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

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  • José Carlos R. Alcantud

    (Universidad de Salamanca)

  • María José M. Torrecillas

    (Universidad de Almería)

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.

Suggested Citation

  • José Carlos R. Alcantud & María José M. Torrecillas, 2017. "Consensus measures for various informational bases. Three new proposals and two case studies from political science," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(1), pages 285-306, January.
    • Handle: RePEc:spr:qualqt:v:51:y:2017:i:1:d:10.1007_s11135-015-0305-y
    DOI: 10.1007/s11135-015-0305-y
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    References listed on IDEAS

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    1. Alcantud, José Carlos R. & de Andres Calle, Rocio & Cascon, José Manuel, 2012. "Approval consensus measures," MPRA Paper 39610, University Library of Munich, Germany.
    2. Lieuwe Dijkstra & Frans Eijnatten, 2009. "Agreement and consensus in a Q-mode research design: an empirical comparison of measures, and an application," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(5), pages 757-771, September.
    3. William V. Gehrlein & Dominique Lepelley, 2015. "Refining measures of group mutual coherence," Post-Print hal-01243405, HAL.
    4. J. C. R. Alcantud & R. Andrés Calle & J. M. Cascón, 2015. "Pairwise Dichotomous Cohesiveness Measures," Group Decision and Negotiation, Springer, vol. 24(5), pages 833-854, September.
    5. Jorge Alcalde-Unzu & Marc Vorsatz, 2013. "Measuring the cohesiveness of preferences: an axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 965-988, October.
    6. Szpiro, George G., 1987. "Hirschman versus Herfindahl: Some topological properties for the use of concentration indexes," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 299-302, December.
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