Yes, that seems like an interesting way to think about your puzzle. Thanks for pointing out the connection. Have you considered what kind of decision theory would be needed to handle these violations of Independence?
Whole strategies need to be considered instead of individual actions, so that there is only one global decision, with individual actions selected as components of the overall calculation of the better global strategy. Indexical uncertainty becomes a constraint on strategy that requires actions to be equal in indistinguishable situations. More generally, different actions of the same agent can be regarded as separate actions of separate agents sharing the same preferences, who cooperate, exchanging info through the history of agent’s development that connects them (it). Even more generally, the same process should take care of cooperation of agents with different preferences. Even in that situation, the best global strategy will take into account (coordinate) all actions performed by all agents, including counterfactual ones (a benefit of reflective consistency enabling to perform calculations on the spot, not necessarily in advance).
So, expected utility (or some other order to that effect) is compared for the global strategies involving not just the agent, but all cooperating agents, and then the agent just plays its part in the selected global strategy. If the agent has a lot of info about where it is (low indexical uncertainty), then it’ll be able to perform a precisely targeted move within the global strategy, suited best for the place it’s in. The counterfactual and other-time/other-place counterparts of the agent will perform different moves for different details of the situation. Uncertainty (of any kind) limits the ability of the agent to custom-make its moves, so it must choose a single move targeted at the larger area of the territory over which it’s uncertain, instead of choosing different moves for each of its points, if it had the possible info discriminating among them.
Yes, that seems like an interesting way to think about your puzzle. Thanks for pointing out the connection. Have you considered what kind of decision theory would be needed to handle these violations of Independence?
Whole strategies need to be considered instead of individual actions, so that there is only one global decision, with individual actions selected as components of the overall calculation of the better global strategy. Indexical uncertainty becomes a constraint on strategy that requires actions to be equal in indistinguishable situations. More generally, different actions of the same agent can be regarded as separate actions of separate agents sharing the same preferences, who cooperate, exchanging info through the history of agent’s development that connects them (it). Even more generally, the same process should take care of cooperation of agents with different preferences. Even in that situation, the best global strategy will take into account (coordinate) all actions performed by all agents, including counterfactual ones (a benefit of reflective consistency enabling to perform calculations on the spot, not necessarily in advance).
So, expected utility (or some other order to that effect) is compared for the global strategies involving not just the agent, but all cooperating agents, and then the agent just plays its part in the selected global strategy. If the agent has a lot of info about where it is (low indexical uncertainty), then it’ll be able to perform a precisely targeted move within the global strategy, suited best for the place it’s in. The counterfactual and other-time/other-place counterparts of the agent will perform different moves for different details of the situation. Uncertainty (of any kind) limits the ability of the agent to custom-make its moves, so it must choose a single move targeted at the larger area of the territory over which it’s uncertain, instead of choosing different moves for each of its points, if it had the possible info discriminating among them.