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Group Decision and Negotiation

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14-12-2017

Reformulating Arrow’s Conditions in Terms of Cardinal Pairwise Comparison Matrices Defined Over a General Framework

Authors: Bice Cavallo, Livia D’Apuzzo, Gaetano Vitale

Published in: Group Decision and Negotiation | Issue 1/2018

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Abstract

In the paper, we deal with cardinal preferences of experts when these are expressed by means of Pairwise Comparison Matrices (PCMs). In order to obtain general results, suitable for several kinds of PCMs proposed in literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. In this framework, firstly, we aggregate several PCMs and we analyse how the aggregated PCM preserves some coherence levels, such as transitivity, weak consistency and consistency. Then, we reformulate Arrow’s conditions in terms of PCMs, and we provide two preference aggregation procedures for representing group preferences that give a social PCM and a social cardinal ranking, respectively. Finally, we analyse how these preference aggregation procedures satisfy reformulated Arrow’s conditions.

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Title: Reformulating Arrow’s Conditions in Terms of Cardinal Pairwise Comparison Matrices Defined Over a General Framework
Authors: Bice Cavallo
Livia D’Apuzzo
Gaetano Vitale
Publication date: 14-12-2017
Publisher: Springer Netherlands
Published in: Group Decision and Negotiation / Issue 1/2018
Print ISSN: 0926-2644
Electronic ISSN: 1572-9907
DOI: https://doi.org/10.1007/s10726-017-9552-8

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