Aggregating Incomplete Individual Ratings in Group Resource Allocation Decisions

Abstract

This paper addresses a decision to be made by a group of evaluators as to how to allocate a pool of monetary resources to a set of candidates. The group decision is an aggregation of the individual allocation recommendations by the evaluators. Evaluators may also be candidates to receive allocations and not allowed to vote a recommendation for themselves. Further, evaluators can elect to exclude some candidates from their evaluations because they do not believe they are qualified to judge some candidates. Two models are presented for aggregation of individual evaluations using the mean and median, respectively, as the basis for the group consensus. In circumstances where some evaluators do not recommend allocations for all candidates, the calculation of the mean recommendations requires the solution of a system of linear equations and the calculation of the median recommendations requires an iterative search algorithm. Conditions for existence of a group consensus allocation for each model are described and the strengths and weaknesses of each model are explored. The models can be applied to a variety of different group decisions, including rating of candidates for a job or allocating a budget.