The reduction from 1 to 2 is fairly obvious, just take the action that maximizes expected value. I think this is common to all decision theories.
This doesn’t hold in prospect theory, in which probabilities are scaled before they are used. (Prospect theory is a descriptive theory of buggy human decision-making, not a prescriptive decision theory.) [Edit] Actually, I think this is a disagreement in how you go from 2 to 3. In order to get a disagreement on how you go from 1 to 2, you’d have to look at the normal criticisms of VNM.
It’s also not universal in decision theories involving intelligent adversaries. Especially in zero-sum games, you see lots of minimax solutions (minimize my opponent’s maximum gain). This difference is somewhat superficial, because minimax does reduce to expected value calculation with the assumption that the opponent will always choose the best option available to him by our estimation of his utility function. If you relax that assumption, then you’re back in EV territory, but now you need to elicit probabilities on the actions of an intelligent adversary, which is a difficult problem.
There’s a subtle point here about whether the explicit mechanisms matter. Expected value calculation is flexible enough that any decision procedure can be expressed in terms of expected value calculation, but many implicit assumptions in EV calculation can be violated by those procedures. For example, an implicit assumption of EV calculation is consequentialism in the sense that the preferences are over outcomes, but one could imagine a decision procedure where the preferences are over actions instead of over outcomes, or more realistically action-outcome pairs. We can redefine the outcomes to include the actions, and thus rescue the procedure, but it seems worthwhile to have a separation between consequentialist and deontological positions. If you relax the implicit assumption that probabilities should be treated linearly, then prospect theory can be reformulated as an EV calculation, where outcomes are outcome-probability pairs. But again it seems worthwhile to distinguish between decision algorithms which treat probabilities linearly and nonlinearly.
So the difference is in how to solve step 3, I agree. I wasn’t trying to obscure anything, of course. Rather, I was trying to advocate that we should focus on problem 3 directly, instead of problem 1. … Do you have some more standard terms I should use?
I’m not sure how much we disagree at this point, if you see the difference between EDT and CDT as a disagreement about problem 3.
This doesn’t hold in prospect theory, in which probabilities are scaled before they are used. (Prospect theory is a descriptive theory of buggy human decision-making, not a prescriptive decision theory.) [Edit] Actually, I think this is a disagreement in how you go from 2 to 3. In order to get a disagreement on how you go from 1 to 2, you’d have to look at the normal criticisms of VNM.
It’s also not universal in decision theories involving intelligent adversaries. Especially in zero-sum games, you see lots of minimax solutions (minimize my opponent’s maximum gain). This difference is somewhat superficial, because minimax does reduce to expected value calculation with the assumption that the opponent will always choose the best option available to him by our estimation of his utility function. If you relax that assumption, then you’re back in EV territory, but now you need to elicit probabilities on the actions of an intelligent adversary, which is a difficult problem.
There’s a subtle point here about whether the explicit mechanisms matter. Expected value calculation is flexible enough that any decision procedure can be expressed in terms of expected value calculation, but many implicit assumptions in EV calculation can be violated by those procedures. For example, an implicit assumption of EV calculation is consequentialism in the sense that the preferences are over outcomes, but one could imagine a decision procedure where the preferences are over actions instead of over outcomes, or more realistically action-outcome pairs. We can redefine the outcomes to include the actions, and thus rescue the procedure, but it seems worthwhile to have a separation between consequentialist and deontological positions. If you relax the implicit assumption that probabilities should be treated linearly, then prospect theory can be reformulated as an EV calculation, where outcomes are outcome-probability pairs. But again it seems worthwhile to distinguish between decision algorithms which treat probabilities linearly and nonlinearly.
I’m not sure how much we disagree at this point, if you see the difference between EDT and CDT as a disagreement about problem 3.