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torekp comments on A fungibility theorem - Less Wrong
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But what if the value an agent assigns to life events depends on the probabilities as well as the final results? Wei Dai gave one example, a concern for fairness, that can make this true, but simple risk aversion or thrill seeking would also suffice. Then it seems to me that the interpretation of the "linear aggregation function" becomes problematic.
Simple risk aversion can be captured in the mapping of results to reals. Prospect-theory style risk aversion, whereby small probabilities are inflated, can't be, but that's a feature, not a bug.
Thrill seeking- in the sense of deriving value from results being determined by randomness- does not seem like it can be fit into a VNM framework. That's a failing descriptively, but I'm not sure it's a failing prescriptively.
Right, if you have values like that, then the hypotheses of the theorem don't obtain.