It’s a little hard to know what you mean by that. Do you mean something like: given the information known at the time, but allowing myself the hindsight of noticing facts about that information that I may have missed, what should I have thought the probability was?
If so, I think my answer isn’t too different from what I believed before the election (essentially 50⁄50). Though I welcome takes to the contrary.
That’s a different question than the one I meant. Let me clarify:
Basically I was asking you what you think the probability is that Trump would win the election (as of a week before the election, since I think that matters) now that you know how the election turned out.
An analogous question would be the following:
Suppose I have two unfair coins. One coin is biased to land on heads 90% of the time (call it H-coin) and the other is biased to land on tails 90% of the times (T-coin). These two coins look the same to you on the outside. I choose one of the coins, then ask you how likely it is that the coin I chose will land on heads. You don’t know whether the coin I’m holding is H-coin or T-coin, so you answer 50% (50%=0.5*.90=+0.5*0.10). I then flip the coin and it lands on heads. Now I ask you, knowing that the coin landed on heads, now how likely do you think it was that it would land on heads when I first tossed it? (I mean the same question by “Knowing how the election turned out, how likely do you think it was a week before the election that Trump would win?”).
Say I have a shuffled deck of cards. You say the probability that the top card is the Ace of Spades is 1⁄52. I show you the top card, it is the 5 of diamonds. I then ask, knowing what you know now, what probability you should have given.
I picked a card analogy, and you picked a dice one. I think the card one is better in this case, for weird idiosyncratic reasons I give below that might just be irrelevant to the train of thought you are on.
Cards vs Dice: If we could reset the whole planet to its exact state 1 week before the election then we would I think get the same result (I don’t think quantum will mess with us in one week). What if we do a coarser grained reset? So if there was a kettle of water at 90 degrees a week before the election that kettle is reset to contain the same volume of water in the same part of my kitchen, and the water is still 90 degrees, but the individual water molecules have different momenta. For some value of “macro” the world is reset to the same macrostate but not the same microstate, it had 1 week before election day. If we imagine this experiment I still think Trump wins every (or almost every) time, given what we know now. For me to think this kind of thermal-level randomness made a difference in one week it would have to have been much closer.
In my head things that change on the coarse-grained reset feel more like unrolled dice, and things that don’t more like facedown cards. Although in detail the distinction is fuzzy: it is based on an arbitrary line between micro an macro, and it is time sensitive, because cards that are going to be shuffled in the future are in the same category as dice.
EDIT: I did as asked, and replied without reading your comments on the EA forum. Reading that I think we are actually in complete agreement, although you actually know the proper terms for the things I gestured at.
EDIT: I did as asked, and replied without reading your comments on the EA forum. Reading that I think we are actually in complete agreement, although you actually know the proper terms for the things I gestured at.
Cool, thanks for reading my comments and letting me know your thoughts!
I actually just learned the term “aleatory uncertainty” from chatting with Claude 3.5 Sonnet (New) about my election forecasting in the last week or two post-election. (Turns out Claude was very good for helping me think through mistakes I made in forecasting and giving me useful ideas for how to be a better forecaster in the future.)
I then ask, knowing what you know now, what probability you should have given.
Sounds like you might have already predicted I’d say this (after reading my EA Forum comments), but to say it explicitly: What probability I should have given is different than the aleatoric probability. I think that by becoming informed and making a good judgment I could have reduced my epistemic uncertainty significantly, but I would have still had some. And the forecast that I should have made (or what market prices should have been is actually epistemic uncertainty + aleatoric uncertainty. And I think some people who were really informed could have gotten that to like ~65-90%, but due to lingering epistemic uncertainty could not have gotten it to >90% Trump (even if, as I believe, the aleatoric uncertainty was >90% (and probably >99%)).
Ah, I think I see. Would it be fair to rephrase your question as: if we “re-rolled the dice” a week before the election, how likely was Trump to win?
My answer is probably between 90% and 95%. Basically the way Trump loses is to lose some of his supporters or have way more late deciders decide on Harris. That probably happens if Trump says something egregiously stupid or offensive (on the level of the Access Hollywood tape), or if some really bad news story about him comes out, but not otherwise.
Knowing how the election turned out, how likely do you think it was a week before the election that Trump would win?
Do you think Polymarket had Trump-wins priced too high or too low?
It’s a little hard to know what you mean by that. Do you mean something like: given the information known at the time, but allowing myself the hindsight of noticing facts about that information that I may have missed, what should I have thought the probability was?
If so, I think my answer isn’t too different from what I believed before the election (essentially 50⁄50). Though I welcome takes to the contrary.
That’s a different question than the one I meant. Let me clarify:
Basically I was asking you what you think the probability is that Trump would win the election (as of a week before the election, since I think that matters) now that you know how the election turned out.
An analogous question would be the following:
Suppose I have two unfair coins. One coin is biased to land on heads 90% of the time (call it H-coin) and the other is biased to land on tails 90% of the times (T-coin). These two coins look the same to you on the outside. I choose one of the coins, then ask you how likely it is that the coin I chose will land on heads. You don’t know whether the coin I’m holding is H-coin or T-coin, so you answer 50% (50%=0.5*.90=+0.5*0.10). I then flip the coin and it lands on heads. Now I ask you, knowing that the coin landed on heads, now how likely do you think it was that it would land on heads when I first tossed it? (I mean the same question by “Knowing how the election turned out, how likely do you think it was a week before the election that Trump would win?”).
(Spoilers: I’d be interested in knowing your answer to this question before you read my comment on your “The value of a vote in the 2024 presidential election” EA Forum post that you linked to to avoid getting biased by my answer/thoughts.)
I think this question is maybe logically flawed.
Say I have a shuffled deck of cards. You say the probability that the top card is the Ace of Spades is 1⁄52. I show you the top card, it is the 5 of diamonds. I then ask, knowing what you know now, what probability you should have given.
I picked a card analogy, and you picked a dice one. I think the card one is better in this case, for weird idiosyncratic reasons I give below that might just be irrelevant to the train of thought you are on.
Cards vs Dice: If we could reset the whole planet to its exact state 1 week before the election then we would I think get the same result (I don’t think quantum will mess with us in one week). What if we do a coarser grained reset? So if there was a kettle of water at 90 degrees a week before the election that kettle is reset to contain the same volume of water in the same part of my kitchen, and the water is still 90 degrees, but the individual water molecules have different momenta. For some value of “macro” the world is reset to the same macrostate but not the same microstate, it had 1 week before election day. If we imagine this experiment I still think Trump wins every (or almost every) time, given what we know now. For me to think this kind of thermal-level randomness made a difference in one week it would have to have been much closer.
In my head things that change on the coarse-grained reset feel more like unrolled dice, and things that don’t more like facedown cards. Although in detail the distinction is fuzzy: it is based on an arbitrary line between micro an macro, and it is time sensitive, because cards that are going to be shuffled in the future are in the same category as dice.
EDIT: I did as asked, and replied without reading your comments on the EA forum. Reading that I think we are actually in complete agreement, although you actually know the proper terms for the things I gestured at.
Cool, thanks for reading my comments and letting me know your thoughts!
I actually just learned the term “aleatory uncertainty” from chatting with Claude 3.5 Sonnet (New) about my election forecasting in the last week or two post-election. (Turns out Claude was very good for helping me think through mistakes I made in forecasting and giving me useful ideas for how to be a better forecaster in the future.)
Sounds like you might have already predicted I’d say this (after reading my EA Forum comments), but to say it explicitly: What probability I should have given is different than the aleatoric probability. I think that by becoming informed and making a good judgment I could have reduced my epistemic uncertainty significantly, but I would have still had some. And the forecast that I should have made (or what market prices should have been is actually epistemic uncertainty + aleatoric uncertainty. And I think some people who were really informed could have gotten that to like ~65-90%, but due to lingering epistemic uncertainty could not have gotten it to >90% Trump (even if, as I believe, the aleatoric uncertainty was >90% (and probably >99%)).
Ah, I think I see. Would it be fair to rephrase your question as: if we “re-rolled the dice” a week before the election, how likely was Trump to win?
My answer is probably between 90% and 95%. Basically the way Trump loses is to lose some of his supporters or have way more late deciders decide on Harris. That probably happens if Trump says something egregiously stupid or offensive (on the level of the Access Hollywood tape), or if some really bad news story about him comes out, but not otherwise.
Yeah, that seems fair.
Seems reasonable to me. I wouldn’t be surprised if it was >99%, but I’m not highly confident of that. (I would say I’m ~90% confident that it’s >90%.)