Theoretical Economics 8 (2013), 59–93

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### Scale-invariant uncertainty-averse preferences and source-dependent constant relative risk aversion

*Costis Skiadas*

#### Abstract

Preferences are defined over payoffs that are contingent on a finite number of states representing a horse race (Knightian uncertainty) and a roulette (objective risk). The class of scale-invariant (SI) ambiguity-averse preferences, in a broad sense, is uniquely characterized by a multiple-prior utility representation. Adding a weak certainty independence axiom is shown to imply either unit CRRA toward roulette risk or SI maxmin expected utility. Removing the weak independence axiom but adding a separability assumption on preferences over pure horse-race bets leads to source-dependent constant-relative-risk-aversion expected utility with a higher CRRA assigned to horse-race uncertainty than to roulette risk. The multiple-prior representation in this case is shown to generalize entropic variational preferences. An appendix characterizes the functional forms associated with SI ambiguity-averse preferences in terms of suitable weak independence axioms in place of scale invariance.

Keywords: Uncertainty aversion, ambiguity aversion, source-dependent risk aversion, scale invariance, homotheticity

JEL classification: D81

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