Let’s suppose a few things. First of all let’s suppose that you care about other people. Let’s quantify that care and say that you care about them, on average, one quarter as much as you care about yourself. This is, I think, a reasonable lower bound on how much most people would want to care, even if, in practice they often care less.
Let’s further suppose also that this article: http://www.stat.columbia.edu/~gelman/research/published/probdecisive2.pdf is still roughly correct about the odds of a single vote influencing the election, and so in the large majority of places your vote has odds of 1 in a billion (or better) of changing the outcome. In most places it’s going to be a fair bit better than one in 1 billion- the median looks to be around 1 in a 100 million, but we’ll say 1 in 1 billion for the sake of argument- using a pessimistic model so our assumptions are conservative.
Now we come to the question of how much your party winning is worth to everyone. Let’s quantify it in dollars for the sake of convenience. 1 dollar means something different depending on whether it goes to a rich person or a poor person, but we’ll abstract away from that here, because it shouldn’t make a difference.
The choice of American president effects not only Americans, but all people on earth, and even future generations. A president is in office for quite some time- four years. In order to stick with the trend of keeping assumptions conservative, let us say that you expect that the choice of the opposite presidential candidate to the one you prefer will have an effect, on average, equivalent to losing 500 dollars for the average American. Let us say that, further, it will have an effect equivalent to losing one hundred dollars for the average non-American- given the military and economic role of the US this seems plausible. This is over four years- or really, over a lifetime, due to to path dependency and long term effects. These are both modest figures which do not require that there be much difference between the two candidates.
There are 300 million Americans and 7.5 Billion non Americans, or thereabouts.
150000000000+750000000000=900,000,000,000 or a value of nine hundred billion dollars to tipping the US election result
Now 900,000,000,000 divided by 4 to represent our how much we care about other people factor is equal to 225 billion dollars.
So we’ve got about a 1 in a billion chance of doing 225 billion dollars worth of good. The normal way to deal with a combination of a probability and a utility or a dollar amount is multiply them: (225 billion)*(1 in a billion)=$225.
So the value of voting turns out to be equivalent to 225 dollars worth of good, spread evenly throughout the population. To put this in perspective, it’s about 12 hours worth of work at the median United States hourly wage.
Suppose you want to aim higher and love others as you love yourself. Thus you do not value the welfare of others only a quarter as much as you value your own welfare, but rather just as much. In this case voting is worth 900 dollars worth of good, or about 47 hours worth of work at the median hourly US wage.
Or suppose you thought that the lifetime effects of the choice of president were higher- this seems very likely true to me. Let us say that on Americans and non Americans respectively the average effects are 5000 dollars and 1000 dollars (and remember- this is over a lifetime). In this case the effect of tipping the election is 9 trillion dollars, and the expected value of a vote is $2250, or about the equivalent of three weeks work at median hourly wage wage. A huge contribution.
Maybe you believe the election will be rigged, a concern more widespread now than in any previous election in my lifetime. Here’s the thing. Rigging generally is a matter of degree- it’s about putting your thumb on the scales rather than erasing one vote total and replacing it with another. It is certain that there will be some activities I consider rigging adjacent on both sides of the aisle. This does not, in and of itself, make the estimate that your vote has about a 1 in a billion chance of swinging the election unreasonable.
So unless you care about other people very little, you should vote.
Responses to critics
Reddit user Barkappara argues: “Voting is fundamentally a collective action problem, not a decision-theoretic problem about individual action. The way I exercise political power through the ballot box shouldn’t be conceptualized in terms of my individual decision to vote: rather, I join a political coalition, and then my vote makes a contribution to the success of that coalition, and then I should view myself as receiving an amortized share of the credit for the outcome. This means my decision to vote is meaningful even in the overwhelmingly likely case that my vote is not “pivotal”.”
My response is that even if there are collective reasons separate from individual reasons for voting- and there may well be, I haven’t decided what I think- At most this shows that there are additional reasons to vote. It doesn’t undermine my case.
Reddit user Augustus_Augustus argues: “If the US presidential election ever literally came down to one vote, that would immediately lead to recounts and lawsuits, and the election would ultimately be decided by whatever some lawyer had for breakfast some day. I’m exaggerating, but remember what happened last time the election came within a couple hundred votes. It was ultimately decided by the Supreme Court. So it’s hard for me to envision a situation where any normal person’s vote “matters,” in the sense of being a clear but-for cause. (Of course, you should vote because it’s your moral duty to do so. If you really need a specifically utilitarian reason to vote, just add the goodness of voting to your utility function. Joking not joking.)”
My response is even if your vote will be irrelevant if it comes down to a tie due to court adjudication, assume that some number of votes for party x would decide the election for party x, and vice versa for party y, there must be some critical threshold at which your vote will make the difference- even if it’s unknowable. There has to be some threshold at which a court challenge wouldn’t be mounted or would fail, even if we don’t know it, just as, when a person is given a coffee and asked whether it is sweet, if they say yes there must be some nth grain of sugar such that if there were n-1 grains they wouldn’t say yes. The probability of your vote swinging a tie seems like a reasonable approximation of being this nth vote.
Kieran wants to know what happens if we redo the maths in terms of hours of time. Well suppose that the right president being elected is worth ten hours of leisure time for everyone on the planet, in terms of utility equivalent. Thus getting the lesser of two evils president is worth 78 billion hours of leisure time (I think it’s probably a lot more than this but whatever). This is, for reference, approximately 112,710 lifetimes. 78 billion divided by 1 billion is of course, 78 hours. 78 hours added to leisure and taken from work is equal to about a two week vacation. The value of gifting a random stranger a two week vacation seems, to me, worth the effort of voting.