Local Geometry of Multiattribute Tradeoff Preferences

PhD thesisExisting preference reasoning systems have been successful insimple domains. Broader success requires more natural and moreexpressive preference representations. This thesis develops arepresentation of logical preferences that combines numericaltradeoff ratios between partial outcome descriptions withqualitative preference information. We argue our system is uniqueamong preference reasoning systems; previous work has focused onqualitative or quantitative preferences, tradeoffs, exceptions andgeneralizations, or utility independence, but none have combinedall of these expressions under a unified methodology.We present new techniques for representing and giving meaning toquantitative tradeoff statements between different outcomes. Thetradeoffs we consider can be multi-attribute tradeoffs relatingmore than one attribute at a time, they can refer to discrete orcontinuous domains, be conditional or unconditional, andquantified or qualitative. We present related methods ofrepresenting judgments of attribute importance. We then buildupon a methodology for representing arbitrary qualitative ceteris paribuspreference, or preferences ``other things being equal," aspresented in MD04. Tradeoff preferences inour representation are interpreted as constraints on the partialderivatives of the utility function. For example, a decision makercould state that ``Color is five times as important as price,availability, and time," a sentiment one might express in thecontext of repainting a home, and this is interpreted asindicating that utility increases in the positive color directionfive times faster than utility increases in the positive pricedirection. We show that these representations generalize both theeconomic notion of marginal rates of substitution and previousrepresentations of preferences in AI

The local geometry of multiattribute tradeoff preferences

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 125-129).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 [MD04].(cont.) 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, availability, and time," 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.by Michael McGeachie.Ph.D

Decision-making Under Ordinal Preferences and Comparative Uncertainty

This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of consequences of acts, describing the DMs preferences. However, contrary to classical approaches to decision theory, we try to do it without resorting to any numerical representation of utility nor uncertainty, and without even using any qualitative scale on which both uncertainty and preference could be mapped. It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty, but leads to the kind of uncertainty theory encountered in non-monotonic reasoning (especially preferential and rational inference), closely related to possibility theory. Moreover the method turns out to be either very little decisive or to lead to very risky decisions, although its basic principles look sound. This paper raises the question of the very possibility of purely symbolic approaches to Savage-like decision-making under uncertainty and obtains preliminary negative results.Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997

Decision-Making under Ordinal Preferences and Comparative Uncertainty

This paper proposes a method that finds a preference relation on a set of acts from the knowledge of an ordering on events describing the decision-maker's uncertainty and an ordering of consequences of acts, describing the decision maker's preferences. However, contrary to classical approaches to decision theory, this method does not resort to any numerical representation of utility nor uncertainty and is purely ordinal. It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the ordinal method, the approach is inconsistent with a probabilistic representation of uncertainty. It leads to the kind of uncertainty theory encountered in nonmonotonic reasoning (especially preferential and rational inference). Moreover the method turns out to be either very little decisive or to lead to very risky decisions, although its basic principles look sound. This paper raises the question of the very possibility of purely symbolic approaches to Savag..