The Local Geometry of Multiattribute Tradeoffs

Michael McGeachie

Existing preference reasoning systems have been successful in simple domains. Broader success requires more natural and more expressive preference representations. This thesis develops a representation of logical preferences that combines numerical tradeoff ratios between partial outcome descriptions with qualitative preference information. We argue our system is unique among preference reasoning systems; previous work has focused on qualitative or quantitative preferences, tradeoffs, exceptions and generalizations, or utility independence, but none have combined all of these expressions under a unified methodology.

We present new techniques for representing and giving meaning to quantitative tradeoff statements between different outcomes. The tradeoffs we consider can be multi-attribute tradeoffs relating more than one attribute at a time, they can refer to discrete or continuous domains, be conditional or unconditional, and quantified or qualitative. We present related methods of representing judgments of attribute importance. We then build upon a methodology for representing arbitrary qualitative ceteris paribus preference, or preferences "other things being equal," as presented in (McGeachie and Doyle, 2004). Tradeoff preferences in our representation are interpreted as constraints on the partial derivatives of the utility function. For example, a decision maker could state that "Color is five times as important as price," a sentiment one might express in the context of repainting a home, and this is interpreted as indicating that utility increases in the positive color direction five times faster than utility increases in the positive price direction. We show that these representations generalize both the economic notion of marginal rates of substitution and previous representations of preferences in AI.

Photograph of Jon Doyle and Michael McGeachie after the McGeachie dissertation defense
Photograph taken by Peter Szolovits after Michael McGeachie's dissertation defense, showing McGeachie on the right and Jon Doyle on the left.

Last modified: Fri Jan 26 13:42:57 EST 2007
Jon Doyle <>