# Ordinal dominance and risk aversion

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## Abstract

We find that, for sufficiently risk-averse agents, strict dominance by *pure or mixed* actions coincides with dominance by *pure* actions in the sense of (Börgers in Econometrica 61(2):423–430, 1993), which, in turn, coincides with the classical notion of strict dominance by pure actions when preferences are asymmetric. Since risk aversion is a *cardinal* feature, all finite single-agent choice problems with *ordinal* preferences admit compatible utility functions which are sufficiently risk averse as to achieve equivalence between pure and mixed dominance. This result extends to some infinite environments.

## Keywords

Rationalizability Dominance Risk aversion Ordinal preferences Revealed preferences## JEL Classification

D81 C72## Notes

### Acknowledgments

This paper originated from a conjecture by Edward Green. We are thankful for his guidance and support, as well as the useful comments from Lisa Posey, Nail Kashaev, Lidia Kosenkova, Jonathan Weinstein, two anonymous referees, and the attendants of the 2014 Spring Midwest Trade and Theory Conference at IUPUI, and the 25\(\mathrm {th}\) International Game Theory Conference at Stony Brook University. We gratefully acknowledge the Human Capital Foundation, (http://www.hcfoundation.ru/en/) and particularly Andrey P. Vavilov, for research support through the Center for the Study of Auctions, Procurements, and Competition Policy (http://capcp.psu.edu/) at the Pennsylvania State University. All remaining errors are our own.

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