This line of thought can be extended even further, in interesting ways. Of people who do vote, many (maybe most) don't vote for the sake of the general good, but rather (at least in part) for egoistic reasons. But since good-doing motivations far outweigh egoistic ones, this isn't merely selfish, it's irrational.
Zach is indeed awesome! But if this is really the whole argument, I have to disagree...
I'm sure this has been discussed ad nauseum in decision theory, but can it really make sense to say that a decision of mine has an "expected difference" when the only way that it will actually *make* any difference at all is if I am that insanely lucky swing voter? The reasoning is a fun little toy that we theorists can use to talk about this abstraction "expected difference", but it bears an extremely tenuous relation to actual decision-making.
The reductios are easy to generate: someone will, soon enough, cure cancer and save 50 billion future lives. Given my social position and location in history, suppose I have a 1 in 1 billion chance of fathering the child that becomes that heroic scientist. It would be absurd to approach the question of whether or not to have a child by telling myself that in doing so I can expect to save 50 lives. I should expect to save no lives. I should expect the state of cancer research to proceed precisely as it would have if I had never had any child. Right? And so the same expectations ought to guide my voting behaviour.
Thanks for this. You are exactly right it does depend on the tiny chance that your vote will actually be the one. And reasonable people can disagree whether we should discount such tiny probabilities to zero. As you might guess, I happen to think that we shouldn’t (https://philarchive.org/versions/HILHTS-4), but some other philosophers think that we should. So that key underlying component of the post that you point to is indeed contentious.
I will say, though, that the odds that one vote will make a difference turn out to be surprisingly high, especially in relation to the potential impact. I think that that makes it a worthwhile exercise even if you disagree with the ultimate conclusion.
And, FWIW, Zach’s argument can show that the odds really aren’t all that low for statewide races like some Senate races. The odds for Nebraska and Wisconsin are both on the order of 1/50,000.
Nice post! For readers who are unsatisfied with the "dead heat" assumption, here's how the argument works, in the context of Avram's Pennsylvania example, if the PA race is close but not a dead heat.
Assume Trump leads in PA on the eve of election day, but it's close enough for Harris to have a >10% chance of winning the state. If Harris does win PA, given that she's behind, it is quite likely to be a narrow victory—so we'll ignore the cases where Harris receives receives more than 55% of the PA vote.
Given this, Harris has a >10% chance of receiving between 5 million and 5.5 million votes in PA. From among these, the outcomes that correspond to a closer race are more probable. After all, Trump is projected to win the state, and outcomes are generally more probable the closer they are to the projected outcome. (This assumption is sometimes called "unimodality," and all election models I am aware of are unimodal.)
So the chance of a 5M to 5M tie is at least 10% × (1 in 500,001) ≈ 1 in 5 million. So you'd have a 1 in 5 million chance of being the deciding vote in Pennsylvania, and if Pennsylvania has a 20% chance of being a decisive state, then (assuming independence between PA's being decisive nationally and your being decisive within PA) your chance of tipping the election would be about 1 in 25 million. I get an expected impact of $100,000 per vote in PA, when combined with the other estimates of value made in the text.
This line of thought can be extended even further, in interesting ways. Of people who do vote, many (maybe most) don't vote for the sake of the general good, but rather (at least in part) for egoistic reasons. But since good-doing motivations far outweigh egoistic ones, this isn't merely selfish, it's irrational.
I wrote a post arguing that last year: https://open.substack.com/pub/dylanrichardson/p/why-not-vote-on-principle?utm_source=share&utm_medium=android&r=rj6jj
Zach is indeed awesome! But if this is really the whole argument, I have to disagree...
I'm sure this has been discussed ad nauseum in decision theory, but can it really make sense to say that a decision of mine has an "expected difference" when the only way that it will actually *make* any difference at all is if I am that insanely lucky swing voter? The reasoning is a fun little toy that we theorists can use to talk about this abstraction "expected difference", but it bears an extremely tenuous relation to actual decision-making.
The reductios are easy to generate: someone will, soon enough, cure cancer and save 50 billion future lives. Given my social position and location in history, suppose I have a 1 in 1 billion chance of fathering the child that becomes that heroic scientist. It would be absurd to approach the question of whether or not to have a child by telling myself that in doing so I can expect to save 50 lives. I should expect to save no lives. I should expect the state of cancer research to proceed precisely as it would have if I had never had any child. Right? And so the same expectations ought to guide my voting behaviour.
Nicholas,
Thanks for this. You are exactly right it does depend on the tiny chance that your vote will actually be the one. And reasonable people can disagree whether we should discount such tiny probabilities to zero. As you might guess, I happen to think that we shouldn’t (https://philarchive.org/versions/HILHTS-4), but some other philosophers think that we should. So that key underlying component of the post that you point to is indeed contentious.
I will say, though, that the odds that one vote will make a difference turn out to be surprisingly high, especially in relation to the potential impact. I think that that makes it a worthwhile exercise even if you disagree with the ultimate conclusion.
And, FWIW, Zach’s argument can show that the odds really aren’t all that low for statewide races like some Senate races. The odds for Nebraska and Wisconsin are both on the order of 1/50,000.
Nice post! For readers who are unsatisfied with the "dead heat" assumption, here's how the argument works, in the context of Avram's Pennsylvania example, if the PA race is close but not a dead heat.
Assume Trump leads in PA on the eve of election day, but it's close enough for Harris to have a >10% chance of winning the state. If Harris does win PA, given that she's behind, it is quite likely to be a narrow victory—so we'll ignore the cases where Harris receives receives more than 55% of the PA vote.
Given this, Harris has a >10% chance of receiving between 5 million and 5.5 million votes in PA. From among these, the outcomes that correspond to a closer race are more probable. After all, Trump is projected to win the state, and outcomes are generally more probable the closer they are to the projected outcome. (This assumption is sometimes called "unimodality," and all election models I am aware of are unimodal.)
So the chance of a 5M to 5M tie is at least 10% × (1 in 500,001) ≈ 1 in 5 million. So you'd have a 1 in 5 million chance of being the deciding vote in Pennsylvania, and if Pennsylvania has a 20% chance of being a decisive state, then (assuming independence between PA's being decisive nationally and your being decisive within PA) your chance of tipping the election would be about 1 in 25 million. I get an expected impact of $100,000 per vote in PA, when combined with the other estimates of value made in the text.