## Statistical Science

### Savage Revisited

Glenn Shafer

#### Abstract

Three decades ago L. J. Savage published The Foundations of Statistics, in which he argued that it is normative to make choices that maximize subjective expected utility. Savage based his argument on a set of postulates for rational behavior. Empirical research during the past three decades has shown that people often violate these postulates, but it is widely believed that this is irrelevant to Savage's argument. This article re-examines Savage's argument and concludes that his postulates cannot be so thoroughly insulated from the empirical facts. The argument actually relies heavily on assumptions that have been empirically refuted. Savage's normative interpretation of subjective expected utility must therefore be revised. The revision suggested here emphasizes the constructive nature of probability and preference. It also emphasizes the constructive nature of small worlds, the frameworks within which probability and utility judgments are made. According to the constructive understanding, an analysis of a decision problem by subjective expected utility is merely an argument, an argument that compares that decision problem to the decision problem of a gambler in a pure game of chance. This argument by analogy may or may not be cogent. In some cases other arguments are more cogent.

#### Article information

Source
Statist. Sci., Volume 1, Number 4 (1986), 463-485.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177013518

Digital Object Identifier
doi:10.1214/ss/1177013518

Mathematical Reviews number (MathSciNet)
MR874479

Zentralblatt MATH identifier
0613.62002

JSTOR
links.jstor.org

#### Citation

Shafer, Glenn. Savage Revisited. Statist. Sci. 1 (1986), no. 4, 463--485. doi:10.1214/ss/1177013518. https://projecteuclid.org/euclid.ss/1177013518

#### See also

• See Comment: D. V. Lindley. [Savage Revisited]: Comment. Statist. Sci., Volume 1, Number 4 (1986), 486--488.
• See Comment: A. P. Dawid. [Savage Revisited]: Comment. Statist. Sci., Volume 1, Number 4 (1986), 488--492.
• See Comment: Peter C. Fishburn. [Savage Revisited]: Comment. Statist. Sci., Volume 1, Number 4 (1986), 492--495.
• See Comment: Robyn M. Dawes. [Savage Revisited]: Comment. Statist. Sci., Volume 1, Number 4 (1986), 495--497.
• See Comment: John W. Pratt. [Savage Revisited]: Comment. Statist. Sci., Volume 1, Number 4 (1986), 498--499.
• See Comment: Glenn Shafer. [Savage Revisited]: Rejoinder. Statist. Sci., Volume 1, Number 4 (1986), 499--501.