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Thursday, December 1, 2022

Can Risk Aversion Survive the Long Run?

Hayden Wilkinson
The Philosophical Quarterly, 2022


Can it be rational to be risk-averse? It seems plausible that the answer is yes—that normative decision theory should accommodate risk aversion. But there is a seemingly compelling class of arguments against our most promising methods of doing so. These long-run arguments point out that, in practice, each decision an agent makes is just one in a very long sequence of such decisions. Given this form of dynamic choice situation and the (Strong) Law of Large Numbers, they conclude that those theories which accommodate risk aversion end up delivering the same verdicts as risk-neutral theories in nearly all practical cases. If so, why not just accept a simpler, risk-neutral theory? The resulting practical verdicts seem to be much the same. In this paper, I show that these arguments do not in fact condemn those risk-aversion-accommodating theories. Risk aversion can indeed survive in the long run.


Where does this leave our most promising risk-aversion-accommodating theories? Do they offer no true alternative to expected value theory, as long-run arguments have suggested?

Such theories do offer an alternative. As shown here, they disagree with expected value theory in various classes of cases: Whenever agents compare options with equal expected value and which one is riskier; when any given pair of options are compared by agents who are simply risk-averse enough; when even agents who are only moderately risk-averse face decisions with particularly high stakes; and, if we reject resolute choice, then also when an agent compares options available to them near the end of their life. And these will include moral decisions on which it is especially important for our theory to get right: high-stakes decisions such as, perhaps, a political leader deciding whether to start a war or an elderly philanthropist deciding where to bequeath their riches. It will not do to simply follow the verdicts of expected value theory in these cases if instead some risk-aversion-accommodating theory is true—disagreement even just in these cases is enough to warrant retaining such theories.

Admittedly, it is true that these theories agree with expected value theory in many cases. We now have formal proof of that. Take any decision between two options (with unequal expected value). If an agent has a suitable risk attitude and faces sufficiently many other decisions in their life, then REU theory and EU theory will agree with expected value theory on the verdict.