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September 2014 Toward Rational Social Decisions: A Review and Some Results
Joseph B. Kadane, Steven N. MacEachern
Bayesian Anal. 9(3): 685-698 (September 2014). DOI: 10.1214/14-BA876

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.

Citation

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Joseph B. Kadane. Steven N. MacEachern. "Toward Rational Social Decisions: A Review and Some Results." Bayesian Anal. 9 (3) 685 - 698, September 2014. https://doi.org/10.1214/14-BA876

Information

Published: September 2014
First available in Project Euclid: 5 September 2014

zbMATH: 1327.62039
MathSciNet: MR3256060
Digital Object Identifier: 10.1214/14-BA876

Rights: Copyright © 2014 International Society for Bayesian Analysis

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Vol.9 • No. 3 • September 2014
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