One day I would like to open up an inverse casino.
The inverse casino would be full of inverse slot machines. Playing the inverse slot machines costs negative twenty-five cents - that is, each time you pull the bar on the machine, it gives you a free quarter. But once every few thousand bar pulls, you will hit the inverse jackpot, and be required to give the casino several thousand dollars (you will, of course, have signed a contract to comply with this requirement before being allowed to play).
You can also play the inverse lottery. There are ten million inverse lottery tickets, and anyone who takes one will get one dollar. But if your ticket is drawn, you must pay me fifteen million dollars. If you don't have fifteen million dollars, you will have various horrible punishments happen to you until fifteen million dollars worth of disutility have been extracted from you.
If you believe what you are saying, it seems to me that you should be happy to play the inverse lottery, and believe there is literally no downside. And it seems to me that if you refused, I could give you the engineer's answer "Look, (buys ticket) - a free dollar, and nothing bad happened to me!"
And if you are willing to play the inverse lottery, then you should be willing to play the regular lottery, unless you believe the laws of probability work differently when applied to different numbers.
The hedge fund industry called. They want their idea of selling far out-of-the-money options back.
For background, see here.
In a comment on the original Pascal's mugging post, Nick Tarleton writes:
Coming across this again recently, it occurred to me that there might be a way to generalize Vassar's suggestion in such a way as to deal with Tarleton's more abstract formulation of the problem. I'm curious about the extent to which folks have thought about this. (Looking further through the comments on the original post, I found essentially the same idea in a comment by g, but it wasn't discussed further.)
The idea is that the Kolmogorov complexity of "3^^^^3 units of disutility" should be much higher than the Kolmogorov complexity of the number 3^^^^3. That is, the utility function should grow only according to the complexity of the scenario being evaluated, and not (say) linearly in the number of people involved. Furthermore, the domain of the utility function should consist of low-level descriptions of the state of the world, which won't refer directly to words uttered by muggers, in such a way that a mere discussion of "3^^^^3 units of disutility" by a mugger will not typically be (anywhere near) enough evidence to promote an actual "3^^^^3-disutilon" hypothesis to attention.
This seems to imply that the intuition responsible for the problem is a kind of fake simplicity, ignoring the complexity of value (negative value in this case). A confusion of levels also appears implicated (talking about utility does not itself significantly affect utility; you don't suddenly make 3^^^^3-disutilon scenarios probable by talking about "3^^^^3 disutilons").
What do folks think of this? Any obvious problems?