# Two More Cents on the Value of Campaign Contributions

My last post suggested that a campaign contribution to your preferred presidential candidate is a very good investment even though the chance of your money changing the result of the election is very small. The argument relies on the estimation that the value of a vote is greater than the approximate cost of adding one vote to a candidate’s margin. We might think of the presidential election as a lottery: when you vote, you obtain a ticket with a 1-in-60 million probability of hitting the jackpot. If the jackpot is worth \$1 trillion, and assuming risk neutrality, the value of a ticket is \$16,667. If an additional \$1 in campaign spending adds more than 0.00006 votes (i.e., 1/16,667) to a candidate’s margin (and, as I note in the previous post, there’s research that suggests it adds much more than that), then giving a \$1 to your preferred candidate seems like a wise allocation of funds.

I’ve heard three objections to this argument in the last few hours, and I’ll try to address them here:

1. Aren’t we risk averse? And if that’s so, wouldn’t we pay much less than \$16,667 for a 1 in 60 million chance of winning \$1 trillion?

Yes, but that doesn’t mean we would pay less than \$16,667 for a 1-in-60 million chance of swaying the presidential election. That’s because the reasons we’re risk averse in other contexts don’t lead us to risk aversion in this context. First, one source of risk aversion is diminishing marginal utility. The value that I assign to one scoop of ice cream is greater than 1/10 of the value I assign to 10 scoops of ice cream, so I wouldn’t give up one scoop for a 1/10 chance of winning 10. (Unless, perhaps, the 10 scoops might be mocha chocolate chip.) For the Clinton supporter, however, there is no diminishing marginal utility to not-Trump. That is, there is no obvious reason why I would value a 2-in-60-million chance of swaying the presidential election to Clinton at any less than 2 times the value I would ascribe to a 1-in-60-million chance of swaying the presidential election to Clinton.

A second reason for risk aversion (and perhaps a more powerful one) is loss aversion: for reasons apart from the diminishing marginal utility of income, most of us perceive the pain of an \$X loss to be greater than the pleasure of an \$X gain. And so I won’t relinquish \$1 for a 1-in-10 chance of winning \$10, because the pain of a \$1 loss is greater than 1/10 the pleasure of a gain of \$10. One might ask whether this is a behavioral bias and, if so, whether I ought to let it drive my rational decisionmaking. But even if loss aversion is rational, I don’t think it changes the analysis here. If I perceive a Trump victory as a loss in relation to my reference point, then loss aversion should weigh in favor of contributing to the Clinton campaign. Put differently, each lottery ticket buys me 1/60 millionth of an insurance policy against a Trump win, and risk aversion and loss aversion lead us to buy more insurance, not less.

2. One friend who lives in a swing state asked me whether I would pay him \$16,000 so that he votes for Clinton instead of Trump. I declined. Doesn’t that suggest that I’m not putting my money where my mouth is?

No. First, vote-buying is a federal crime carrying a maximum prison term of two years, and the value of a vote to me is less than the cost to me of two years in prison. Second, and perhaps more significantly, I assign a very high value to living in a democracy in which votes can’t be swapped for cash. To be sure, campaign spending appears to add to a candidate’s vote total, and that’s a bit like buying votes, but persuasion of an independent mind is still an intervening step on the causal chain. We still can have a functioning democracy even though financial resources affect electoral outcomes, but I don’t think we can have a functioning democracy in which votes are sold at auction. And the reason why I’m willing to assign such a high value to the outcome of this year’s presidential election is because I think that one of the candidates is a threat to our democracy. I’m willing to trade cash for a well-functioning democracy, but I’m not willing to trade cash and a well-functioning democracy for a well-functioning democracy.

3. If I think that each additional \$1 increases my preferred candidate’s total by more than 0.00006 votes, and if I assign a value of more than \$1 to 0.00006 tickets in the presidential election lottery, wouldn’t this lead me to give everything I can to my preferred candidate?

No. Under the Federal Election Campaign Act (FECA), the most I can give to a single candidate for a single election is \$2,700. I can give an unlimited amount to super PACs, but again, we get to the question of democratic values. My own view is that individual contributions to candidates within the FECA limits are consistent with a well-functioning democracy, while unlimited spending by super PACs is not. One might say that super PACs will exist whether or not I participate, so what’s the harm of throwing my dollars into the hat too? I’d offer a response along the same lines as the initial argument for the value of a vote. Just as a very small likelihood of making a very big difference still can be worth a lot, a very small contribution to a very big problem still can carry a high cost.