I just flipped a coin. Are you willing to offer me a wager on the outcome I have already seen? Yet tradition would suggest you have a degree of belief in the most probable possibilities.
The offering of the wager itself can act as useful information. Some people wager to win.
I see what you mean. Yes, actual, literal, wagers are messier than beliefs. Another example is a bet that the world is going to end: which you should obviously always bet against at any odds even if you believe the last days are upon us. The equivalence between degree of belief and fair betting odds is a more abstract equivalence with an idealized bookie who offers bets on everything, doesn’t take a cut for himself and pays out even if you’re dead.
Actually, I like that metaphor! Let me work this out:
The bookie would see heads and tails with equal probability. However, the bookie would also sees twice as many bets when tails comes up. In order to make the vig zero, the bookie should pay out as much as comes in for whichever bet comes up, and that works out to 1:2 on heads and 2:1 on tails! Thus, the bookie sets the probability for Beauty at 1⁄3.
Another example is a bet that the world is going to end: which you should obviously always bet against at any odds even if you believe the last days are upon us.
To make an end of the world bet, person A who believes the world is not about to end will give some money to person B who believes the world is about to end. If after an agreed upon time, it is observed that the world has not ended, person B then gives a larger amount of money to person A.
It is harder to recover probabilities from the bets of this form that people are willing to make, because interest rates are a confounding factor.
Bets with money assume fairly constant and universal utility/$ rate. But that can’t be assumed in this case since money isn’t worth nearly as much if the world is about to end.
So you’d have to adjust for that. And of course even if you can figure out a fair wager given this issue it won’t be equivalent to the right degree of belief.
It is harder to recover probabilities from the bets of this form that people are willing to make, because interest rates are a confounding factor.
It isn’t that hard, is it? We just find the interest rate on the amount B got to begin with, right?
But if person B is right she only gets to enjoy the money until the world ends. It seems to me that money is less valuable when you can only derive utility from it for a small, finite period of time. You can’t get your money’s worth buying a house, for example. Plus if belief in the end of the world is widespread the economy will get distorted in a bunch of ways (in particular, the best ways to spend money with two weeks left to live would get really expensive) making it really hard to figure out what the fair bet would be.
I just flipped a coin. Are you willing to offer me a wager on the outcome I have already seen? Yet tradition would suggest you have a degree of belief in the most probable possibilities.
The offering of the wager itself can act as useful information. Some people wager to win.
I see what you mean. Yes, actual, literal, wagers are messier than beliefs. Another example is a bet that the world is going to end: which you should obviously always bet against at any odds even if you believe the last days are upon us. The equivalence between degree of belief and fair betting odds is a more abstract equivalence with an idealized bookie who offers bets on everything, doesn’t take a cut for himself and pays out even if you’re dead.
Actually, I like that metaphor! Let me work this out:
The bookie would see heads and tails with equal probability. However, the bookie would also sees twice as many bets when tails comes up. In order to make the vig zero, the bookie should pay out as much as comes in for whichever bet comes up, and that works out to 1:2 on heads and 2:1 on tails! Thus, the bookie sets the probability for Beauty at 1⁄3.
To make an end of the world bet, person A who believes the world is not about to end will give some money to person B who believes the world is about to end. If after an agreed upon time, it is observed that the world has not ended, person B then gives a larger amount of money to person A.
It is harder to recover probabilities from the bets of this form that people are willing to make, because interest rates are a confounding factor.
Bets with money assume fairly constant and universal utility/$ rate. But that can’t be assumed in this case since money isn’t worth nearly as much if the world is about to end.
So you’d have to adjust for that. And of course even if you can figure out a fair wager given this issue it won’t be equivalent to the right degree of belief.
It isn’t that hard, is it? We just find the interest rate on the amount B got to begin with, right?
But if person B is right she only gets to enjoy the money until the world ends. It seems to me that money is less valuable when you can only derive utility from it for a small, finite period of time. You can’t get your money’s worth buying a house, for example. Plus if belief in the end of the world is widespread the economy will get distorted in a bunch of ways (in particular, the best ways to spend money with two weeks left to live would get really expensive) making it really hard to figure out what the fair bet would be.