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.
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.