Does the horizontal axis of the decision tree in section 3 represent time? If so, I’d advocate smearing those red triangles out over the whole history of actions and events. Even though, in the particular example, it’s unlikely that the agent cares about having been insured as such, apart from the monetary payoffs, in the general case agents care about the whole history. I think that forgetting this point sometimes leads to misapplications of decision theory.
Does the horizontal axis of the decision tree in section 3 represent time?
Yes and no. Yes, because presumably the agent’s end result re: house and money occurs after the fire and the fire will happen after the decision to take out insurance (otherwise, there’s not much point taking out insurance). No, because the diagram isn’t really about time, even if there is an accidental temporal component to it. Instead, the levels of the diagram correspond to different factors of the decision scenario: the first level is about the agent’s choice, the second level about the states of natures and the third about the final outcome.
Given that this is how the diagram works, smearing out the triangles would mix up the levels and damage the clarity of the diagram. To model an agent as caring about whether they were insured or not, we would simply modify the text next to the triangles to something like “Insurance, no house and $99,900”, “Insurance, house and - $100″ and so on (and then we would assign different utilities to the agent based partly on whether they were insured or not as well as whether they had a house and how much money they had).
I think that forgetting this point sometimes leads to misapplications of decision theory.
I agree, though I think that talking of utility rather than money solves many of these problems. After all, utility should already take into account an agents desire to be insured etc and so talk about utility should be less likely to fall into these traps (which isn’t to say there are never any problems)
Does the horizontal axis of the decision tree in section 3 represent time? If so, I’d advocate smearing those red triangles out over the whole history of actions and events. Even though, in the particular example, it’s unlikely that the agent cares about having been insured as such, apart from the monetary payoffs, in the general case agents care about the whole history. I think that forgetting this point sometimes leads to misapplications of decision theory.
Yes and no. Yes, because presumably the agent’s end result re: house and money occurs after the fire and the fire will happen after the decision to take out insurance (otherwise, there’s not much point taking out insurance). No, because the diagram isn’t really about time, even if there is an accidental temporal component to it. Instead, the levels of the diagram correspond to different factors of the decision scenario: the first level is about the agent’s choice, the second level about the states of natures and the third about the final outcome.
Given that this is how the diagram works, smearing out the triangles would mix up the levels and damage the clarity of the diagram. To model an agent as caring about whether they were insured or not, we would simply modify the text next to the triangles to something like “Insurance, no house and $99,900”, “Insurance, house and - $100″ and so on (and then we would assign different utilities to the agent based partly on whether they were insured or not as well as whether they had a house and how much money they had).
I agree, though I think that talking of utility rather than money solves many of these problems. After all, utility should already take into account an agents desire to be insured etc and so talk about utility should be less likely to fall into these traps (which isn’t to say there are never any problems)