Minimum cost consensus with quadratic cost functions

Authors:
David Ben-Arieh;Todd Easton;Brandon Evans
Affiliations:
Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS;Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS;Lockheed Martin Aeronautics Company, Fort Worth, TX
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special section: Best papers from the 2007 biometrics: Theory, applications, and systems (BTAS 07) conference
Year:
2009

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Abstract

Group consensus is an important method for making business decisions. In this paper, the consensus process is defined as a dynamic and interactive group decision process, which is coordinated by a moderator who helps the experts to gradually move their opinions closer to each other. This paper describes the importance of group consensus and the need to minimize the cost of this process. Furthermore, this paper describes the costs associated with decision making using group consensus and then describes three methods of reaching consensus assuming quadratic costs for a single-criterion decision problem. The first method finds the group opinion (consensus) that yields the minimum cost of reaching throughout the group. The second method finds the opinion with the minimum cost of the consensus provided that all experts must be within a given distance of the group opinion. The last method finds the maximum number of experts that can fit within the consensus, given a specified budget constraint.