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Quality & Quantity

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16-01-2016

Consensus measures for various informational bases. Three new proposals and two case studies from political science

Authors: José Carlos R. Alcantud, María José M. Torrecillas

Published in: Quality & Quantity | Issue 1/2017

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Abstract

We study consensus measures that quantify the cohesiveness of the information generated when a group of decision-makers express their evaluations of a number of issues. Particularly, in social choice an approval consensus measure (ACM) is used to evaluate the degree of cohesiveness in a group of agents that have dichotomous opinions on the issues. In this paper we propose three novel consensus indexes that take advantage of the specific information about such opinions: namely, the Herfindahl–Hirschman ACM, the majoritarian ACM and the weighted majoritarian ACM. To illustrate their performance we apply them to the analysis of popular votes in Switzerland and Italy. The first analysis has a fixed population of agents (the cantons) and all votes are known. In the second analysis we have a variable population (the voters) and unknown individual votes. In both real case studies, we show empirical evidence that the new indexes can be used to assess consensus.

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Now we can complete the claim in Remark 2 by showing that the pairwise and Herfindahl–Hirschman consensus indexes are in general different: observe \({\mathcal{C}}_{HH} (V_1) = \frac{20}{27} \ne \frac{31}{45} = {\mathcal{C}}_{p} (P_1).\)

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Title: Consensus measures for various informational bases. Three new proposals and two case studies from political science
Authors: José Carlos R. Alcantud
María José M. Torrecillas
Publication date: 16-01-2016
Publisher: Springer Netherlands
Published in: Quality & Quantity / Issue 1/2017
Print ISSN: 0033-5177
Electronic ISSN: 1573-7845
DOI: https://doi.org/10.1007/s11135-015-0305-y

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