Benchmarking real-valued acts
A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark B; that is, an act f is evaluated by means of the functional V(f) = P(f > B). Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P.
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- Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
- Hong, Chew Soo & Wakker, Peter, 1996. "The Comonotonic Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 12(1), pages 5-27, January.
- Chateauneuf, Alain, 1999. "Comonotonicity axioms and rank-dependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 21-45, August.
- Robert Bordley & Marco LiCalzi, 2000. "Decision analysis using targets instead of utility functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 23(1), pages 53-74.
- Segal, Uzi., 1991.
"The Measure Representation: A Correction,"
781, California Institute of Technology, Division of the Humanities and Social Sciences.
- LiCalzi, Marco, 1998. "Variations on the measure representation approach," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 255-269, April.
- W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
- Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, EconWPA.
- Wakker, Peter, 1993. "Counterexamples to Segal's Measure Representation Theorem," Journal of Risk and Uncertainty, Springer, vol. 6(1), pages 91-98, January.
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