The irrationally vocal proponents of the notion that ‘voting is instrumentally irrational’ have become perceptibly more vocal as it has become sure that there is a large difference between the two major-party nominees for President this year—which is unfortunate, since a large candidate differential weakens their claim.
What’s the basis for the notion that voting is an ‘instrumentally irrational’ activity? It’s that the expected benefit of a single vote to the voter herself is not substantial. That conclusion comes about from studying this equation:
Expected social benefit of a vote = (Probability of casting deciding vote)(Candidate differential)
There is no definitive method for estimating either of the values on the right-hand side, but the size of the probability value is less in doubt. Andrew Gelman, Nate Silver, and Aaron Edlin (2012) review the credible literature and persuasively peg the probability of deciding a contemporary U.S. Presidential election at one in 60 million for the typical voter.
How to estimate the candidate differential? Form your own. Do you think, say, that U.S. GDP would be one tenth of one percentage point higher, each year under a Clinton administration, than under a Trump administration? Well, U.S. GDP is $18 trillion a year, so over four years that difference amounts to over 70 billion dollars. GDP is far from everything that matters, but in a quantitative exercise, it gives one a starting point, from which one can make whatever adjustments one likes. Take your own estimate of candidate differential and divide it by 60 million to get the expected social benefit of a vote. Seventy billion divided by 60 million, for example, is over one thousand dollars.
The tension comes in with the recognition that the social benefit of a single vote is not paid directly to the individual voter. The voter bears the cost of making the decision and taking an hour to cast a ballot, but the benefits of each single vote are spread over the nation and world. One thousand dollars divided by 320 million persons is a quarter of an eighth of a hundredth of a cent, and so if the voter ‘acts alone,’ uncoordinated to others, she personally gains almost nothing. But all this is to say only that the voters face an ordinary free-rider problem—little different from any problem of providing public goods—and so voters can benefit personally from the overcoming of the problem.
Imagine that 20 million persons who had planned not to vote become otherwise coordinated, perhaps by a compelling meme that convinces them to vote for Clinton. The election swings from, say, roughly a tossup, to a sure Clinton victory, at the cost of, say, an hour for each of the 20 million voters. Counting that as a $50 cost for each voter, that’s a total social cost of $1 billion—but the increased certainty of Clinton’s election equates to an increase in expected GDP over four years of $35 billion, using the GDP-based hypothetical above. If the sixteenth part of that gain accrues evenly to the 20 million marginal voters, they will each eventually have about $100 in extra income—twice the $50 cost incurred in one’s casting a vote. In other words, 20 million fractions of a cent do add up.
I don’t much endorse this Downsian framework for purposes of understanding why 125 million Americans vote, but it is a worthy exercise in service of one’s own decisionmaking process. The kind of person who is enough engaged in political talk to be reading this blog post should be aware of the size of the expected social gain that one declines to confer, in return for an opportunity to ‘express’ one’s idealism through an also-ran candidate, or alternately for an hour of free time.
Sweet Talk 
It’s interesting that you see voting as overcoming the free-rider problem when I see it as a manifestation of the free-rider problem. I guess it’s because I take into the account the fact that lots of voters don’t pay income taxes. Which means that they are voting to receive benefits that other people paid for.
After 9/11 there was quite a bit of popular support for the war on terror. But lots of people who supported the war weren’t exactly the ones who were going to have to be directly bearing the burden of war. It’s a problem when people can’t directly feel the burden of their decisions. Their decisions become a lot less rational. Democracy minimizes the rationality of decisions. Spending does the opposite. This is why we should replace voting with spending (coasianism).
Neither strategic voting nor protest voting make any sense in a presidential election. Thankfully, the decision-making process for voting in a presidential election is blessedly simple: just vote for who you actually want to become president. http://gillette-torvik.blogspot.com/2012/09/on-voting.html
The paper quite persuasively gives a very different number for swing states than other states, with some order of magnitude difference. The same logic in the paper would also strongly recommend confidently announcing one’s support for the ideal candidate and attempting to persuade people in the months before the election, only moving to a strategic vote at the last minute based on polling – and changing one’s vote only if one’s state is close. This is indeed what most people who profess third party intentions do in reality, so there is little concern.
Indeed, similar logic would find it dubious to dissuade people from indicating third party preference at any early stage in the process, for fear of missing out on the unlikely chance of starting a preference cascade that leads the independent or third-party option of being the strategic choice, if that option would positively affect GDP.
John, good comments.
Some third-candidate supporters fail to go through with it, but we still see results like John Anderson getting 6% in 1980, Perot getting 19% in 1992 and 8% in 1996, and so on, so there is more than “little concern.”
We will also disagree on what is an “early stage in the process.” June of the election year, when third-party candidates usually start to be heard from, is to me very, very late in the election cycle. The prospect of convincing 40% of Democrats and 40% of Republicans to abandon their nominees between June and November should appear to you to be an all but hopeless prospect, particularly when you observe that it is not happening this year. Candidates serious about winning start two years ahead of time and pursue the nomination of one of the major parties. I think activists should contest the primaries behind a good (not “ideal” candidate, there is no such thing), vote for the better major-party candidate in the general election, and then contest the next cycle’s primary, etc.