Agreement with reservation of judgment under risk

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.