Bayesian Analysis

Toward Rational Social Decisions: A Review and Some Results

Joseph B. Kadane and Steven N. MacEachern

Full-text: Open access

Abstract

Bayesian decision theory is profoundly personalistic. It prescribes the decision d that minimizes the expectation of the decision-maker’s loss function L(d,θ) with respect to that person’s opinion π(θ). Attempts to extend this paradigm to more than one decision-maker have generally been unsuccessful, as shown in Part A of this paper. Part B of this paper explores a different decision set-up, in which Bayesians make choices knowing that later Bayesians will make decisions that matter to the earlier Bayesians. We explore conditions under which they together can be modeled as a single Bayesian. There are three reasons for doing so:

1. To understand the common structure of various examples, in some of which the reduction to a single Bayesian is possible, and in some of which it is not. In particular, it helps to deepen our understanding of the desirability of randomization to Bayesians.

2. As a possible computational simplification. When such reduction is possible, standard expected loss minimization software can be used to find optimal actions.

3. As a start toward a better understanding of social decision-making.

Article information

Source
Bayesian Anal., Volume 9, Number 3 (2014), 685-698.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1409921110

Digital Object Identifier
doi:10.1214/14-BA876

Mathematical Reviews number (MathSciNet)
MR3256060

Zentralblatt MATH identifier
1327.62039

Keywords
social decisions compromise randomization

Citation

Kadane, Joseph B.; MacEachern, Steven N. Toward Rational Social Decisions: A Review and Some Results. Bayesian Anal. 9 (2014), no. 3, 685--698. doi:10.1214/14-BA876. https://projecteuclid.org/euclid.ba/1409921110


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