Ranking Alternatives from Opinions on Criteria

Abstract A primary challenge in collective decision-making is that achieving unanimous agreement is difficult, even at the level of criteria. The history of social choice theory illustrates this: numerous normative criteria on voting rules have been proposed; however, disagreements persist regarding which criteria should take precedence. This study addresses the problem of ranking alternatives based on the aggregation of opinions over criteria that the alternatives might fulfill. Using the opinion aggregation model, we propose a new rule—termed the Intersection Initial Segment (IIS) rule—and characterize it using five axioms: neutrality, independence of the worst set, independence of the best set, weak intersection very important player, and independence of non-unanimous improvement. We illustrate our approach using a running example in which the objective is to rank voting rules—showing that our opinion aggregation model is particularly well-suited to this context—and that the IIS rule is a counterpart to the method discussed as reported by Nurmi (The choice of voting rules based on preferences over criteria. In: Bogumił Kamiński, Gregory E. Kersten, and Tomasz Szapiro, editors, Outlooks and Insights on Group Decision and Negotiation. GDN 2015. Lecture Notes in Business Information Processing 218:241–252, 2015).