We prove the existence of arbitrary (resp., semicontinuous, continuous) utility representations for arbitrary (resp., semicontinuous, continuous) preorders satisfying some weakened Debreu order separability conditions. In this way we widely generalize a classical result for total preorders that...

Given n experts, a set X of alternative projects, and various classes of individual utility functions u1,...,un on X, we characterize collective utility functions (CUFs) of the form where [alpha]i are positive numbers.