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 even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
Dowding. 2005. Is it rational to vote? Five types of answer and a suggestion. BJPIR 7:442-459.
Dowding begins by reviewing attempts to resolve the rational paradox of non-voting. I omit a summary of this review; see notes on Geys (2006) or Feddersen (2004) instead. Note, though, that Dowding does group the various works slightly differently. He views the various approaches through an explicit P*B-C+D lens; that is, he categorizes each proposed solution as modifying one of these terms in Riker and Ordeshook's calculus of voting.
Dowding is dismissive of "learning" or "adaptive" models of voting--in contrast to Geys, who was quite optimistic about them. He sees these models as plausible, but not rational. If we wish to resolve the rational paradox of voting, then, this model won't fit the bill. Similarly, this model leads to the empirically incorrect prediction that non-voting losers will almost always vote in the next election, and voting losers will almost never vote at the next election--despite evidence that the many of the same people turn out at every election, regardless of the outcome.
Dowding's main argument is a criticism of our attention to the paradox in the first place. First, the paradox is easily resolved by a D term--people 'do' claim to vote for expressive reasons, or to affirm their support for democracy. Though this begs the question of why some people have these motivations and others do not, it is still a rational answer to the paradox, so problem solved. Humans, after all, "are political animals and maybe we vote in order to justify our interest in politics."
Second, the paradox is less severe than we might think. It arises from the fact that no voter is likely to be a decisive voter, so the P*B is vanishingly small. But, Dowding asks, is this really true? Who wants to be decisive anyway? Prime ministers want strong support in parliament, not minimal support, and members of Congress want a "safe" seat, not a narrow victory. So if voters support these politicians, why would they want only for the politician to win by a minimal amount? There are real political benefits to having an overwhelming majority, and these benefits can certainly be felt by individual voters. Thus, individual voters do not need to be pivotal to have a desire to vote. They might want to turn out to support their side, to strengthen their leaders even more. Decisiveness, the core of the rational paradox, "has always been a red herring."
Dowding really wants us to step back and rethink what we want from a theory of turnout. We cannot plug values into a P*B-C+D equation and give a perfect approximation of turnout. But we do have an understanding of the marginal affect of these values. We know from repeated studies that an increase in B, or a decrease in C, or an increase in D, or an increase in P will lead to an increase in turnout. And, as Dowding points out, this is excellent. We can obtain real empirical predictions from these marginal relationships. It is frequently the case in economics and political science that we can understand only slopes, not the entire objective equation, and that is acceptable. Knowing the whole equation--why individuals actually vote--is interesting, but let's leave it to the political psychologists to sort out. For the rest of us, we should be quite satisfied with what we have learned so far, and we should continue doing what we can to understand these marginal effects even better.
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