# Separate aggregation of beliefs and values under ambiguity

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## Abstract

*Maximin expected utility* model for individual decision making under ambiguity prescribes that the individual posits independently a utility function and a set of probability distributions over events to represent the values and belief, respectively. It assumes that individual evaluates each act on the basis of its minimum expected utility over this class of distributions. In this paper, we attempt to generalize the model to social decision making. It is assumed that the society’s belief is formed through a linear aggregation of individual beliefs and society’s values through a linear aggregation of individual values. We propose principles which characterize such separate aggregation procedures. We also generalize *Choquet expected utility* model, which posits a nonadditive measure over events and a utility function to represent belief and values, respectively. We prove that the only aggregation procedures that respect our principles are the separate linear aggregations of beliefs and values.

### Keywords

Linear aggregation Ambiguity Maximin expected utility Choquet expected utility### JEL Classification

D7 D8## Notes

### Acknowledgments

I wish to thank Eric Danan, Itzhak Gilboa, Ani Guerdjikova, Jean-Marc Tallon, especially David Schmeidler, for helpful discussions and many detailed comments.

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