In Savage’s setup, the world has some state (that you end up having uncertainty about), and then you have some set of actions that maps states to outcomes (that you have preferences about). Savage’s theorem basically says to do something isomorphic to EUM over actions.
The trick is noticing that what plays the role of “actions” is identified functionally, by their role as a function from states-you-have-uncertainty-about to outcomes-you-have-preferences-about. They are not identified by their natural-language role in a story, or what they would look like to an observer, they’re identified by the fact that they fit into this orthodox progression of states → actions → outcomes. An “action” in Savage’s theorem might actually be what we would call a policy, if it’s the policies that fill the functional role. This is the case in the absent-minded driver: the things that seem like actions don’t actually fill the role of actions in Savage’s theorem, which is why you get different results by choosing a policy.
A plug for Savage’s theorem: it’s also great for resolving the absent-minded driver paradox.
In Savage’s setup, the world has some state (that you end up having uncertainty about), and then you have some set of actions that maps states to outcomes (that you have preferences about). Savage’s theorem basically says to do something isomorphic to EUM over actions.
The trick is noticing that what plays the role of “actions” is identified functionally, by their role as a function from states-you-have-uncertainty-about to outcomes-you-have-preferences-about. They are not identified by their natural-language role in a story, or what they would look like to an observer, they’re identified by the fact that they fit into this orthodox progression of states → actions → outcomes. An “action” in Savage’s theorem might actually be what we would call a policy, if it’s the policies that fill the functional role. This is the case in the absent-minded driver: the things that seem like actions don’t actually fill the role of actions in Savage’s theorem, which is why you get different results by choosing a policy.