Agreement with reservation of judgment under risk

TL;DR

This paper introduces a new aggregation rule for preferences under risk that accounts for indecisiveness by reserving judgment, ensuring desirable properties that standard methods lack.

Contribution

It proposes the Paretian principle for preference aggregation with indecisiveness, providing a method to construct social utility functions as weighted sums.

Findings

Existence of a social utility function for any combination of individual utilities.

Aggregation rules satisfy natural properties overlooked by classical Pareto.

Framework accommodates indecisiveness in preference aggregation.

Abstract

This paper studies preference aggregation under risk. In our model, each agent has an incomplete preference relation represented by a set of expected utility functions. The classical Pareto principle is silent on agreement involving indecisiveness. To examine the implications of respecting such agreement, we introduce the Paretian principle that can be applied when some individuals reserve their judgment. Our main result shows that, under this principle, for each combination of individuals' utility functions, there exists a corresponding social utility function constructed as a weighted sum of the individual ones. These aggregation rules guarantee natural properties that the standard Pareto principle fails to ensure.