Comment on indexical uncertainty and the Axiom of Independence

Mon, 08 Jun 2009 20:41:53 GMT

This idea that possible worlds can trade with each other seems to have fairly radical implications. Together with Eliezer's idea that agents who know each other's source code ought to play cooperate in one-shot PD, doesn't it imply that all sufficiently intelligent and reflective agents across all possible worlds should do a global trade and adopt a single set of preferences that represents a compromise between all of their individual preferences? (Note: the resulting unified preferences are not necessarily characterized by expected utility maximization.)

Let me trace the steps of my logic here. First take 2 agents in the same world who know each other's source code. Clearly, each adopting a common set of preferences can be viewed as playing Cooperate in a one-shot PD. Now take an agent who has identified a counterfactual agent in another possible world (who has in turn identified it). Each agent should also adopt a common set of preferences, in the expectation that the other will do so as well. Either iterating this process, or by doing a single global trade across all agents in all possible worlds, we should arrive at a common set of preferences between everyone.

Hmm, maybe this is just what you meant by "one global decision"? Since my original interest was to figure out what probabilities mean in the context of indexical uncertainty, let me ask you, do probabilities have any role to play in your decision theory?

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