## Why it can be rational to vote

Just a reminder.

1. I still worry that the calculation requires the marginal would-be voter to place themselves in an epistemically privileged position: if half of all voters disagree with you, you should upweight the chances you’re wrong and they’re right. And in that case, how sure can you really be that you’re providing a public good rather than a public bad?

I expect my argument doesn’t hold in the current circumstances. But once America has returned to normality, it should.

• Eddie says:

Couldn’t agree more. And there should be an option in every race that says, “I do not consent.” Wonder how that would change the statistical argument.

2. Olav says:

It seems to me that all of these calculations that are supposed to show the probability of casting a decisive vote don’t really apply in practice, at least in the really high stakes elections. In practice, if the race is extremely close, then there will be recounts, legal complaints, and then more recounts, more legal complaints, and then ultimately the election will be settled more or less arbitrarily at some point. That’s what happened in 2000 after all!

I am also skeptical of using expected utility calculations when the probabilities are so low. Call me irrational, but I wouldn’t even spend \$50 on a lottery ticket that only has a one in ten million chance of winning, even if the prize were 30 billion –with those odds, I essentially know I’m going to lose, so I’d rather just hang on to the \$50.

• Andrew says:

Olav:

Regarding your second paragraph: The utility calculation is what it is. I don’t think utility calculations explain human behavior but they are relevant to answering a normative question—recall that in my essay I am, in part, responding to people making the normative claim that voting is irrational, so I think it’s worth responding on those terms.

Regarding your first paragraph: No no no no no. The point is somewhat subtle but with care it can be explained mathematically, that the possibility of recounts does not affect our calculation. Here’s what I write in the linked post:

And, no, it’s not true that “the closer an election is, the more likely that its outcome will be taken out of the voters’ hands.” See the appendix on the last page of this article for a full explanation, with calculus!

You can follow the link and read the appendix. This is a point that confuses lots of people, which is why we wrote it up mathematically.

• Olav says:

Ah that’s very interesting! I can see that my first paragraph is wrong.

But I don’t just doubt that expected utility calculations are descriptively accurate when the probabilities are small; at some point, expected utility breaks down as a normatively meaningful tool when the stakes are high and you’re dealing with events that have extremely low probabilities. I think that’s clear when we make the numbers even more extreme than they are in the election case. No rational (and non-rich) person would bet \$100,000 on a lottery in which there was a one in a billion chance of winning \$200 trillion (and no other prize). Granted, the election case isn’t that extreme, but voting (especially informed voting) costs time and effort and the probability of having an effect is extremely small, as your calculations show.

• Olav says:

To put the point another way: in large lotteries in the US, it actually regularly happens that the prize is large enough that one ought (from an expected utility point of view) buy a ticket. But I’d say that playing the lottery is still not rational in those cases.

• Andrew says:

Olav:

Once you consider taxes, net present value, and the possibility of having to split the prize, I don’t think it’s so common at all for lottery playing to have positive expected monetary value.

• Olav says:

Maybe you are right. But do you think it’s rational to play the lottery, provided the expected payoff is greater than 0?

• Andrew says:

Olav:

It depends on the odds and what you’d do with the money. If we’re just talking expected monetary value, I wouldn’t be responding to blog comments, an activity that takes time and pays me \$0. Nor would I go to the movies . . .

• Olav says:

Sure, the payoff from an activity is usually not just monetary, though in a lottery I’d think the payoff is pretty much just monetary. In any case, it sounds like you’re agreeing that the odds are important over and above the role they play in the expected utility calculation..?

• Pretty sure for most people the monetary payout of the lottery is just the incidental means to the real end, which is the secretion of various hormones and neurotransmitters, which is the effect that people are mainly purchasing. Kinda like taking drugs or looking at porn.

3. Thanatos Savehn says:

Because I’m the only real person and all the rest of you are (amusing) simulations?

• Dzhaughn says:

That is no reason to vote. We simulations are legion, and have marginal cost near zero.

4. “Surveys show that voters choose based on who they think will do better for the country as a whole, rather than their personal betterment.” So how many people think what’s good for them is good for the country? More seriously, how do we even measure how the “country as a whole” is doing?

Isn’t there also the sending a signal part of voting? I didn’t expect my presidential vote in 2016 to be decisive because I live in NY. But it did get counted in national election numbers (hopefully, anyway). But how representative are the votes of people’s intentions? It’s a user interface problem that can be manipulated. Let’s say I’m making the ballots and Joe is running against Susie, but I want to help Joe’s chances a little. I write the ballot this way:

Joe [ ] Susie [ ]

Some number of voters will mistakenly vote for Joe thinking they’re voting for Susie because Joe’s box is in front of Susie’s name. I seem to recall Steve Ansolabehere telling me that there was at least 1% voter error in most elections (that is, people voting for candidates they didn’t think they were voting for). This can obviously be helped with good UI. Here’s an article on Florida’s UI issues in 2000, which cites the MIT/Caltech voting project Steve was part of and it claims more like 4% error (though I didn’t read closely enough to see if that’s per ballot or per choice).

P.S. That Monkey Cage post is an ad crapshow. I need a better browser if I want to visit aggressive advertising sites.

5. theoryistic says:

Andrew, I’d like to see where specifically you got your fivethirtyeight information from and what they had to say. Can you post links and/or article info to find the specific original source(s)? Thanks.

• Andrew says:

Theoryistic:

I got it all from the fivethirtyeight site, just going from their home page which has links to the House and Senate elections, a few days ago when I wrote the post.

6. David Marcus says:

If you believe that there are other rational voters, then it is rational to vote. This is for the same reason that the Nash equilibrium is not relevant for rational players in the Prisoner’s Dilemma. See https://www.davidmarcus.com/Doc/Paradoxes.htm.

7. steven t johnson says:

I have to disagree…The point of voting for the winner is to express your political views. Unless you’ve placed a bet, it is not to make someone win. The real rationale against voting is not that it isn’t likely to make a difference…it’s that there is either no one whose views remotely match yours to vote for, a two party system effectively disenfranchising you. Or, because a two party system is basically In and Outs, voting your views does not affect policy. Again, this effectively disenfranchises you. Most educated people love the way the Founding Fathers devised a system to keep government from actually following the will of the majority. This is generally regarded as the essence of freedom. I suppose if you are a major property owner whose continued prosperity demands a government opposed to the welfare of the majority, this makes sense.

• Andrew says:

Steven:

This may be the case for you, that you don’t care about who wins the election. But most people who vote do care. Even if you don’t love your party, you might really dislike what the other party might do.

• steven t johnson says:

You are assuming it is rational to think that voting for a party you don’t like is somehow voting against the party you dislike more. That is the error. Consider the example of WV. The current governor ran as a Democrat, then switched to Republican. Voting Democratic wasn’t a vote against what Republicans might do. The Republicans in the legislature sat on a wasteful spending scandal until the now-Republican governor could make appointments, rather than call special elections. When convenient for them, they impeached the entire WV state Supreme Court. The dude promptly appointed Republicans to “interim” appointments, leaving incumbency advantage to Republicans and shortening Democratic Party campaigning. Voting for a Democratic governor wasn’t opposing what the other party might do. And of course the senator whose seat is up for re-election is Joe Manchin, who is notorious as a Trump supporter on many issues. Voting for Manchin is not voting for Trump.

I repeat, the two party system, with plurality single-district seats, rural overrepresentation, the anti-majority aspects of the Senate and Electoral College, plus deliberate favoring of the two extant parties, turns elections into In vs. Outs. Voting rarely aligns with policy, which is not an accident. This is regarded as a good thing. It simply is not possible to vote against. The votes are always for. Always. It doesn’t matter how much you dislike the other party, you cannot vote against them. If that makes you feel powerless, you should.

My opinions of course.