Maybe I’m missing something, but it seems to me that all of this is straightforwardly justified through simple selfish pareto-improvements.
Take a look at Critchs cake-splitting example in section 3.5. Now imagine varying the utility of splitting. How high does it need to get, before [red->Alice;green->Bob] is no longer a pareto improvement over [(split)] from both player’s selfish perspective before the observation? It’s 27, and thats also exactly where the decision flips when weighing Alice 0.9 and Bob 0.1 in red, and Alice 0.1 and Bob 0.9 in green.
Intuitively, I would say that the reason you don’t bet influence all-or-nothing, or with some other strategy, is precisely because influence is not money. Influence can already be all-or-nothing all by itself, if one player never cares that much more than the other. The influence the “losing” bettor retains in the world where he lost is not some kind of direct benefit to him, the way money would be: it functions instead as a reminder of how bad a treatment he was willing to risk in the unlikely world, and that is of course proportional to how unlikely he thought it is.
So I think all this complicated strategizing you envision in influence betting, actually just comes out exactly to Critches results. Its true that there are many situations where this leads to influence bets that don’t matter to the outcome, but they also don’t hurt. The theorem only says that actions must be describable as following a certain policy, it doesn’t exclude that they can be described by other policies as well.
I think you are right, I was confused. A pareto-improvement bet is necessarily one which all parties would selfishly consent to (at least not actively object to).
Maybe I’m missing something, but it seems to me that all of this is straightforwardly justified through simple selfish pareto-improvements.
Take a look at Critchs cake-splitting example in section 3.5. Now imagine varying the utility of splitting. How high does it need to get, before [red->Alice;green->Bob] is no longer a pareto improvement over [(split)] from both player’s selfish perspective before the observation? It’s 27, and thats also exactly where the decision flips when weighing Alice 0.9 and Bob 0.1 in red, and Alice 0.1 and Bob 0.9 in green.
Intuitively, I would say that the reason you don’t bet influence all-or-nothing, or with some other strategy, is precisely because influence is not money. Influence can already be all-or-nothing all by itself, if one player never cares that much more than the other. The influence the “losing” bettor retains in the world where he lost is not some kind of direct benefit to him, the way money would be: it functions instead as a reminder of how bad a treatment he was willing to risk in the unlikely world, and that is of course proportional to how unlikely he thought it is.
So I think all this complicated strategizing you envision in influence betting, actually just comes out exactly to Critches results. Its true that there are many situations where this leads to influence bets that don’t matter to the outcome, but they also don’t hurt. The theorem only says that actions must be describable as following a certain policy, it doesn’t exclude that they can be described by other policies as well.
I think you are right, I was confused. A pareto-improvement bet is necessarily one which all parties would selfishly consent to (at least not actively object to).