Optimal Decision Rules for the Discursive Dilemma

TL;DR

This paper investigates optimal decision rules for the discursive dilemma, aiming to minimize combined false positive and false negative probabilities under mild rule restrictions.

Contribution

It introduces a quantitative criterion for selecting the best decision rule in the discursive dilemma, considering probabilistic assessments of committee members.

Findings

Identifies the optimal decision rule under probabilistic accuracy assumptions.

Provides a framework for evaluating decision rules based on false positive/negative trade-offs.

Offers insights into decision-making processes in collective reasoning.

Abstract

We study the classical discursive dilemma from the point of view of finding the best decision rule according to a quantitative criterion, under very mild restrictions on the set of admissible rules. The members of the deciding committee are assumed to have a certain probability to assess correctly the truth or falsity of the premisses, and the best rule is the one that minimises a combination of the probabilities of false positives and false negatives on the conclusion.