Parametric representation of preferences

A preference is invariant with respect to a transformation τ if its ranking of acts is unaffected by a reshuffling of the states under τ . We show that any invariant preference must be parametric: there is a unique sufficient set of parameters such that the preference ranks acts according to their expected utility given the parameters. This property holds for all non-trivial preferences, provided only that they are reflexive, transitive, monotone, continuous and mixture linear. ∗The present paper subsumes DeCastro and Al-Najjar (2009), available on the authors’ webpages. Many of the ideas presented here, including subjective sufficient statistic theorem, parametric representations, and parameter-based acts appeared there, as did the major technical results on ergodic theory. †We thank Paolo Ghirardato, Ben Polak and Marciano Siniscalchi for extensive discussions and thoughtful comments when we presented to them the main ideas of this project during the summer and fall of 2009. We also thank Simone Galperti for his research assistance. ‡ Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston IL 60208. § Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston IL 60208.