Mean - Dispersion Preferences

The starting point for this paper is the variational preference model introduced by Maccheroni et al [2006]), which includes Gilboa-Schmeidler multiple-prior preferences and Hansen-Sargent multiplier preferences. First, we show that any variational preferences admit a `primal' representation with a natural interpretation: a `mean' expected-utility of the act minus a `dispersion measure' that depends only on state-by-state dierences from that mean. The second term can be thought of as reeecting the agent's dislike of dispersion: it is the premium (in terms of the mean utility) that the individual would be willing to pay to remove all subjective uncertainty associated with the act. The primal representation thus highlights a key behavioral aspect of all variational preferences: the premium does not depend on the average utility of an act. That is, variational preferences exhibit constant absolute ambiguity aversion. Second, we develop a generalization of the variational preference model. The generalization is still based on a mean utility and a dispersion measure that depends only on the state-wise dierences from the mean. But the new model is only weakly separable in terms of these two summary statistics. Thus, the ambiguity premium need not be constant in this model. Mean-dispersion preferences can accommodate many existing models. We show how these correspond to diierent attitudes toward dispersion. Finally, we use the model to compare dierent notions of aversion to variation across states such as uncertainty aversion, second-order risk aversion and issue preference.