Committee Decision Making: The Multicategory Case.

• Author: Britto, Ronald

Ronald Britto [*]

If a committee of n members is asked to make a decision to accept or reject a proposal and each committee member summarizes his/her assessment of the proposal by selecting one of several options (like "highly recommend," "recommend," etc.), how are these to be aggregated so as to come up with an overall recommendation? I show, on the assumption that the judgements of the individual committee members are statistically independent, that this is to be done by weighting the numbers of members selecting each option by some suitable weights; if the resulting number is larger than some benchmark number, the proposal is accepted, and otherwise rejected.

1. Introduction

   Committees are often formed to enable a central decision maker to come to a yes or no decision on a project or a series of projects. Examples are loan committees in banks that evaluate applications for loans, planning committees for firms or planning agencies that have to evaluate projects for adoption, recruiting committees in universities evaluating candidates for positions, and so on. In all such cases, the idea is to pool the judgements of the committee members so as to come up with an assessment of the project (as I shall henceforth call it) that is superior to the assessment that any individual would make. The underlying assumption is that whether the project is acceptable or not is not known in advance, but that nevertheless the degree of uncertainty about its merits can be reduced by using a committee--in a sense to be made precise later. This paper deals with the determination of a rule whereby the judgements of the individual committee members are aggregated optimally, enabling the final decision m aker to come to a quick decision on the acceptability of the project.

   The papers in the literature on this topic have considered two types of models. In the first, the discrete case, both the set of projects as well as the set of outcomes that the committee members can select from are discrete, indeed binary. Thus the projects fall into one of two types--acceptable or nonacceptable--and the committee members provide their assessments in yes/no terms: yes if they believe that the project is acceptable and no in the other case. The problem investigated is the nature of the optimal consensus, that is, the minimum number of suitably weighted yes votes necessary for approval of the project. Models of this type appear in papers by Nitzan and Paroush (1981, 1982), Sah and Stiglitz (1986, 1988), Sah (1990), and most recently, in Ben-Yashar and Nitzan (1997). In the last paper, Ben-Yashar and Nitzan generalized the previous models and showed that the optimal decision rule requires that the votes of the individual committee members be suitably weighted and then aggregated. They called t his the qualified weighted majority rule. [1]

   The second type of models deals with the case where both the set of projects as well as the set of options available to the committee members are continuous sets. The numbers provided by the committee members are then aggregated optimally and the resulting number is used to determine the acceptability of the project. Klevorick, Rothschild, and Winship (1984) have used such a model to analyze jury decision making in criminal cases where the decision is whether to bring in a verdict of guilty or not guilty. In their case, the continuous variable describing the "project" can only take on one of two values, because there are only two projects (states).

   There is an extension of the first type of model that has not been considered in the literature, although it occurs in many situations in real life. Here the committee members are asked to check one of several categories summarizing their overall assessment. In letters of recommendation, for instance, one commonly is asked to check one of the categories "highly recommend," "recommend," "recommend with reservation," and "do not recommend." If each committee member records a summary evaluation in this fashion, how are these evaluations to be aggregated so as to come up with an overall evaluation? This question has not been tackled in the literature. The present paper offers an answer for one important set of cases, viz., when the judgements of the individual committee members are statistically independent. I show that, in this set of cases, the numbers of committee members voting in each category are weighted and then aggregated; the resulting number is then...