Orderings Based on the Banks Set: Some New Scoring Methods for Multi-Criteria Decision Making

Abstract

This paper introduces new methods for ranking alternatives in multi-criteria decision making situations. Each is based on the normative position that the strength of an alternative is inversely related to the number of alternatives that could prevent it from being chosen. The scores discriminate among elements of the Banks set [Banks, 85]. The new scoring methods are compared to traditional scoring methods and related to the amount of intransitivity (specifically, the size of the top-cycle) of aggregated preference. The new scores are shown to measure important aspects of alternatives not captured by extant scoring methods and illustrated in collective choice settings.