**Les Cahiers de Recherche - HEC Paris**
# No 883:

When is there state independence?

*HILL Brian *()

**Abstract:** It has been noticed that whether a preference relation can
be represented by state-independent utilities as opposed to state-dependent
utilities may depend on which acts count as constant acts [Schervish et
al., 1990]. Indeed, this remark underlies an extension of Savage’s expected
utility theory to the state-dependent case that was proposed by Edi Karni
[Karni, 1993]. This paper contains a characterisation of the preference
relations that permit a choice of acts which can play the role of constant
acts, and relative to which there is a representation involving a
state-independent utility function. This result applies both in the Savage
and in the Anscombe & Aumann frameworks. It has as an immediate corollary
an extension of Karni’s representation theorem. Finally, it is of
methodological interest, insofar that it harnesses techniques from
mathematical logic to prove a theorem of interest to decision theorists and
economists.

**Keywords:** Subjective expected utility; State-dependent utility; Monotonicity axiom; (follow links to similar papers)

**JEL-Codes:** C69; D81; (follow links to similar papers)

883 pages, November 22, 2007

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