That example also relies on your utility being the sum of components that are determined from your various actions.
Choosing to bound an unbounded utility function to avoid muggers does not.
To be clear, I was not suggesting that you have an unbounded utility function that it would make sense for you to maximize if it weren’t for Pascal’s mugger, so you should bound it when there might be a Pascal’s mugger around. I was suggesting that the utility function it makes sense for you to maximize is bounded. Unbounded utility functions are so loony they never should have been seriously considered in the first place; Pascal’s mugger is merely a dramatic illustration of that fact.
Edit: I probably shouldn’t rely on the theoretical reasons to prefer bounded utility functions, since they are not completely airtight and actual human preferences are more important anyway. So let’s look at actual human preferences. Suppose you’ve got a rational agent with preference relation “<”, and you want to test whether its utility function is bounded or unbounded. Here’s a simple test: First find outcomes A and B such that A<B (if you can’t even do that, its utility function is constant, hence bounded). Then pick an absurdly tiny probability p>0. Now see if you can find such a terrible C and such a wonderful D that pC+(1-p)B < pD + (1-p)A. If, for every p>0 you can find such C and D, then its utility function is unbounded. But if for some p>0, you cannot find any C and D that will suffice, even when you probe the extremes of goodness and badness, then its utility function is bounded. This test should sound familiar. What I’m getting at here is that one does not bound their unbounded utility function so that they don’t have to pay Pascal’s mugger; your preferences were simply bounded all along, and your response to Pascal’s mugger is proof.
The more concrete argument you made previous does rely on it. If what you’re saying now doesn’t, then I guess I don’t understand it.
I don’t follow. Maximizing the expected value of a bounded utility functions does respect independence.
That was an example. There’s another one in http://lesswrong.com/lw/1d5/expected_utility_without_the_independence_axiom/ which relies on “not risk loving”. That post doesn’t mention the median, but it does mention the standard deviation, and we know the mean must be within one SD of the mean (and often much closer).
Choosing to bound an unbounded utility function to avoid muggers does not.
That example also relies on your utility being the sum of components that are determined from your various actions.
To be clear, I was not suggesting that you have an unbounded utility function that it would make sense for you to maximize if it weren’t for Pascal’s mugger, so you should bound it when there might be a Pascal’s mugger around. I was suggesting that the utility function it makes sense for you to maximize is bounded. Unbounded utility functions are so loony they never should have been seriously considered in the first place; Pascal’s mugger is merely a dramatic illustration of that fact.
Edit: I probably shouldn’t rely on the theoretical reasons to prefer bounded utility functions, since they are not completely airtight and actual human preferences are more important anyway. So let’s look at actual human preferences. Suppose you’ve got a rational agent with preference relation “<”, and you want to test whether its utility function is bounded or unbounded. Here’s a simple test: First find outcomes A and B such that A<B (if you can’t even do that, its utility function is constant, hence bounded). Then pick an absurdly tiny probability p>0. Now see if you can find such a terrible C and such a wonderful D that pC+(1-p)B < pD + (1-p)A. If, for every p>0 you can find such C and D, then its utility function is unbounded. But if for some p>0, you cannot find any C and D that will suffice, even when you probe the extremes of goodness and badness, then its utility function is bounded. This test should sound familiar. What I’m getting at here is that one does not bound their unbounded utility function so that they don’t have to pay Pascal’s mugger; your preferences were simply bounded all along, and your response to Pascal’s mugger is proof.