Value aggregation (1/2)
Theorem (Harsanyi 1955, Keeney 1975):
Let vi(·) be a measurable value function describing the preferences of DMi. There exists a k-dimensional differentiable function vg() with positive partial derivatives describing group preferences >g in the definition space such that
a >gb ? vg[v1(a),…,vk(a)] ? vg[v1(b),…,vk(b)]
and conditions 1-6 are satisfied.