I'm glad to see someone citing Dan M. Kahan. I used to read his entertaining Cultural Cognition blog a decade ago. It was one of my earliest experiences wading into various survey methodologies and data presentations. His observations, including the one you cited, have stuck with me.
I wish he were still writing his blog. The domain seems to have been taken over and reformatted; some of the pages are empty or seemingly AI drivel, but much of the original content can be found, albeit without dates, via the site map. I'm not sure what he's up to these days but I hope he's ok. I guess one reason academic journals exist is to last longer than blogs.
Your own survey results suggest that readers of this blog aren't in much agreement about who the better president is, casting a big doubt on those assumptions. Besides, actual regressions of economic growth (or whatever) and party in power show basically nothing. Most presidential elections don't matter. Maybe this one is a black swan (Elon thinks so), but it's a bad prior. It's also pretty unlikely to assume a potential efficiency improvement of 2.5% given the above findings. And furthermore unlikely much of this would be beneficial to you specifically. Governments would just spend that money on some half-brained idea.
The poll is very specific to the readership, so I don't think it tells us much about the broader principle, which is: If you could beat the median voter at even betting, you should vote.
Party in power may have no correlation with growth historically, but the individual candidates could still be very explanatory. Just as, when you're hiring someone, Harvard vs Yale on the resume may not have a statistically significant sign -- but having a good hiring manager is still important to get the right employee.
Regarding "unlikely much of this would be beneficial to you specifically": Certainly, market reactions to election day seem to say it'll matter to anyone with a stake in the economy. Additionally, anyone with social preferences, whether it's abortion or immigration, have a further incentive, if they care about the country going in a certain direction. As my article notes, it's true that the "selfish" value of a vote is low, but it's very high if one cares about the direction of the country as whole, not just as it relates economically to ones self.
I'm confused; you said specifically that you expect readers of this blog to be better than the median voter at picking good candidates, yet the readers of this blog are split close to 50/50 on who the correct candidate is. Doesn't this have to disprove your claim, at least with regards to this particular election? (It's possible in principle that readers are still better than the median American on average, but this particular election is harder to tell or something. Seems unlikely, but is consistent with the data.)
I guess that's true about this particular election, at least to the extent readers are split. (It seems to be shifting to a somewhat clearer conclusion as the day goes on.)
But yeah, I don't see much reason to think that generalizes to elections in general.
If you have a panel of expert job recruiters, and they deadlock about picking one applicant or another ... and a poll of the general public also deadlocks, that doesn't prove that the experts are no better in general.
I do see one problem in the math that no one else called out, which is that too much weight is assigned to the tails (i.e., too low of confidence on the most probable events). But I think it's because you're taking these probabilities directly from Nate Silver, who has been rightly criticized for this by e.g. Carl Allen.
Here Mississippi has like 3% of the value of PA, which is crazy. The probability of Mississippi being the tipping point state in this election is higher than the atoms in the state of Mississippi spontaneously arranging themselves into Godzilla and marching into the Gulf of Mexico, but not THAT much higher. Functionally zero, in either event.
But if anything, I think Silver's error here INCREASES the value of swing state votes.
Thanks. I think I agree with you that Silver's numbers overstate longshots. I did look into taking 538's estimates instead of Silver's for this reason, but theirs didn't seem much better. I don't have time to calculate those odds myself, so unless someone else does it better than Silver, this is for now the best estimate available.
Oh, I actually have a footnote on that: "I use Silver’s estimates, because his model has been good in the past, and because he’s the only one besides 538 who estimates this. I find some of his results surprising (are New Mexico, Mississippi, and Alaska really as valuable as he thinks?) but 538 actually has pretty similar estimates for those states, so — I guess the data is trying to tell us something."
Yes I think the 538 (Morris) numbers are even worse for this type of error. If you dig into the individual scenarios that his model generates they’re just wild. Like assigning non-trivial probabilities to Trump wins CA while Kamala wins TX kinds of events.
Again, read some of what Carl Allen has said here. Maybe there are others who have pointed it out.
When one of your five data points is so implausible that you throw it out, it's probably best to throw out any conclusion with it. Still an interesting attempt and worth sharing.
That thought crosses my mind, but I disagree, because:
A) There's a reason that datapoint doesn't work, while the others do: only 10% of the value is in the market signal, and hence it gets drowned out by the noise. When 50% or 80% of the signal of the President is in the market change, it IS likely to be valid.
B) It's still better than guessing, which is the next-best alternative.
The S&P500 only reflects the expected profits of 500 companies! You need to also account for smaller businesses, increased wages to employees, and of course consumer surplus. So the true value is likely 100x what you calculated, unless I'm making an error somewhere (possible).
I think Brennan's calculation is clearly wrong. If voting for the right candidate adds $3000, that's relative to voting for the wrong candidate; doing so then adds $0. It doesn't subtract $3000! There's no plausible scenario where neither candidate gets in and the dollar amount is zero. (Of course you can just as well say that voting for the wrong candidate subtracts $3000, and voting for the right one subtracts $0.)
I might accept +$1500 and -$1500 as compromise amounts, for a difference of $3000. But the other way gives a difference of $6000, which looks like double counting.
We thrash this sort of thing out in tabletop roleplaying games all the time. . . .
“ 1-in-a-million is the hard, proven, lower bound.”
Sorry, this is simply incorrect.
Because each outcome is NOT in fact equally likely.
Even with a fairly evenly divided electorate
Barnett said this was the case ONLY “If, for some reason, each of these outcomes were equally likely, then the probability that your vote is decisive would be exactly 1/1,000,001”
But there is NO reason the outcomes are equally likely, and overwhelming reason that they are not remotely equally likely.
But when we consider that they are not equally likely, we realize that it's outcomes in the middle that are much more likely, which increases the value of a vote. That's why it's a lower bound.
My apologies. You are correct in this case (there are “weird”, or at least uncommon, cases where you would not be, but basically you’re right).
OTOH there is clearly something wrong with your formula for “value” of vote that non-swing states have such relatively high values compared to swing states. Because the odds of one of those non-swing states tipping the election is pretty small in the first place, on top of the chance that your vote will be the deciding vote in that state.
There is just no way, e.g. that Idaho vote value is as high as 1/1000th of Pennsylvania.
(The absolute values, of course, are impossible to know and relatively uninteresting, even as I *do* agree with your premise of a high social value of a “correct” vote in a swing state.)
The problem with using the stock market as a valuation tool for the importance of politics is that there is some literature suggesting that share price growth is negatively correlated with growth and thus may (likely) has an overall negative relationship with welfare, but at an unknown rate (e.g. there's no guarantee that $1 dollar extra in the sharemarket = -$1 dollar of welfare). Others find not much evidence of correlation in either direction e.g.: https://www.boeckler.de/pdf/v_2022_10_22_joebges.pdf
I don't think this works to justify voting. Even if your vote is worth ~$10,000 to society as a whole, you personally capture essentially zero of that value. Voting is still not personally rational.
Good attempt, but it's still not convincing about the rationality to vote. The sheer amount of issues you'd have to know and be rational about are absurd. For example, despite being someone who has obsessed over political issues for years to try be "right" about them, I had no idea that PEPFAR was a real program until Bentham's Bulldog mentioned it. If he's right, it saves a lot of lives, and so it should play an important role in our calculation for who should win the president.
Further, I have many hours thinking and reading about political issues as a "rationalist" type, yet I *still* don't feel informed enough about many issues. While I'm sure of libertarianism, I'm not nearly certain about how libertarian I should be even if I lean towards anarchy. I assume libertarianism based on economic/philosophical theory as a presumption/prior even on issues I don't know much about, but i came to this position through hours of research as a "rationalist" type. For most people, being this well-researched is a full time job beyond the cost of voting in a swing state, and this probably includes rationalists. And to be certain and have more than just a prior, I still feel like I need to read a lot more about the issues.
Even then, I don't think even the most rational prediction people could have predicted the Iraq War or Trump as a backlash to Obama vs. some other generic Republican candidate. I think the best case for voting you can make is that one could vote for the libertarian candidate to possibly be the decisive vote that forces the parties to pander to libertarians more. But even then, they have to follow through on their promises, which is too difficult to predict, like dovish Bush.
But are you sure you're setting the bar at the right level? Do you perhaps already know more than enough to beat the median voter in a wide range of bets about the future? If so, you would add rather than subtract from the picking of a President.
It's not just whether I would add to the expected value of the vote, it's how much I would add.
I think there's a small chance that Trump could attempt to establish a dictatorship based on 2020. I also think there's a small chance that Kamala actually attempts a net zero emissions plan, flings the US into an economic free fall, and then mass poverty. I don't know how to weigh all of these things. Just because I'd do *better* than the majority of the population doesn't mean I'd do good enough to justify a few more dollars of expected value.
can the dollar value of a vote really be calculated in this way?
Say person a promises to give person b 1 trillion dollars a week into the future if person b gives person a the contents of their wallet immidietally.
The chances of person a following through on their promise is infinitessimally small. But does it then follow that if person a offers an infinitely high number that at some point person b should agree and cough up the money?
Or to pick a more tangible example, can't this same argument be made to assasinate a world leader or for everyone to runndor US president?
It's kind of similar to Pascal's wager in this way.. At a certain high level of improbability, I'm just not persuaded that any level of consequence is sufficient to justify action on an individual basis.
Especially when, for example, refusing to vote in a secured state serves as a protest throwaway try and vote to hold candidates accountable.
That hypothetical isn't relevant, though, because we're not talking about an implausible promise to give money -- we're talking about market projections of what will happen to the country. And we know the President has a big impact on the economy, though policy. So it's very different from the hypothetical you floated.
I disagree that "refusing to vote in a secured state serves as a protest throwaway" -- or at least, it's certainly not an effective one. Voting 3rd party might register as such a protest, but nobody is looking at turnout being 55% instead of 60% and becoming more accountable over that.
My dc vote is worth $0 !
Why isn't there a vote for "Not an American citizen"? :)
Otherwise, great article.
Was limited to 5 options, sorry!
I think, it's included in "Other" option. At least, I voted so. :)
I'm glad to see someone citing Dan M. Kahan. I used to read his entertaining Cultural Cognition blog a decade ago. It was one of my earliest experiences wading into various survey methodologies and data presentations. His observations, including the one you cited, have stuck with me.
I wish he were still writing his blog. The domain seems to have been taken over and reformatted; some of the pages are empty or seemingly AI drivel, but much of the original content can be found, albeit without dates, via the site map. I'm not sure what he's up to these days but I hope he's ok. I guess one reason academic journals exist is to last longer than blogs.
Nice post!
Your own survey results suggest that readers of this blog aren't in much agreement about who the better president is, casting a big doubt on those assumptions. Besides, actual regressions of economic growth (or whatever) and party in power show basically nothing. Most presidential elections don't matter. Maybe this one is a black swan (Elon thinks so), but it's a bad prior. It's also pretty unlikely to assume a potential efficiency improvement of 2.5% given the above findings. And furthermore unlikely much of this would be beneficial to you specifically. Governments would just spend that money on some half-brained idea.
My responses:
The poll is very specific to the readership, so I don't think it tells us much about the broader principle, which is: If you could beat the median voter at even betting, you should vote.
Party in power may have no correlation with growth historically, but the individual candidates could still be very explanatory. Just as, when you're hiring someone, Harvard vs Yale on the resume may not have a statistically significant sign -- but having a good hiring manager is still important to get the right employee.
Regarding "unlikely much of this would be beneficial to you specifically": Certainly, market reactions to election day seem to say it'll matter to anyone with a stake in the economy. Additionally, anyone with social preferences, whether it's abortion or immigration, have a further incentive, if they care about the country going in a certain direction. As my article notes, it's true that the "selfish" value of a vote is low, but it's very high if one cares about the direction of the country as whole, not just as it relates economically to ones self.
I'm confused; you said specifically that you expect readers of this blog to be better than the median voter at picking good candidates, yet the readers of this blog are split close to 50/50 on who the correct candidate is. Doesn't this have to disprove your claim, at least with regards to this particular election? (It's possible in principle that readers are still better than the median American on average, but this particular election is harder to tell or something. Seems unlikely, but is consistent with the data.)
I guess that's true about this particular election, at least to the extent readers are split. (It seems to be shifting to a somewhat clearer conclusion as the day goes on.)
But yeah, I don't see much reason to think that generalizes to elections in general.
If you have a panel of expert job recruiters, and they deadlock about picking one applicant or another ... and a poll of the general public also deadlocks, that doesn't prove that the experts are no better in general.
I like this thought exercise overall.
I do see one problem in the math that no one else called out, which is that too much weight is assigned to the tails (i.e., too low of confidence on the most probable events). But I think it's because you're taking these probabilities directly from Nate Silver, who has been rightly criticized for this by e.g. Carl Allen.
Here Mississippi has like 3% of the value of PA, which is crazy. The probability of Mississippi being the tipping point state in this election is higher than the atoms in the state of Mississippi spontaneously arranging themselves into Godzilla and marching into the Gulf of Mexico, but not THAT much higher. Functionally zero, in either event.
But if anything, I think Silver's error here INCREASES the value of swing state votes.
Thanks. I think I agree with you that Silver's numbers overstate longshots. I did look into taking 538's estimates instead of Silver's for this reason, but theirs didn't seem much better. I don't have time to calculate those odds myself, so unless someone else does it better than Silver, this is for now the best estimate available.
Oh, I actually have a footnote on that: "I use Silver’s estimates, because his model has been good in the past, and because he’s the only one besides 538 who estimates this. I find some of his results surprising (are New Mexico, Mississippi, and Alaska really as valuable as he thinks?) but 538 actually has pretty similar estimates for those states, so — I guess the data is trying to tell us something."
Yes I think the 538 (Morris) numbers are even worse for this type of error. If you dig into the individual scenarios that his model generates they’re just wild. Like assigning non-trivial probabilities to Trump wins CA while Kamala wins TX kinds of events.
Again, read some of what Carl Allen has said here. Maybe there are others who have pointed it out.
When one of your five data points is so implausible that you throw it out, it's probably best to throw out any conclusion with it. Still an interesting attempt and worth sharing.
That thought crosses my mind, but I disagree, because:
A) There's a reason that datapoint doesn't work, while the others do: only 10% of the value is in the market signal, and hence it gets drowned out by the noise. When 50% or 80% of the signal of the President is in the market change, it IS likely to be valid.
B) It's still better than guessing, which is the next-best alternative.
The S&P500 only reflects the expected profits of 500 companies! You need to also account for smaller businesses, increased wages to employees, and of course consumer surplus. So the true value is likely 100x what you calculated, unless I'm making an error somewhere (possible).
I think Brennan's calculation is clearly wrong. If voting for the right candidate adds $3000, that's relative to voting for the wrong candidate; doing so then adds $0. It doesn't subtract $3000! There's no plausible scenario where neither candidate gets in and the dollar amount is zero. (Of course you can just as well say that voting for the wrong candidate subtracts $3000, and voting for the right one subtracts $0.)
I might accept +$1500 and -$1500 as compromise amounts, for a difference of $3000. But the other way gives a difference of $6000, which looks like double counting.
We thrash this sort of thing out in tabletop roleplaying games all the time. . . .
“ 1-in-a-million is the hard, proven, lower bound.”
Sorry, this is simply incorrect.
Because each outcome is NOT in fact equally likely.
Even with a fairly evenly divided electorate
Barnett said this was the case ONLY “If, for some reason, each of these outcomes were equally likely, then the probability that your vote is decisive would be exactly 1/1,000,001”
But there is NO reason the outcomes are equally likely, and overwhelming reason that they are not remotely equally likely.
But when we consider that they are not equally likely, we realize that it's outcomes in the middle that are much more likely, which increases the value of a vote. That's why it's a lower bound.
My apologies. You are correct in this case (there are “weird”, or at least uncommon, cases where you would not be, but basically you’re right).
OTOH there is clearly something wrong with your formula for “value” of vote that non-swing states have such relatively high values compared to swing states. Because the odds of one of those non-swing states tipping the election is pretty small in the first place, on top of the chance that your vote will be the deciding vote in that state.
There is just no way, e.g. that Idaho vote value is as high as 1/1000th of Pennsylvania.
(The absolute values, of course, are impossible to know and relatively uninteresting, even as I *do* agree with your premise of a high social value of a “correct” vote in a swing state.)
The problem with using the stock market as a valuation tool for the importance of politics is that there is some literature suggesting that share price growth is negatively correlated with growth and thus may (likely) has an overall negative relationship with welfare, but at an unknown rate (e.g. there's no guarantee that $1 dollar extra in the sharemarket = -$1 dollar of welfare). Others find not much evidence of correlation in either direction e.g.: https://www.boeckler.de/pdf/v_2022_10_22_joebges.pdf
I don't think this works to justify voting. Even if your vote is worth ~$10,000 to society as a whole, you personally capture essentially zero of that value. Voting is still not personally rational.
Yes, but that doesn’t mean it doesn’t justify voting.
Do a command-F on the article for “To be clear” — I discuss this there.
I'm sorry for off-topic, but it would be really interesting to know your opinion about this text: https://quantian.substack.com/p/market-prices-are-not-probabilities
Good attempt, but it's still not convincing about the rationality to vote. The sheer amount of issues you'd have to know and be rational about are absurd. For example, despite being someone who has obsessed over political issues for years to try be "right" about them, I had no idea that PEPFAR was a real program until Bentham's Bulldog mentioned it. If he's right, it saves a lot of lives, and so it should play an important role in our calculation for who should win the president.
Further, I have many hours thinking and reading about political issues as a "rationalist" type, yet I *still* don't feel informed enough about many issues. While I'm sure of libertarianism, I'm not nearly certain about how libertarian I should be even if I lean towards anarchy. I assume libertarianism based on economic/philosophical theory as a presumption/prior even on issues I don't know much about, but i came to this position through hours of research as a "rationalist" type. For most people, being this well-researched is a full time job beyond the cost of voting in a swing state, and this probably includes rationalists. And to be certain and have more than just a prior, I still feel like I need to read a lot more about the issues.
Even then, I don't think even the most rational prediction people could have predicted the Iraq War or Trump as a backlash to Obama vs. some other generic Republican candidate. I think the best case for voting you can make is that one could vote for the libertarian candidate to possibly be the decisive vote that forces the parties to pander to libertarians more. But even then, they have to follow through on their promises, which is too difficult to predict, like dovish Bush.
But are you sure you're setting the bar at the right level? Do you perhaps already know more than enough to beat the median voter in a wide range of bets about the future? If so, you would add rather than subtract from the picking of a President.
It's not just whether I would add to the expected value of the vote, it's how much I would add.
I think there's a small chance that Trump could attempt to establish a dictatorship based on 2020. I also think there's a small chance that Kamala actually attempts a net zero emissions plan, flings the US into an economic free fall, and then mass poverty. I don't know how to weigh all of these things. Just because I'd do *better* than the majority of the population doesn't mean I'd do good enough to justify a few more dollars of expected value.
In section "The Enormous Value of A Correct Vote in a Swing State" the article says
"... Pennsylvania has a .29% chance of tipping an election..."
However, the following calculation drops the percent:
".29 * (1 / 1,710,069) * $182 billion"
Should the percent be included, dividing the result by 100?
It is 29%, not .29%. The "." was a typo. Thanks for noting.
can the dollar value of a vote really be calculated in this way?
Say person a promises to give person b 1 trillion dollars a week into the future if person b gives person a the contents of their wallet immidietally.
The chances of person a following through on their promise is infinitessimally small. But does it then follow that if person a offers an infinitely high number that at some point person b should agree and cough up the money?
Or to pick a more tangible example, can't this same argument be made to assasinate a world leader or for everyone to runndor US president?
It's kind of similar to Pascal's wager in this way.. At a certain high level of improbability, I'm just not persuaded that any level of consequence is sufficient to justify action on an individual basis.
Especially when, for example, refusing to vote in a secured state serves as a protest throwaway try and vote to hold candidates accountable.
That hypothetical isn't relevant, though, because we're not talking about an implausible promise to give money -- we're talking about market projections of what will happen to the country. And we know the President has a big impact on the economy, though policy. So it's very different from the hypothetical you floated.
I disagree that "refusing to vote in a secured state serves as a protest throwaway" -- or at least, it's certainly not an effective one. Voting 3rd party might register as such a protest, but nobody is looking at turnout being 55% instead of 60% and becoming more accountable over that.