**Les Cahiers de Recherche - HEC Paris**
# No 882:

An additively separable representation in the Savage framework

*HILL Brian *()

**Abstract:** This paper elicits an additively separable representation
of preferences in the Savage framework (where the objects of choice are
acts: measurable functions from an infinite set of states to a potentially
finite set of consequences). A preference relation over acts is represented
by the integral over the subset of the product of the state space and the
consequence space which corresponds to the act, where this integral is
calculated with respect to a “state-dependent utility” measure on this
space. The result applies at the stage prior to the separation of
probabilities and utilities, and requires neither Savage’s P3
(monotonicity) nor his P4 (likelihood ordering). It may thus prove useful
for the development of state-dependent utility representation theorems in
the Savage framework.

**Keywords:** Expected utility; additive representation; state-dependent utility; monotonicity; (follow links to similar papers)

**JEL-Codes:** D81; (follow links to similar papers)

14 pages, October 29, 2007

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