Are you rejecting Pascal’s mugging because of the prospect of relying on uncertain models that you do not expect to confirm?
My intuition is that in a one-shot problem, gambling everything on an extremely low probability event is a bad idea, even when the reward from that low probability event is very high, because you are effectively certain to lose. This is the basis for me not paying up in Pascal’s Mugging and in the casino problem in the post.
I’m trying to keep my reasoning simple, so in my examples I always assume that there are no infinities, no unknown unknowns, every outcome of every choice is statistically independent, and all the assigned probabilities are statistically correct (if there is a 1⁄6 chance of an outcome and you get to repeat the problem, you will get that outcome on average 1⁄6 of the time).
Is all your intuition captured by maximizing utility over all but the extreme billionth of the distribution?
Honestly, I have no idea how to solve the problem. My intuition is hopelessly muddled on this, and every idea I’ve been able to come up with seems flawed, including the one you’ve just asked about.
Here’s a one-shot problem for your intuition to answer: You get to design the probability distribution to draw the number of paperclips from, except that its expectation must be at most its negative kolgomorov complexity. What distribution makes for a good choice?
My first thought is 1/googolplex chance of losing 3^^^^3 paperclips, and the rest of the probability giving as many paperclips as the kolmogorov complexity constraint allows. I could do better by increasing the probability of the loss, for example 1/googol would be a better probability. However, I have no idea where to draw the line, at what point it stops being a good idea to increase the probability.
In a market of bettors that draw the line of how much risk to take at different points, the early game will be dominated by the most risk-taking folks and as the game grows older, the line that was chosen by the current winners moves. Perhaps your intuition is merely the product of evolution playing this game for as long as it took for the line to reach its current point?
Thank you for your response!
My intuition is that in a one-shot problem, gambling everything on an extremely low probability event is a bad idea, even when the reward from that low probability event is very high, because you are effectively certain to lose. This is the basis for me not paying up in Pascal’s Mugging and in the casino problem in the post.
I’m trying to keep my reasoning simple, so in my examples I always assume that there are no infinities, no unknown unknowns, every outcome of every choice is statistically independent, and all the assigned probabilities are statistically correct (if there is a 1⁄6 chance of an outcome and you get to repeat the problem, you will get that outcome on average 1⁄6 of the time).
Honestly, I have no idea how to solve the problem. My intuition is hopelessly muddled on this, and every idea I’ve been able to come up with seems flawed, including the one you’ve just asked about.
My first thought is 1/googolplex chance of losing 3^^^^3 paperclips, and the rest of the probability giving as many paperclips as the kolmogorov complexity constraint allows. I could do better by increasing the probability of the loss, for example 1/googol would be a better probability. However, I have no idea where to draw the line, at what point it stops being a good idea to increase the probability.
In a market of bettors that draw the line of how much risk to take at different points, the early game will be dominated by the most risk-taking folks and as the game grows older, the line that was chosen by the current winners moves. Perhaps your intuition is merely the product of evolution playing this game for as long as it took for the line to reach its current point?