I personally think decision theory is more important than probability theory. And anthropics does introduce some subtleties into the betting setup—you can’t bet or receive rewards if you’re dead.
But there are ways around it. For instance, if the cold war is still on, we can ask how large X has to be if you would prefer X units of consumption after the war, if you survive, to 1 unit of consumption now.
Obviously the you that survived the cold war and knows they survived, cannot be given a decent bet on the survival. But we can give you a bet on, for instance “new evidence has just come to light showing that the cuban missile crisis was far more dangerous/far safer than we thought. Before we tell you the evidence, care to bet in which direction the evidence will point?”
Then since we can actually express these conditional probabilities in bets, the usual Dutch Book arguments show that they must update in the standard way.
I personally think decision theory is more important than probability theory. And anthropics does introduce some subtleties into the betting setup—you can’t bet or receive rewards if you’re dead.
But there are ways around it. For instance, if the cold war is still on, we can ask how large X has to be if you would prefer X units of consumption after the war, if you survive, to 1 unit of consumption now.
Obviously the you that survived the cold war and knows they survived, cannot be given a decent bet on the survival. But we can give you a bet on, for instance “new evidence has just come to light showing that the cuban missile crisis was far more dangerous/far safer than we thought. Before we tell you the evidence, care to bet in which direction the evidence will point?”
Then since we can actually express these conditional probabilities in bets, the usual Dutch Book arguments show that they must update in the standard way.