04271 Abstracts Collection -- Preferences: Specification, Inference, Applications

From 27.06.04 to 02.07.04, the Dagstuhl Seminar 04271 ``Preferences: Specification, Inference, Applications\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

Great Expectations. Part II: Generalized Expected Utility as a Universal Decision Rule

Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent essentially all other decision rules.Comment: Preliminary version appears in Proc. 18th International Joint Conference on AI (IJCAI), 2003, pp. 297-30

On measurable uncertainty and the fight for taking uncertainty seriously in economics

This paper discusses the engagement of economists with the issue of the measurability of uncertainty. Since Knight’s seminal distinction between risk, intended as measurable uncertainty, and unmeasurable uncertainty, the question has been to what extent the extension of the theory of choice from certainty to risk through von Neumann and Morgenstern’s expected utility hypothesis would allow dealing with uncertain events. The paper develops from a study of the rationale underlying the theories of those authors who objected to the mainstream view that the axiomatic approach developed in the early 1950s, mainly through Leonard Savage’s generalization of expected utility, makes it, indeed, possible to reduce uncertainty to risk. After a summary of the meaning attributed by authors such as Knight, Keynes, Shackle and Ellsberg to the contention that uncertainty is irreducible to risk and unmeasurable, the paper aims to investigate why this view did not emerge as a significant alternative to the mainstream up until recently. A main reason, at times alluded to but never openly discussed in the literature, is shown to be the close link between Savage and the group of decision theorists at the Cowles Commission for Research in Economics under the directorship of Jacob Marschak and Tjalling Koopmans. Archival evidence suggests that arguing that a theory of decision under uncertainty could be developed on the basis of “axioms that seem unobjectionable,” as Koopmans put it, was indeed an integral part of the attempt undertook at Cowles to move forward in economic theory by prioritizing scientific rigour in the form of mathematical models engaging with new mathematical tools

Preference Modelling

This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with "compact representation of preferences" introduced for special purpoes. We end the paper with some concluding remarks

Reasons and Means to Model Preferences as Incomplete

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review some of the reasons that have been put forward to justify more complex modeling, and review some of the techniques that have been proposed to obtain models of such preferences