You’re on a game show. You can’t leave with negative money. There are 3 doors, 2 with $6,000 cash, 1 with a goat (worth nothing…). You can pick a door, but first you can offer the host $x from your winnings (currently $0) to replace the goat with the prize. What do you offer?
Same situation, 6 doors, 2 prizes, 4 goats. What do you offer from your winnings to replace 1 goat with a prize?
Note that you only pay if you win. It’s very clever, but slightly incomplete. When he wrote “what do you offer?”, he really meant “at what $x amount are you indifferent between offering and not not offering the money?”. Is there a way to fix this annoyance, and really formulate the question as a “what do you offer?”.
Of course, there are many plausible utility functions that make it cease to be an equivalent reformulation. For example, if you don’t like giving money to murderers and kidnappers. Or the kind of loss aversion that I discussed.
In this reformulation it feels obvious to me that I should pay the same amount in both cases. But it’s not obvious to me that the reformulation is equivalent to the original problem, because dying is not necessarily the same as surviving but losing all your utility, if some of the utility is due to experiences you can only get when you’re alive.
I agree. But am I wrong to think that your exchange with steven0461 already cleared this up as much as it is possible?
By the way, it is amusing that Michael Dekker got his version by getting rid of the blood in Zeckhauser’s version, and Zeckhauser got his version by adding some blood to Allais’ version.
There is a clever reformulation by a Michael Dekker at Landsburg’s blog:
Note that you only pay if you win. It’s very clever, but slightly incomplete. When he wrote “what do you offer?”, he really meant “at what $x amount are you indifferent between offering and not not offering the money?”. Is there a way to fix this annoyance, and really formulate the question as a “what do you offer?”.
Of course, there are many plausible utility functions that make it cease to be an equivalent reformulation. For example, if you don’t like giving money to murderers and kidnappers. Or the kind of loss aversion that I discussed.
In this reformulation it feels obvious to me that I should pay the same amount in both cases. But it’s not obvious to me that the reformulation is equivalent to the original problem, because dying is not necessarily the same as surviving but losing all your utility, if some of the utility is due to experiences you can only get when you’re alive.
I agree. But am I wrong to think that your exchange with steven0461 already cleared this up as much as it is possible?
By the way, it is amusing that Michael Dekker got his version by getting rid of the blood in Zeckhauser’s version, and Zeckhauser got his version by adding some blood to Allais’ version.