11 June 2019, Computational Social Choice Seminar, Hossein Khani

Abstract

The problem of evaluating the influence of individuals in a society when the ranking of teams formed by them is given is of great relevance in the context of decision theory, social choice theory, and game theory. Consider, for instance, the problem of estimating the "power" of countries in the process of collective decision making in an international parliament, or the ranking of researchers in a department based on the relative performance of research teams. In many such situations it is not possible to evaluate the worth (value) of teams (or coalitions) precisely due to several factors: uncertain data, the complexity of the analysis, missing information, or difficulties in the update. Therefore, the main objective in this talk is to answer the general question of how to obtain an ordinal ranking over a finite set of individuals (called social ranking solution), given an ordinal ranking over coalitions of individuals (called power relation). We answer this question using two approaches: First, using classical social choice theory and based on the "Ceteris Paribus principle", we define a social ranking solution that ranks any two individuals according to their performance when they join the same coalition. By defining a restriction of the structure of the power relation called "social single-peakedness" we guarantee the transitivity of the resulting ranking on individuals. Second, in the context of cooperative game theory, we introduce a social ranking solution by extending the classical notion of the Banzhaf index to our ordinal framework. We investigate both of these social ranking solutions using a property-driven approach, and we characterize them by a set of well-defined axioms. Finally we emphasize the similarity of the two proposed solutions by indicating that they belong to a larger family of solutions.

For more information on the Computational Social Choice Seminar, please consult https://staff.science.uva.nl/u.endriss/seminar/.