What Is Risk Aversion?

Abstract

According to the orthodox treatment of risk attitudes in decision theory, such attitudes are explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for con ‡ating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that we model risk attitudes in terms of a risk function that is independent of the agent's utility and probability functions. The main problem with that approach is that it suggests that attitudes to risk are wholly distinct from people's (non-instrumental) desires. To overcome this problem, we develop a framework where an agent's utility function is partly de…ned over chance propositions (i.e., propositions describing objective probability distributions), and argue that one should represent di¤erent risk attitudes in terms of di¤erent forms of the utility function over such propositions.

Ambiguity aversion behind the veil of ignorance

“…The importance of attitudes to ambiguity was originally brought to the attention of decision theorists and economists through the so-called Ellsberg paradox (Ellsberg 1961), one version of which is presented in the Appendix (A.1). But they can be illustrated much more simply with the following example (Stefánsson and Bradley 2019). 13 Suppose that you have in front of you a coin, C 1 , that you know to be perfectly symmetric, and that you know to have been tossed a great number of times and has come up heads exactly as many times as it has come up tails.…”

“…The decision theory that Buchak applies to her veil of ignorance argument, that is, her "risk weighted expected utility theory", cannot capture ambiguity aversion (for a discussion, see Stefánsson and Bradley's 2019). Nor, of course, can the theory that Harsanyi applied, that is, expected utility theory as developed by von Neumann and Morgenstern (1944).…”

“…We can partition this proposition into two possibilities according to whether the coin comes up heads or tails (for simplicity, we can assume that it cannot land and stay on its edge). Hence, Desirability entails that the desirability of G equals the utility of the gamble when the coin comes up heads, weighted by your conditional subjective probability for the coin coming up heads given G, plus the utility of the gamble when the coin comes up tails, weighted by your conditional subjective probability for the coin coming up tails given G. 21 Now let's briefly see how the theory sketched above can simultaneously account for the Allais preference and ambiguity aversion (but see Stefánsson and Bradley 2019 for a more thorough discussion). The simple reason why it can account for both these attitudes, is that since chance distributions are included in the domain of the utility function, it can accommodate the idea that the added benefit of an increase in the chance of a good might depend on the prior chance; for instance, the idea that a 0.1 gain in the chance of a good is more valuable when the prior chance was 0 than when the prior chance was 0.4.…”

“…Stefánsson and Bradley (2015) argue at length that Chance Neutrality is not a requirement of rationality. In fact, it is the denial of Chance Neutrality that allows for a unified treatment of the Allais preference and ambiguity aversion (Stefánsson and Bradley 2019). Hence, if we want to allow for both types of attitudes behind the veil, 25 "Standard" Utilitarianism is the view that the moral value of a distribution is a linear additively separable function of the (final) welfare of the individuals in the distribution.…”

“…The claim that ambiguity aversion is a form of risk aversion is defended byBradley (2016) andStefánsson and Bradley (2019).…”