There are no actions in decision theory, only preferences. Or put another way, an agent takes only one action, ever, which is to choose a maximal element of their preference ordering. There are no sequences of actions over time; there is no time. To bring sequences of actions into the fold of “decision theory”, the outcomes of those sequences would be the things over which the preference ordering ranges, and once again there is only the action of choosing a most preferred. In the limit, there is only the single action of choosing the most preferred entire future history of the agent’s actions, evaluated according to their influence on the agent’s entire future light-cone, and their preference over different possible future light-cones. But this is absurdly impractical, and this is “monkeys typing Shakespeare” levels of impracticality, not mere Heath Robinson.
This, I think, is a weakness of “decision theory”, which might better be called “preference theory”. For example, the SEP article on decision theory hardly mentions any of the considerations you bring up.
Though the usual money pump justification for transitivity does rely on time and a “sequence of actions”. Which is strange insofar decision theory doesn’t even model such temporal sequences.
Yes, the money pump argument is an intuition pump for transitivity. Yet it is not formalised within, say, the VNM or Savage axioms, but is commentary upon them. The common response to it, that “I’d notice and stop doing that” goes outside the scope of the theory.
Game theory takes things further, as do things like Kelly betting and theories that prescribe not individual actions but policies, but my impression is that there is as yet no unified theory of action over time in a world that is changed by one’s actions.
There are no actions in decision theory, only preferences. Or put another way, an agent takes only one action, ever, which is to choose a maximal element of their preference ordering. There are no sequences of actions over time; there is no time.
There are no actions in decision theory, only preferences. Or put another way, an agent takes only one action, ever, which is to choose a maximal element of their preference ordering. There are no sequences of actions over time; there is no time. To bring sequences of actions into the fold of “decision theory”, the outcomes of those sequences would be the things over which the preference ordering ranges, and once again there is only the action of choosing a most preferred. In the limit, there is only the single action of choosing the most preferred entire future history of the agent’s actions, evaluated according to their influence on the agent’s entire future light-cone, and their preference over different possible future light-cones. But this is absurdly impractical, and this is “monkeys typing Shakespeare” levels of impracticality, not mere Heath Robinson.
This, I think, is a weakness of “decision theory”, which might better be called “preference theory”. For example, the SEP article on decision theory hardly mentions any of the considerations you bring up.
It seems that the OP is simply confused about the fact that preferences should be over the final outcomes—this response equivocates a bit too much.
Though the usual money pump justification for transitivity does rely on time and a “sequence of actions”. Which is strange insofar decision theory doesn’t even model such temporal sequences.
Yes, the money pump argument is an intuition pump for transitivity. Yet it is not formalised within, say, the VNM or Savage axioms, but is commentary upon them. The common response to it, that “I’d notice and stop doing that” goes outside the scope of the theory.
Game theory takes things further, as do things like Kelly betting and theories that prescribe not individual actions but policies, but my impression is that there is as yet no unified theory of action over time in a world that is changed by one’s actions.
That’s not true. Dynamic/sequential choice is quite a large part of decision theory.