An Integral Representation for Non Simple Acts with Certainty Equivalents

In this paper we considera continuous subjective expected unity model with a connected space of consequences (CSEU, for brevity). This class of models has recently received attention (see Wakker (1989)). Like in Savage (1954), we consider a finitely additive probability measure on a [sigma]-field of events. The aim of the paper is to show that in such a Savagean set-up the appropriate condition to impose on the set of acts to get a CSEU model is to require the existence of certainty equivalents. While quite intuitive, several technical difficulties had to be solved in order to make this argument rigorous, as emerges in the appendix. Nevertheless, the results of the paper are clear and easy to understand.