His prior is uniform because uniform is max entropy. If your prior is less than max entropy, you must have had information to update on. What is your information?
No, you don’t get it. The space of possible universes may be continuous instead of discrete. What’s a “uniform” prior over an arbitrary continuous space that has no canonical parameterization? If you say Maxent, why? If you say Jeffreys, why?
It’s possible to have uniform distributions on continuous spaces. It just becomes probability density instead of probability mass.
The reason for max entropy is that you want your distribution to match your knowlege. When you know nothing, thats maxiumum entropy, by definition. If you update on information that you don’t have, you probabilistically screw yourself over.
If you have a hard time drawing the space out and assigning the maxent prior, you can still use the indifference prinicple when asked about the probability of being in a larger universe vs a smaller universe.
Consider “antipredictions”. Say I ask you “is statement X true? (you can’t update on my psychology since I flipped a coin to determine whether to change X to !X). The max entropy answer is 50⁄50 and it’s just the indifference principle.
If I now tell you that X = “I will not win the lottery if I buy a ticket?” and you know nothing about what ball will come up, just that the number of winning numbers is small and the number of not winning numbers is huge, you decide that it is very likely to be true. We’ve only updated on which distribution we’re even talking about. If you’re too confused to make that jump in a certain case, then don’t.
Or you could just say that for any possible non uniformity, it’s possible that there’s an opposite non uniformity that cancels it out. Whats the direction of the error?
No, it doesn’t. In fact I don’t think you even parsed my question. Sorry.
Let’s simplify the problem: what’s your uninformative prior for “proportion of voters who voted for an unknown candidate”? Is it uniform on (0,1) which is given by maxent? What if I’d asked for your prior of the square of this value instead, masking it with some verbiage to sound natural—would you also reply uniform on (0,1)? Those statements are incompatible. In more complex real world situations, how exactly do you choose the parameterization of the model to feed into maxent? I see no general way. See this Wikipedia page for more discussion of this problem. In the end it recommends the Jeffreys rule for use in practice, but it’s not obviously the final word.
I see what you’re saying, but I don’t think it matters here. That confusion extends to uncertainty about the nth digit of pi as well-it’s nothing new about different universes. If you put a uniform prior on the nth digit of pi instead of uniform of the square of the nth digit or Jeffreys prior, why don’t you do the same in the case of different universes? What prior do you use?
The point I tried to make in the last comment is that if you’re asked any question, you start with the indifference principle. which is uniform in nature, and upon receiving new information, (perhaps the possibility that the original phrasing wasn’t the ‘natural’ way to phrase it, or however you solve the confusion) then you can update. Since the problem never mentioned a method of parameterizing a continuous space of possible universes, it makes me wonder how you can object to assigning uniform priors given this parameterization or even say that he required it.
Changing the topic of our discussion, it seems like your comment is also orthogonal to the claim being presented. He basically said “given this discrete set of two possible universes (with uniform prior) this ‘proves’ SIA (worded the first way)”. Given SIA, you know to update on your existence if you find yourself in a continuous space of possible universes, even if you don’t know where to update from.
His prior is uniform because uniform is max entropy. If your prior is less than max entropy, you must have had information to update on. What is your information?
No, you don’t get it. The space of possible universes may be continuous instead of discrete. What’s a “uniform” prior over an arbitrary continuous space that has no canonical parameterization? If you say Maxent, why? If you say Jeffreys, why?
It’s possible to have uniform distributions on continuous spaces. It just becomes probability density instead of probability mass.
The reason for max entropy is that you want your distribution to match your knowlege. When you know nothing, thats maxiumum entropy, by definition. If you update on information that you don’t have, you probabilistically screw yourself over.
If you have a hard time drawing the space out and assigning the maxent prior, you can still use the indifference prinicple when asked about the probability of being in a larger universe vs a smaller universe.
Consider “antipredictions”. Say I ask you “is statement X true? (you can’t update on my psychology since I flipped a coin to determine whether to change X to !X). The max entropy answer is 50⁄50 and it’s just the indifference principle.
If I now tell you that X = “I will not win the lottery if I buy a ticket?” and you know nothing about what ball will come up, just that the number of winning numbers is small and the number of not winning numbers is huge, you decide that it is very likely to be true. We’ve only updated on which distribution we’re even talking about. If you’re too confused to make that jump in a certain case, then don’t.
Or you could just say that for any possible non uniformity, it’s possible that there’s an opposite non uniformity that cancels it out. Whats the direction of the error?
Does that explain any better?
No, it doesn’t. In fact I don’t think you even parsed my question. Sorry.
Let’s simplify the problem: what’s your uninformative prior for “proportion of voters who voted for an unknown candidate”? Is it uniform on (0,1) which is given by maxent? What if I’d asked for your prior of the square of this value instead, masking it with some verbiage to sound natural—would you also reply uniform on (0,1)? Those statements are incompatible. In more complex real world situations, how exactly do you choose the parameterization of the model to feed into maxent? I see no general way. See this Wikipedia page for more discussion of this problem. In the end it recommends the Jeffreys rule for use in practice, but it’s not obviously the final word.
I see what you’re saying, but I don’t think it matters here. That confusion extends to uncertainty about the nth digit of pi as well-it’s nothing new about different universes. If you put a uniform prior on the nth digit of pi instead of uniform of the square of the nth digit or Jeffreys prior, why don’t you do the same in the case of different universes? What prior do you use?
The point I tried to make in the last comment is that if you’re asked any question, you start with the indifference principle. which is uniform in nature, and upon receiving new information, (perhaps the possibility that the original phrasing wasn’t the ‘natural’ way to phrase it, or however you solve the confusion) then you can update. Since the problem never mentioned a method of parameterizing a continuous space of possible universes, it makes me wonder how you can object to assigning uniform priors given this parameterization or even say that he required it.
Changing the topic of our discussion, it seems like your comment is also orthogonal to the claim being presented. He basically said “given this discrete set of two possible universes (with uniform prior) this ‘proves’ SIA (worded the first way)”. Given SIA, you know to update on your existence if you find yourself in a continuous space of possible universes, even if you don’t know where to update from.