Two Thoughts on the ‘Voter’s Paradox’

Freakonomics guest blogger Ian Ayres links to some interesting new work on the problem of voting:

A Poll Tax on Selfishness – Freakonomics – Opinion – New York Times Blog:

On a wintry night a few weeks ago, I was walking with Aaron Edlin across the Harvard campus when he casually claimed that the “voter’s paradox” wasn’t generally true — that it could be rational for people to vote for purely instrumental reasons.

I did a double take, because the chance that my vote will change the result of any election in my lifetime is vanishingly small. People might vote because it gives them pleasure, or because of its expressive value, but most economists think that it would never be worth your while to vote in order to impact an election, because of the small probability that any one vote is “pivotal.” But Aaron, together with co-authors Andrew Gelman and Noah Kaplan, has written a very important article showing that it can be rational to vote if you care about other people. If you care even a little bit about the welfare of your fellow citizens, then as the electorate increases, even though the probability of being pivotal becomes small, the impact of being pivotal becomes large. Thus, it can be instrumentally rational to vote even in winner-take-all elections with very large number of voters.

Two quick thoughts on the rational voter problem, i.e. why would any rational person vote if the odds of their vote being decisive were small?

First, while Gelman and Kaplan provide an interesting solution by invoking an “other-regarding preference” (i.e. the radical notion that a person might care about the well-being of others*), I don’t know that you need it. One other way that I have not seen discussed much is the idea of a voter caring about the margin of victory. The argument would go like this – the more votes a candidate wins by, the bigger the mandate that candidate will have as an elected official, and thus the easier it will be for that candidate to enact policies. Assuming you vote for a candidate whose policies you like, the increased odds of that candidate being able to enact those policies gives you an expected benefit. The parameter is nearly continuous – every vote counts – and so we don’t need to assume that your vote is all at decisive. It also deals with the issue of strategic voting – a vote for a 3rd party candidate with no chance of winning because it does not increase the margin of victory (or decrease the margin of defeat) for your 2nd most preferred candidate.

A second possibility invokes a notion I am still trying to work through that looks something like ‘buy-in’ or ‘ownership’**. Basically, I want to argue that people care more about things they are somewhat responsible for. As an example, there is a satisfaction from cooking a meal yourself that you don’t get by eating out, even if the food is ‘tastier’. Because you feel responsible, the highs are higher and the lows are lower. I wonder if we see something similar in elections. For example, the “Don’t blame me, I didn’t vote for him” sorts of campaigns, but also the feeling of victory you get when ‘your’ candidate wins.

What I love about the voting paradox is that it’s a perfect example of the usefulness of rational choice theory. The paradox isn’t really a paradox, because the assumptions are clearly false. The question is, what assumption do we do away with and how? It makes us drill deeper as to try to understand why people vote or not, strategically or not, etc.

* Oh, economists.
** I bet someone with a psych or social psych background could refer me to some studies that could clarify this idea.

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