Terence Tao on Nostr: Given the general tendency to prefer risk aversion, one possible strategy is to try ...

Given the general tendency to prefer risk aversion, one possible strategy is to try to minimize "value at risk" - the value that one might realize in a bad (though not absolutely worst case) scenario. Here, a simple such metric would be "reward minus risk" - the lower end of the range of typical outcomes. For instance, in the above model, the "safe" action has a value at risk of 5-3 = +2: even in a somewhat bad-luck scenario, one would still expect to make a small gain. In contrast, the value at risk for the "bold" would have a value at risk of 9-10=-1, so with bad luck one would actually have a small loss. The advice would then be to take the safe action instead of the bold one.

One interesting thing about this model is that it is not affected by predictable exogenous shocks. Suppose for instance there is an event that causes all projected outcomes to be revised downward by the same constant factor, let's say -5 to sake of argument. The projected return from the safe action now revises downward from 5±3 to 0±3, with value at risk going down from +2 to -3; and the projected return from the bold action similarly revises downward from 9±10 to 4±10, with the value at risk going down from -1 to -6. This is obviously not good news for the person having to make the choice, but the shock does not actually change one's decision making; the safe action continues to have less value at risk than the bold one, and so this decision framework would still recommend taking the safe action. (2/4)