When betting, you should discount the scenarios where you’re unable to enjoy the reward to zero. In less accurate terms, any doom scenario that involves you personally dying should be treated as impossible, because the expected utility of winning is zero.
Suppose I think the probability of me dying in a car accident is 20%, and I don’t care about what happens to my wealth in that world (rather than caring about my heirs having more money). Should I buy a contract that pays out $100 if I die in a car accident at the cost of $10?
The claim is: no, because it pays out only in situations where the money is worthless to me. If you try to back out my estimate from my willingness-to-pay, it will look a lot like I think the probability of me dying in a car accident is 0%. [And the reverse contract—the “I don’t die in a car accident” one—I should buy as tho my price were 100%, which basically lets me move all of my money from worlds that I don’t care about to ones that I do, basically setting my bet counterparties as my heirs.]
You can get milder forms of this distortion from ‘currency changes’. If I make a dollar-denominated bet on the relative value of the dollar and the euro, and I mostly buy things in euros, then you need to do some work to figure out what I think the real probabilities are (because if I’m willing to buy a “relative value of the dollar halves” contract at 30%, well, I’m expecting to get $50 in current value back instead of $100 in current value back).
[This is to say, I think you’re right that those are different things, but the “because” statement is actually pointing at how those different things construct the conclusion.]
Could you explain more about the difference.and what it looks like to give one vs. the other?
When betting, you should discount the scenarios where you’re unable to enjoy the reward to zero. In less accurate terms, any doom scenario that involves you personally dying should be treated as impossible, because the expected utility of winning is zero.
Oh, this is definitely not what I meant.
“Betting odds” == Your actual belief after factoring in other people’s opinions
“Inside view” == What your models predict, before factoring in other opinions or the possibility of being completely wrong
Though I understood what you meant, perhaps a clearer terminology is all-things-considered beliefs vs. independent impressions.
Er, treated as impossible != treated as zero utility.
Suppose I think the probability of me dying in a car accident is 20%, and I don’t care about what happens to my wealth in that world (rather than caring about my heirs having more money). Should I buy a contract that pays out $100 if I die in a car accident at the cost of $10?
The claim is: no, because it pays out only in situations where the money is worthless to me. If you try to back out my estimate from my willingness-to-pay, it will look a lot like I think the probability of me dying in a car accident is 0%. [And the reverse contract—the “I don’t die in a car accident” one—I should buy as tho my price were 100%, which basically lets me move all of my money from worlds that I don’t care about to ones that I do, basically setting my bet counterparties as my heirs.]
You can get milder forms of this distortion from ‘currency changes’. If I make a dollar-denominated bet on the relative value of the dollar and the euro, and I mostly buy things in euros, then you need to do some work to figure out what I think the real probabilities are (because if I’m willing to buy a “relative value of the dollar halves” contract at 30%, well, I’m expecting to get $50 in current value back instead of $100 in current value back).
[This is to say, I think you’re right that those are different things, but the “because” statement is actually pointing at how those different things construct the conclusion.]
No, because you don’t get $100 worth of utility function increase if you die. This is distinct from there being a 0% probability of you dying.
No one said it should be treated as zero utility
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