Orderings based on the banks set: Some new scoring methods for multicriteria decision making

Abstract

This article introduces new methods for ranking alternatives in multicriteria 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, Soc Choice Welfare, 1985, 1, 295-306). 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 are illustrated in collective choice settings. 13 This definition differs slightly from those in [28] and [29].In this article, I am only concerned with complete, asymmetric relations, and hence these definitions coincide. 14 However, as Ordeshook and Schwartz [30] and Schwartz[31] argue, amendment agendas are quite unique among legislative amendment procedures. 15 In what follows, for any scoring method, S, alternatives with largest S-scores are called S-winners.Alternative 3 has low SHCH score and low NUMCH score. 22 Use of the word ''needs'' here is related to, but distinct from, the needing relation of [13] and [14].

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