The Value of a Vote — and of a Campaign Contribution

Thought experiment: Imagine that you have the power to pick the next President (and, for purposes of the thought experiment, set aside the obvious democratic legitimacy concerns that arise from a single individual having the ability to determine the election result). Now ask yourself: If you had this power, and if a stranger on the street offered to buy the power from you, what’s the lowest price you would be willing to accept? (Assume that the stranger doesn’t know your political views and that you don’t know the stranger’s.)

The answer, at least in my case, would be a lot. Definitely more than $1 million. Definitely more than $1 billion. This presidential election, I think I would put it above $1 trillion. The value of keeping our nuclear keys out of a certain candidate’s hands is, in my view, astronomically high. (Not that $1 trillion in spending money wouldn’t be nice too.)

Aaron Edlin, Andrew Gelman, and Noah Kaplan have used similar logic to show that voting is entirely rational even if the probability that your vote will sway the outcome is very, very small. Let’s say that the probability of any one vote determining the outcome is 1 in 60 million. (That’s what Gelman, Nate Silver, and Edlin estimated was the average voter’s chance of being decisive in the 2008 presidential election, based on state-by-state forecasts one week out.) Multiply $1 trillion by 1/60 million and you arrive at a value of $16,667 per vote — higher in some states, lower in others. Another way to think of this: If I believe that the rest of humanity will be at least $1 trillion better off if my preferred candidate wins next Tuesday, then voting is like making a $16,667 charitable contribution — and a worthy allocation of a half hour or so of my time.

Edlin, Gelman, and Kaplan calculate the value of a vote state by state for the 2008 election using a $300 billion value for the overall election outcome— a figure that seems plausible in the context of a Barack Obama vs. John McCain race but too low this time around. In any event, my objective here is not to rehash their logic but to suggest an extension.

Other research indicates that spending on a candidate’s campaign increases that candidate’s probability of victory. Alan Gerber canvassed various studies and found that estimates of the approximate cost of adding one vote to a congressional candidate’s vote margin ranged from $12 per vote to $367 per vote. (In his own experiment, Gerber estimated that the cost of adding one vote to a congressional incumbent’s general election total was about $165.) Extrapolating from congressional elections to presidential elections is unreliable, but even if the high-end estimate for House races is an order of magnitude too low, that’s a cost of $3,670 per vote, versus a value (per above) of more than $16,667.

There are, to be sure, caveats to attach. There is probably diminishing marginal utility to an additional $1 in campaign spending (and the candidates plus their parties plus supporting super PACs have raised more than $2 billion so far). And it might well be the case that the marginal utility of an additional $1 at this point is zero. But then again, this is all a probability game: if there is a 50% chance that the marginal value of an additional $1 is zero, and a 50% chance that it’s $3,670, then it still makes a lot of sense to donate to your preferred candidate if the value of a vote is $16,667.

This isn’t to suggest that you should direct your browser to your preferred candidate’s website right now and donate $3,670 so as to increase the candidate’s expected vote total by 0.5 (or maybe by 10, or maybe by zero). For one thing, that would be illegal: the maximum contribution to a federal candidate is $2,700 per election (note that you can give more to PACs and parties, and an unlimited amount to super PACs). This is to suggest, though, that contributing to your preferred candidate’s campaign may be a very, very good investment, even though the chance that your contribution will put that candidate over the edge is very, very small. One might even ask whether it’s irrational for individuals with strong feelings and spare funds not to max out this election cycle, assuming that they can part with $2,700 and not experience too much personal pain. Individuals with less to spend might choose a smaller sum. You might consider it an insurance policy against the extreme guilt that you will feel if your preferred candidate loses by the narrowest of margins and you’re stuck wondering whether your contribution might have made the difference.