## Bayesian Analysis

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

### Toward Rational Social Decisions: A Review and Some Results

Joseph B. Kadane and Steven N. MacEachern

#### Abstract

Bayesian decision theory is profoundly personalistic. It prescribes the decision $d$ that minimizes the expectation of the decision-maker’s loss function $L(d,\theta )$ with respect to that person’s opinion $\pi (\theta )$. 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