Uncertain Value Functions

Value theory plays an essential role in the formal solution of decision problems, but the experimental determination of value functions is subject to errors of various kinds. Sensitivity analyses are methodologically invalid. An attempt is made to overcome the uncertainties in derivation of value functions, in a manner which is similar to the economist's “Pareto optimality” approach.

Results are presented for the 2-dimensional situation, and extended to the more general n-dimensional case. In the case when preferences and indifferences are certain the usual results follow.

It is shown how the results can be used to cut down the region of initial feasible solutions to a region within which the decisionmaker makes no initial discrimination, when the boundary regions are convex.

A comparison is made with the approaches of Luce and Aumann, whose work is of a similar, but not equivalent, nature.