How Valuable Are Chances?

Abstract

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What Is Risk Aversion?

“…We will not pursue this normative issue any further however as it has been argued at length elsewhere that Linearity and Chance Neutrality are not requirements of rationality (see Stefánsson and Bradley 2015). Instead let us return to the opening observation that dislike of risk per se, rational or otherwise, is psychologically very di¤erent from the decreasing marginal desirability of quantities of concrete goods, even though the two phenomena may give rise to the same choice behaviour.…”

“…The utility function is supposed to represent desire ... and the probability function is supposed to represent belief ... We try to make beliefs '…t the world,'and we try 6 Another problem with EU theory that REU theory cannot solve, unlike the theory developed in the next section, is the Diamond (1967) 'paradox', which is based on EU theory's inability to account for the intuition that sometimes it is valuable to give people a chance at a good even if they do not end up receiving the good. See Stefánsson and Bradley (2015) for an explanation of how the framework discussed in the next section is partly motivated by the problem raised by Diamond, and Stefánsson (2015: sec. 4) for a demonstration of REU theory's inability to solve it.…”

“…Informally, we can think of it as capturing the idea that chances do not matter intrinsically to the agent; they matter only instrumentally, as means to the attainment of the prizes that they are chances of. More exactly, as shown in Stefánsson and Bradley (2015: Theorem 1), Linearity encodes the neutrality of chances, the idea that one should not care about the chance of a (maximally speci…c) outcome once one knows whether or not the outcome has been realised. Formally (and adopting the convention that the status quo has desirability zero):…”

Ambiguity aversion behind the veil of ignorance

“…However, if we assume that rational people behind the veil of ignorance satisfy what Stefánsson and Bradley (2015) call Chance Neutrality (to be explained below), then the conclusion of the veil of ignorance argument is standard 25 Utilitarianism. So, what I have called Distribution-Sensitive Utilitarianism is not inconsistent with (standard) Utilitarianism; rather, the latter is a special case of the former.…”

“…Informally, Chance Neutrality is the view that once it is known which outcome obtained, it is a matter of ethical and practical irrelevance what the chances were. As Stefánsson and Bradley (2015) note, Chance Neutrality entails what we could call instrumentalism about chances: chances only matter in so far as they make good or bad outcomes more or less likely, but they are of no value in and of themselves. To take an example, Chance Neutrality entails that if a patient dies of kidney failure, then the fact that he had, say, the same chance as any other patient of receiving the hospital's only kidney makes no difference.…”