E(U|NS) = 0.8, E(U|SN) = 0.8 Are the best options from a strict U perspective, and exactly tie. Since you’ve not included mixed actions, the agent must arbitrarily pick one, but arbitrarily picking one seems like favouring an action that is only better because it affects the expected outcome of the war, if I’ve understood correctly? I’m pretty sure this is resolved by mixed actions though: The agent can take the policy {NS at 0.5, SN at 0.5}, which also gets U of 0.8 and does not effect the expected outcome of the war, and claim supreme unbiasedness for having done so. If the scores were very slightly different, such that the mixed strategy that had no expected effect wasn’t also optimal, it does have to choose between maximising expected utility and preserving that its strategy doesn’t only get that utility by way of changing the odds of the event, I think on this model it has to only decide to favour one to the extent it can justify it without considering the measure of the effect it has on the outcome by shifting its own decision weights, but it’s not worth it in that case so it still does the 50⁄50 split?
E(U|NS) = 0.8, E(U|SN) = 0.8
Are the best options from a strict U perspective, and exactly tie. Since you’ve not included mixed actions, the agent must arbitrarily pick one, but arbitrarily picking one seems like favouring an action that is only better because it affects the expected outcome of the war, if I’ve understood correctly?
I’m pretty sure this is resolved by mixed actions though: The agent can take the policy {NS at 0.5, SN at 0.5}, which also gets U of 0.8 and does not effect the expected outcome of the war, and claim supreme unbiasedness for having done so.
If the scores were very slightly different, such that the mixed strategy that had no expected effect wasn’t also optimal, it does have to choose between maximising expected utility and preserving that its strategy doesn’t only get that utility by way of changing the odds of the event, I think on this model it has to only decide to favour one to the extent it can justify it without considering the measure of the effect it has on the outcome by shifting its own decision weights, but it’s not worth it in that case so it still does the 50⁄50 split?