Those are consistent path-dependent preferences, so they can be modeled by a committee of subagents by the method outlined in the post. It would require something like n2n−1 states, I think, one for each current topping times each possible set of toppings tried already. Off the top of my head, I’m not sure how many dimensions it would require, but you can probably figure it out by trying a few small examples.
That said, the right way to model those particular preferences is to introduce uncertainty and Bayesian reasoning. The “hidden state” in this case is clearly information the agent has learned about each topping.
This raises another interesting question: can we just model all path-dependent preferences by introducing uncertainty? What subset can be modeled this way? Nonexistence of a representative agent for markets suggests that we can’t always just use uncertainty, at least without changing our interpretations of “system” or “preference” or “state” somewhat. On the other hand, in some specific cases it is possible to interpret the wealth distribution in a market as a probability distribution in a mixture model—log utilities let us do this, for instance. So I’d guess that there’s some clever criteria that would let us tell whether a committee/market with given utilities can be interpreted as a single Bayesian utility maximizer.
Those are consistent path-dependent preferences, so they can be modeled by a committee of subagents by the method outlined in the post. It would require something like n2n−1 states, I think, one for each current topping times each possible set of toppings tried already. Off the top of my head, I’m not sure how many dimensions it would require, but you can probably figure it out by trying a few small examples.
That said, the right way to model those particular preferences is to introduce uncertainty and Bayesian reasoning. The “hidden state” in this case is clearly information the agent has learned about each topping.
This raises another interesting question: can we just model all path-dependent preferences by introducing uncertainty? What subset can be modeled this way? Nonexistence of a representative agent for markets suggests that we can’t always just use uncertainty, at least without changing our interpretations of “system” or “preference” or “state” somewhat. On the other hand, in some specific cases it is possible to interpret the wealth distribution in a market as a probability distribution in a mixture model—log utilities let us do this, for instance. So I’d guess that there’s some clever criteria that would let us tell whether a committee/market with given utilities can be interpreted as a single Bayesian utility maximizer.