So once the duplication has happened, I anticipate having won the lottery. This causes a preference reversal, as my previous version would pay to have my copies denied that choice.....
....This causes a money-pumpable preference reversal.
I’m not sure this is really a preference reversal, at least as I understand them. Your terminal values have remained the same, what’s changed is the knowledge you have about how effectively you’ll be able to implement them.
To make my point clearer let’s look at a situation that does not involve copies:
Omega approaches you and gives you a few pieces of information:
One hour from now Omega’s cousin, Beyonder is going to offer you a trade. If you give him one chocolate bar now, he’ll give you five chocolate bars two hours from then.
In ten minutes you will have a nervous breakdown. This breakdown will have two important effects. First, it will give you temporary amnesia of the previous ten minutes, causing you to forget this entire conversation with Omega. Second, it will cause you to mistakenly believe the odds of your dying in less than an hour are close to .9999. Omega helpfully informs you that he estimates your real probability of dying in less than an hour to be .00000001.
Fortunately, this nervous breakdown will only last an hour. After that you will recover your memory, and have a much more accurate probability estimate of your longevity.
Now, this is obviously bad news. Besides the psychological trauma this breakdown will cause, you’ll miss out on a productive trade with Beyonder! After all, since you’ll believe that you are almost certain to die in less than an hour you’ll certainly be unwilling to give Beyonder a chocolate bar now, in order to receive five after you die!
Fortunately, Omega has a helpful suggestion. If you give him two chocolate bars right now, he’ll give one to Beyonder on your behalf (the other bar is to cover administrative fees). You should agree to this. You’ll still end up three chocolate bars in the black.
As with the copy lottery, this creates a preference reversal with a money pump. You end up having to give Omega a chocolate bar to deprive your future self of a choice. But I can’t think of any way to get out of this money pump. You could develop some sort of axiomatic utility function that would get your crazy self to still make the trade with Beyonder, but that same function would likely cause you to act insane in normal scenarios.
I think all we can do is simply accept that in scenarios where our knowledge about the relevant facts is lost (such as amnesia) we will sometimes make choices our past selves will we wouldn’t, because we lost a valuable piece of knowledge that we needed to make the right choice. The copy-lottery is a particularly weird example of such a scenario (we lose the knowledge of whether we’re the copy that’s going to survive or not), but it doesn’t differ from amnesia scenarios in any important decision theoretic way.
This might result in us being money pumped in knowledge-loss scenarios, but these aren’t infinite money pumps we’re talking about, like in the case of a genuine inconsistency in terminal values. Omega’s maxes out at four chocolate bars. I’m leery about the conclusion you drew with the axiomatic approach, so I’m willing to accept limited money pumps in amnesia scenarios.
I’m not sure this is really a preference reversal, at least as I understand them. Your terminal values have remained the same, what’s changed is the knowledge you have about how effectively you’ll be able to implement them.
To make my point clearer let’s look at a situation that does not involve copies:
Omega approaches you and gives you a few pieces of information:
One hour from now Omega’s cousin, Beyonder is going to offer you a trade. If you give him one chocolate bar now, he’ll give you five chocolate bars two hours from then.
In ten minutes you will have a nervous breakdown. This breakdown will have two important effects. First, it will give you temporary amnesia of the previous ten minutes, causing you to forget this entire conversation with Omega. Second, it will cause you to mistakenly believe the odds of your dying in less than an hour are close to .9999. Omega helpfully informs you that he estimates your real probability of dying in less than an hour to be .00000001.
Fortunately, this nervous breakdown will only last an hour. After that you will recover your memory, and have a much more accurate probability estimate of your longevity.
Now, this is obviously bad news. Besides the psychological trauma this breakdown will cause, you’ll miss out on a productive trade with Beyonder! After all, since you’ll believe that you are almost certain to die in less than an hour you’ll certainly be unwilling to give Beyonder a chocolate bar now, in order to receive five after you die!
Fortunately, Omega has a helpful suggestion. If you give him two chocolate bars right now, he’ll give one to Beyonder on your behalf (the other bar is to cover administrative fees). You should agree to this. You’ll still end up three chocolate bars in the black.
As with the copy lottery, this creates a preference reversal with a money pump. You end up having to give Omega a chocolate bar to deprive your future self of a choice. But I can’t think of any way to get out of this money pump. You could develop some sort of axiomatic utility function that would get your crazy self to still make the trade with Beyonder, but that same function would likely cause you to act insane in normal scenarios.
I think all we can do is simply accept that in scenarios where our knowledge about the relevant facts is lost (such as amnesia) we will sometimes make choices our past selves will we wouldn’t, because we lost a valuable piece of knowledge that we needed to make the right choice. The copy-lottery is a particularly weird example of such a scenario (we lose the knowledge of whether we’re the copy that’s going to survive or not), but it doesn’t differ from amnesia scenarios in any important decision theoretic way.
This might result in us being money pumped in knowledge-loss scenarios, but these aren’t infinite money pumps we’re talking about, like in the case of a genuine inconsistency in terminal values. Omega’s maxes out at four chocolate bars. I’m leery about the conclusion you drew with the axiomatic approach, so I’m willing to accept limited money pumps in amnesia scenarios.