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

DOI: 10.1007/978-3-662-48561-3_8

Volume 9394 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Gaifman H., Liu Y. (2015) Context-Dependent Utilities. In: van der Hoek W., Holliday W., Wang W. (eds) Logic, Rationality, and Interaction. Lecture Notes in Computer Science, vol 9394. Springer, Berlin, Heidelberg

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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of PhilosophyColumbia UniversityNew YorkUSA