Dynamic Proportional Rankings

Proportional ranking rules aggregate approval-style preferences of agents into a collective ranking such that groups of agents with similar preferences are adequately represented. Motivated by the application of live Q&A platforms, where submitted questions need to be ranked based on the interests of the audience, we study a dynamic extension of the proportional rankings setting. In our setting, the goal is to maintain the proportionality of a ranking when alternatives (i.e., questions)---not necessarily from the top of the ranking---get selected sequentially. We propose generalizations of well-known aggregation rules to this setting and study their monotonicity and proportionality properties. We also evaluate the performance of these rules experimentally, using realistic probabilistic assumptions on the selection procedure.

Aggregating multiple ordinal rankings in engineering design: the best model according to the Kendall’s coefficient of concordance

Aggregating the preferences of a group of experts is a recurring problem in several fields, including engineering design; in a nutshell, each expert formulates an ordinal ranking of a set of alternatives and the resulting rankings should be aggregated into a collective one. Many aggregation models have been proposed in the literature, showing strengths and weaknesses, in line with the implications of Arrow's impossibility theorem. Furthermore, the coherence of the collective ranking with respect to the expert rankings may change depending on: (i) the expert rankings themselves and (ii) the aggregation model adopted. This paper assesses this coherence for a variety of aggregation models, through a recent test based on the Kendall's coefficient of concordance (W), and studies the characteristics of those models that are most likely to achieve higher coherence. Interestingly, the so-called Borda count model often provides best coherence, with some exceptions in the case of collective rankings with ties. The description is supported by practical examples.

Majority Judgment

This book argues that the traditional theory of social choice offers no acceptable solution to the problems of how to elect, judge, or rank. It finds that the traditional model—transforming the “preference lists” of individuals into a “preference list” of society—is fundamentally flawed in both theory and practice. The authors propose a different model, which leads to a new theory and method: majority judgment. Majority judgment is meaningful, resists strategic manipulation, elicits honesty, and is not subject to the classical paradoxes encountered in practice, notably Condorcet’s paradox and Arrow’s paradox. The authors offer theoretical, practical and experimental evidence—from national elections to figure skating competitions—to support their arguments. Drawing on wine, sports, music, and other competitions, they argue that the question should not be how to transform many individual rankings into a single collective ranking but rather, after defining a common language of grades to measure merit, how to transform the many individual evaluations of each competitor into a single collective evaluation of all competitors. The crux of the matter is a new model in which the traditional paradigm—to compare—is replaced by a new paradigm: to evaluate.

AN APPROACH TO GROUP DECISION MAKING BASED ON INCOMPLETE FUZZY PREFERENCE RELATIONS

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in incomplete fuzzy preference relations. In order to make the collective opinion close each decision maker's opinion as near as possible, an optimization model is constructed to integrate the incomplete fuzzy preference relations and to compute the collective ranking values of alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.