Multiple Objective Mathematical Programming with Respect to Multiple Decision-Makers

We consider the important problem of obtaining a “majority consensus” among a number of individuals on the solution to a multiple objective optimization problem. When the number of objectives is greater than two, we observe that such a consensus exists-only under strong symmetry conditions. However, in the bi-objective situation, a “consensus” exists in the convex case and we show how to find it via direct and interactive approaches. In the nonconvex bi-objective situation, a “local consensus” always exists under rather weak regularity conditions.