Groupe d’études et de recherche en analyse des décisions


Consensus Decision Process: Models, Theory and Experimental Verification (Revised and Extended)


A management decision based on voting by a team of experts has been commonly used and has been examined by the social scientists. Various approaches have been considered for optimizing the probability of obtaining a correct consensus decision while minimizing that of making an erroneous one. We have derived a mathematical model which independently proves and extends the results of Condorcet to a group of individuals with different abilities in making correct decisions and avoiding risks in making wrong decisions. Our derivations include some quantitative conditions based on which we would be able to choose optimally a team of experts from a pool of those with diverse capabilities. One would also tend to attach different weights to different individuals so as to attain the best possible results. However, we have found that if the difference in abilities among those experts is not so diverse, the assignment of equal weighting to all the individuals seems to be locally maximal. Thus we have to assign a significantly uneven weight-distribution to such a group for a substantial improvement. As a consequence, a thorough investigation in some basic procedures in augmenting weights has been carried out. More crucial results so obtained together with extensive experimental verifications lead to a much better understanding of the consensus decision process as well as the possibility of constructing a combinatorial algorithm which would give the optimal enhancement in those cases where this method is useful and acceptable.

, 28 pages

Ce cahier a été révisé en février 2002