes turnout rational under "evidential" decision theory.
On pg 994, we read, "Over time, of course, an agent can act out of character and foil the statistical dependence. By the same token, acting out of character cannot be the agent's expected, rational behavior, since a change of type is not something an agent simply wills into existence." Did Grafstein just shoot himself in the foot?
In particular, is the colleague example a false analogy? I locate my colleague by choosing the path that I like most between his home and his office; we have such similar preferences that this method works. But if I acted against my first preference and chose to use a different path, would I have any reason to expect my colleague to switch paths as well? Absolutely not.
Yet when it comes to voting, this is exactly the story Grafstein wishes us to accept. It is probably correct that I can estimate whether people like me are likely to vote based on my own desires to vote or not. Therefore, when I follow my honest desires, it is true that my actions will correlate with those of people like me. But suppose my honest desire is to abstain. Should I believe that by acting against this desire (and voting) that others like me will do likewise? Absolutely not. (But see Quattrone and Tversky 1984 for evidence to the contrary.) []
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