= 27d567bc2d48d9f40e9ccc20ea370b15)
Eliezer_Yudkowsky comments on Expected utility without the independence axiom - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (65)
Is the new axiom sufficient to show that the agent cannot be money-pumped?
It's enough to show that an agent cannot be repeatedly money-pumped. The more opportunities for money pumping, the less chances there are of it succeeding.
Contrast household applicance insurance versus health insurance. Both are a one-shot money-pump, as you get less than your expected utility out of then. An agent following these axioms will probably health-insure, but will not appliance insure.
Can you write out the math on that? To me it looks like the Allais Paradox or a simple variant would still go through. It is easy for the expected variance of a bet to increase as a result of learning additional information - in fact the Allais Paradox describes exactly this. So you could prefer A to B when they are bundled with variance-reducing most probable outcome C, and then after C is ruled out by further evidence, prefer B to A. Thus you'd pay a penny at the start to get A rather than B if not-C, and then after learning not-C, pay another penny to get B rather than A.
I'll try and do the maths. This is somewhat complex without independence, as you have to estimate what the total results of following a certain strategy is, over all the bets you are likely to face. Obviously you can't money pump me if I know you are going to do it; I just combine all the bets and see it's a money pump, and so don't follow it.
So if you tried to money pump me repeatedly, I'd estimate it was likely that I'd be money pumped, and adjust my strategy accordingly.
I believe SilasBarta has correctly (if that is the word) noted that it does not - it is perfectly possible for an agent to satisfy the new axioms and fall victim to the Allais Paradox.
Edit: correction - he does not state this.
That sounds more like the exact opposite of my position.
I apologize. In the course of conversation with you, I came to that conclusion, but you reject that position.
To summarize my point: if you follow the new axioms, you will act differently in one-shot vs. massive-shot scenarios. Acting like the former in the latter will cause you to be money-pumped, but per the axioms, you never actually do it. So you can follow the new axioms, and still not get money-pumped.