Gerry Mackie writes, regarding our work on the rationality of voting. He had a specific question about the probability of a decisive vote. I’ll give his question, then my reply, then some more paragraphs of his, discussing motivations for voting.
Did you notice the fairly comprehensive review article by Keith Dowding in the British Journal of Politics and IR, “Is it Rational to Vote? Five Types of Answer and a Suggestion,” 7:442-459, 2005?
Keith dismisses the public-interest argument, saying that p would be too minuscule. In the article he cites McLean, Mueller, Brennan and Lomasky, and Carling to this effect. In a footnote he mentions varied estimates by Riker and Ordeshook, Owen and Grofman, Beck, Mayer and Good, Margolis, Peters, Shachar and Nalebuff, Fischer, and Gelman et al. 1998. Another review is Feddersen, “Rational Choice Theory and the Paradox of Not Voting,” Journal of Economic Perspectives, 18:99-112, 2004.
The low p mentioned by Dowding is as low as 10 EXP -90, which would gut the public-interest account. Thus, a well-argued canvassing of the various estimates would be welcome.
Me: 10^(-90) is not even close to a reasonable estimate of p. 10^(-7) is more like it. I do not think p is too small for the public-interest argument because the benefit is multiplied by the number of people in the country.
I looked up the Dowling article and like his intro:
We know why people vote, or at least we know why people think they vote, because in surveys they have told us. . . . People
vote in order to express their preference for their preferred candidate, increase his or her chances of winning and because they feel they ought to.
However, I completely disagree with Dowding’s claim, also on the first page of his article, that “In decision-theoretic terms it is not rational to vote.” He ignores the social benefit from voting, which allows the benefit term to increase as as fast as the probability term decreases. (See here for more, including a link to our paper on the topic.)
At the top of page 448 of his article, Dowling briefly discusses some estimates of the probability of a decisive vote, but these are based on the so-called binomial model in which all voters are voting at random. More realistic probabilities can be obtained by election forecasting models (see our 1998 JASA paper) or by looking directly at the frequency of close elections (see our 2004 BJPS paper). We discuss these models in more detail in our 2002 Statistical Science paper. In short, the probability of your vote being decisive is on the order of 1/#voters.
The anarcho-capitalist economist at GMU, Bryan Caplan is writing a book on
voting, and there are some interesting things on his webpage.
http://www.gmu.edu/departments/economics/bcaplan/ See Economics 410
button, for example. In one paper, with references, he says that even the
most hard-bitten ego theorist would acknowledge that people are selfish no
more than 95% of the time. That would allow an alpha of 5/100, which
would yield an instrumental-altruist decision to vote in many
circumstances. Caplan follows Brennan in asserting that people vote for
its expressive value, a mistake I made in my Democracy Defended, Ch. 5.
To quote from what I’m writing now,
“Voting does have expressive value for most, but there are at least two
problems in counting expressive value as primary for most voters. Mass
voting is usually by secret ballot. If the expression is to self, one can
express the value to self without having to bother further with the fuss
of voting. If the expression is to others, then one could pretend to have
voted. Or, with greater expressive satisfaction than checking off a box
in a curtained booth, one could write letters, organize demonstrations,
conduct vigils. If the expressive value of voting were primary, then no
one would object if voting were made advisory rather than binding.” Also,
“For Nader voters in Florida in 2000, it could be that the expressive
value of voting for Ralph exceeded any instrumental benefit from Gore
beating Bush. Or perhaps the balance of the expressive and instrumental
value was not well understood in 2000, as the Florida vote for Nader
dropped from 97,488 in 2000 to 32,971 in 2004.” The second problem with
expressive voting is the incidence of strategic voting in mass elections.
The decisiveness criterion seems fishy at times. For a nice philosophical
discussion, see Alvin Goldman, “A Causal Responsibility Approach to
Voting,” in David Estlund’s edited volume, Democracy. The issue is
overdetermination and causal responsibility. To give you an
idea…suppose a firing squad of ten who fire at the same time and hit
their victim. Suppose I’m one of the shooters. I say that if I had not
shot he would have died anyway. Thus, I’m not responsible for his death,
but neither is any other individual. There’s much more. If decisiveness
is wrong, and something like Goldman is right, voting is still about
contributing to the public interest.