Consider a pizza-eating agent with the following “grass is always greener on the other side of the fence” preference: it has no “initial” preference between toppings but as soon as it has one it realises it doesn’t like it and then prefers all other not-yet-tried toppings to the one it’s got (and to others it’s tried).
There aren’t any preference cycles here—if you give it mushroom it then prefers pepperoni, but having switched to pepperoni it then doesn’t want to switch back to mushroom. If our agent has no opinion about comparisons between all toppings it’s tried, and between all toppings it hasn’t tried, then there are no outright inconsistencies either.
Can you model this situation in terms of committees of subagents? Can you do it without requiring an unreasonably large number of subagents?
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.
Consider a pizza-eating agent with the following “grass is always greener on the other side of the fence” preference: it has no “initial” preference between toppings but as soon as it has one it realises it doesn’t like it and then prefers all other not-yet-tried toppings to the one it’s got (and to others it’s tried).
There aren’t any preference cycles here—if you give it mushroom it then prefers pepperoni, but having switched to pepperoni it then doesn’t want to switch back to mushroom. If our agent has no opinion about comparisons between all toppings it’s tried, and between all toppings it hasn’t tried, then there are no outright inconsistencies either.
Can you model this situation in terms of committees of subagents? Can you do it without requiring an unreasonably large number of subagents?
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.