In the comments thread to Chris’ post on tactical voting, Michael Otsuka very sensibly suggests
I believe there’s an extensive, sophisticated social science literature on the expected utility of voting in elections which has made some progress beyond the speculations posted above. Could anyone who’s up-to-speed post a reference to an accessible summary to save us the trouble of trying to reinvent the wheel?
This brings me to one of those papers I’ve been meaning to write for years (I wrote a several drafts of a joint paper with Geoff Brennan, but we never quite converged), and which has finally (2005!) been written by someone else. The idea was to prove an assertion I’ve made quite a few times in academic papers, and here at CT, that, as long as voters have ‘social’ rather than ‘egoistic’ preferences, the expected utility of voting is independent of the size of the electorate, and potentially large enough to justify high levels of participation. You can read this paper by Edlin, Gelman and Kaplan (PDF file). There’s an excellent appendix on why the probability of a decisive vote is of order 1/n.
There’s still the question of why people vote when one side or the other is bound to win. EGK have a go at this, and in my paper[1] on the subject, I say
This approach, in which b [the social benefit of the preferred party winning] is a simple step- function, may be replaced by a more sophisticated one in which b depends not only on the party elected, but on the size of its majority. This would be consistent with the fact that there is a substantial, though normally reduced, turnouts in elections which are perceived as foregone conclusions.)
That’s not a complete solution, and I think it’s also important to consider that voting per se is considered as a social duty or as yielding social benefits, but I think it’s at least as important as expressive motives.
fn1. Quiggin, J. (1987), Egoistic rationality and public choice: a critical review of theory and evidence’, Economic Record 63(180), 10–21.
{ 7 comments }
Michael Otsuka 04.16.05 at 6:24 pm
Thanks for the post and the link!
Chris 04.17.05 at 2:57 am
Nice paper.
I think I mused in one of the comments threads about whether the expected social benefit of party A rather than party B winning could normally be rationally justified as large enough (given uncertainties about how things will turn out etc.). With some elections I’m willing to grant that it could (Bush-Kerry?). But what about two-party systems where the parties really have converged because of competition for our old friend the median voter? I guess this model should predict lower turnouts in those cases, but my hunch is (based on not looking at any data whatsoever) that this isn’t what actually happens in elections answering that description.
John Quiggin 04.17.05 at 4:15 am
I wouldn’t like to push a claim of full rationality here, but I think the correlation between turnout and perceived difference goes the right way. For example, IIRC, turnout rose in the US in 2004 after a long period of decline, which would match our shared perception of party differences.
Again, I think you have to include social duty to vote as a partial explanation. But this works fine as against egoistic or expressive voting. Suppose you think the preservation of parliamentary democracy in Britain is worth 5 billion pounds, and assume for simplicity that 100 per cent turnout would guarantee this, while zero turnout would mean no democracy. Then, while there may be some nonlinearity somewhere in the scale, that yields an average social benefit of 100 pounds from voting as opposed to non-voting.
Justin 04.17.05 at 11:55 am
Shouldn’t answers be tied to actual behavior. Socially, we know that certain people will vote no matter what, out of a sense of obligation, out of a sense of participating in the democratic process, etc. In other words, if Schumpeter is correct, in order to continue the ruse that democracy really provides choice.
If economics wants to continue to be viewed as a serious field, it should not only attempt to find answers to paradoxes it cannot explain that are no longer paradoxically but also actually connected to the real reasons things happen. OTherwise economics becomes nothing more than an irrelevant game of consistency-with-false-premise.
km 04.19.05 at 11:52 am
Sorry to keep harping on the 1/n business, but I don’t see how their assumption that the difference is of distribution f(d), *independent* of the number of voters, is all that reasonable.
If I were conjuring a model, I’d probably end up with something like a binomial model with n trials where the parameter is chosen according some distribution. Unless the parameter is exactly 1/2, then the chance of being a decider is exponential in n.
Michael Otsuka 04.20.05 at 6:11 am
_Shouldn’t answers be tied to actual behavior._
It depends on the question, and it’s not clear from your post which question you had in mind.
Andrew Gelman 04.20.05 at 10:10 am
Thanks for the plug. In brief: we understand voting as a rational act, given that a voter is voting to benefit not just himself or herself, but also the country (or the world) at large. (This “social” motivation is in fact consistent with opinion polls, which find, for example, that voting decisions are better predicted by views on the economy as a whole than by personal financial situations.)
This rational social motivation can have implications not only on whether to vote, but also on which candidates you will choose to vote for.
We discuss further here: http://tinyurl.com/84xos
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