International Workshop on Logic, Rationality and Interaction

Logic, Rationality, and Interaction pp 90-101

# Context-Dependent Utilities

A Solution to the Problem of Constant Acts in Savage
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9394)

## Abstract

Savage’s framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to consequences. Savage’s derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a “constant act” which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous – including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions.

### Keywords

subjective expected utility Savage’s postulates constant acts context-dependent decision making

## Preview

### References

1. 1.
Fishburn, P.: Subjective expected utility: A review of normative theories. Theory and Decision 13(2), 139–199 (1981)
2. 2.
Fishburn, P.C.: Utility Theory for Decision Making. Wiley, New York (1970)
3. 3.
Pratt, J.W.: Some comments on some axioms for decision making under uncertainty. In: Balch, M., McFadden, D., Wu, S. (eds.) Essays on Economic Behavior Under Uncertainty, pp. 82–92. North-Holland Pub. Co., American Elsevier Pub. Co., Amsterdam, New York (1974)Google Scholar
4. 4.
Savage, L.J.: The Foundations of Statistics. John Wiley & Sons, Inc. (1954)Google Scholar
5. 5.
Savage, L.J.: The Foundations of Statistics. Second revised edn. Dover Publications, Inc. (1972)Google Scholar
6. 6.
Seidenfeld, T., Schervish, M.: A conflict between finite additivity and avoiding dutch book. Philosophy of Science, 398–412 (1983)Google Scholar
7. 7.
Shafer, G.: Savage revisited. Statistical Science 1(4), 463–485 (1986)