Generalized Invariant Preferences: Two-parameter Representations of Preferences

Abstract

In this paper, we generalize the model of Quiggin and Chambers (2004) to allow for ambiguity, and derive conditions, referred to as generalized invariance, under which a two argument representation of preferences may be obtained independent of the existence of a unique probability measure. The first of these two arguments inherits the properties of standard means, namely, that they are upper semi-continuous, translatable and positively linearly homogeneous. But instead of being additive, these generalized means are superadditive. Superadditivity allows for means that are computed (conservatively) with respect to a set of prior probability measures rather than a singleton probability measure. The second argument of the preference structure is a further generalization of the risk index derived in Quiggin and Chambers (2004). It is sublinear in deviations from the generalized mean discussed above.

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