Upper and Lower Bound Evaluation of Multiattribute Objects: Comparison Models Using Linear Programming

We argue that three points of comparison which people use in everyday thinking are: comparison of an object relative to the next best object; relative to the average object; or relative to the worst object. We present formal models of comparison, based on linear programming, for multiattribute objects. We present upper and lower bound evaluations for each type of comparison: that is, relative to each of the three natural points of comparison we may determine an object′s most favorable standing, and its least favorable. The six models are illustrated with an example. Potential applications in marketing, decision analysis, social cognition, and negotiation are briefly sketched.