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.]
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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