DIMACS/LAMSADE PARTNERSHIP on Computer Science and Decision Theory: Applications of Notions of Consensus
LAMSADE Working Group Website
Title: A conjoint measurement view on fuzzy integrals
In the field of MCDM, the dominant model is the additive value function model that has received a thorough axiomatic treatment in the framework of conjoint measurement following the works of Gérard Debreu and Duncan Luce. This model however implies that criteria are mutually independent. Choquet and Sugeno integrals have recently attracted much interest in MCDM as convenient tools to model interactions between criteria. The purpose of this paper is to review the existing literature on these two models from the point of view of conjoint measurement, i.e., within a framework in which the only primitive is a preference relation defined on a product set that does not have to be homogeneous. Whereas the measurement-theoretic foundations of Choquet and Sugeno integrals have been well studied in the area of decision making under uncertainty, a comparable analysis is still lacking in the area of MCDM. Indeed, the very conception of these two techniques implies a "commensurability" hypothesis that is not easy to formalize within the framework of conjoint measurement. We shall first review the various attempts that have been made to axiomatize Choquet and Sugeno integrals within a classical conjoint measurement framework. We then concentrate on the Sugeno integral, showing that existing axiomatic analyses of this tool allow suggesting new and simple interpretation the aggregation it promotes. This will lead to a novel interpretation of the Sugeno integral that will emphasize its ordinal character and links it with "noncompensatory" aggregation models. This analysis is builds on uses recent work in the area by Salvatore Greco, Benedetto Matarazzo and Roman Slowinski.
Title: Voting Systems That Combine Approval and Preference
Information on the rankings and information on the approval of candidates in an election, though related, are fundamentally different-one cannot be derived from the other. Both kinds of information are important in the determination of social choices. We propose a way of combining them in two hybrid voting systems, preference approval voting (PAV) and fallback voting (FV), that satisfy several desirable properties, including monotonicity. Both systems may give different winners from standard ranking and nonranking voting systems. PAV, especially, encourages candidates to take coherent majoritarian positions, but it is more information-demanding than FV. PAV and FV are manipulable through voters' contracting or expanding their approval sets, but a 3-candidate dynamic poll model suggests that Condorcet winners, and candidates ranked first or second by the most voters if there is no Condorcet winner, will be favored, though not necessarily in equilibrium.
Title: Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications
This tutorial provides an introduction and overview of the book with the same title by Regenwetter, Grofman, Marley and Tsetlin (2006, Cambridge University Press).
The fundamental purpose of a behavioral theory of social choice processes is the development of descriptive models for real actors' social choice behavior and the statistical evaluation of such models against empirical data. Our notion of behavioral social choice research builds on and, at the same time, complements much of classical social choice theory in the tradition of leading figures such as the Marquis de Condorcet, Duncan Black, Kenneth Arrow, and Amartya Sen. Most classic approaches follow an axiomatic, normative line of reasoning. They formulate desirable properties of "rational" social choice and provide numerous "possibility" or "impossibility" theorems that classify groups of such axioms into whether or not they lead to 'feasible' aggregation procedures, given various theoretical assumptions about the nature, domain, and distribution of individual preferences. A principal task of behavioral social choice research is to evaluate such normative benchmarks of rational social choice against empirical evidence on real world social choice behavior. We attempt to evaluate our models against a wide range of empirical evidence drawn from large scale real-world data sets from three different countries. To the extent that classical/normative theories fail to be descriptive of observed social choice behavior, they motivate and inspire the development of (alternative) behavioral theories that completement classical approaches by descriptively capturing the social choice behavior of real actors.
Michel Regenwetter, Aeri Kim, Arthur Kantor, University of Illinois at Urbana-Champaign, USA and Moon-Ho R. Ho, Nanyang Technological University, Singapore
Title: The unexpected empirical consensus among consensus methods. (Manuscript in press in Psychological Science)
The theoretical social choice literature on voting procedures in Economics and Political Science routinely highlights worst case scenarios and emphasizes the inexistence of a universally 'best' voting method. Behavioral social choice is grounded in Psychology and tackles consensus methods descriptively and empirically. We analyze four elections of the American Psychological Association using a state-ofthe art multi-model, multi-method approach. These elections provide rare access to (likely sincere) preferences of large numbers of decision makers over five choice alternatives. We analyze three classical rational choice rivals: Condorcet, Borda and Plurality. The literature routinely depicts these procedures as irreconcilable. We find strong statistical support for an unexpected degree of empirical consensus among these procedures in these elections. Our empirical findings contrast two centuries of pessimistic thought experiments and computer simulations in social choice theory and demonstrate the need for more systematic descriptive and empirical research on social choice than exists to date.
Fred Roberts, DIMACS
Title: Computer Science and Decision Making
An old problem in the social sciences is to find a consensus given different opinions or preferences or votes. The social science methods developed over the years for dealing with this and other decision making problems are beginning to find novel and important applications in computer science. In turn, new computer science methods developed in connection with these newer applications are finding uses in modern, algorithmic decision theory. This talk will briefly describe the use of social science methods in computer science problems such as meta-search (finding the results from multiple search engines), image processing, collaborative filtering, and software measurement, as well as methods of algorithmic decision theory.
Title: Using mathematics to explain surprises in voting theory
Voting theory is full of unexpected paradoxes and surprises. Changing the way ballots are tallied, or dropping a candidate can create surprising differences in the election ranking. The big mystery is to understand why all of this happens. In this lecture, I will explain why all of this occurs.