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

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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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Notes

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

References

  • Alcalde, J., Vorsatz, M.: Measuring the cohesiveness of preferences: an axiomatic analysis. Soc. Choice Welf. 41, 965–988 (2013)

    Article  Google Scholar 

  • Alcantud, J.C.R., de Andrés Calle, R., Cascón, J.M.: On measures of cohesiveness under dichotomous opinions: some characterizations of approval consensus measures. Inf. Sci. 240, 45–55 (2013)

    Article  Google Scholar 

  • Alcantud, J.C.R., de Andrés Calle, R., Cascón, J.M.: Pairwise dichotomous cohesiveness measures. Group Decis. Negot. 24, 833–854 (2015)

    Article  Google Scholar 

  • Alesina, A., Devleeschauwer, A., Easterly, W., Kurlat, S., Wacziarg, R.: Fractionalization. J. Econ. Growth 8, 155–194 (2003)

    Article  Google Scholar 

  • Bosch, R.: Characterizations of voting rules and consensus measures. Ph.D. thesis, Tilburg University (2005)

  • Dijkstra, L., van Eijnatten, F.: Agreement and consensus in a q-mode research design: an empirical comparison of measures, and an application. Qual. Quant. 43(5), 757–771 (2009)

    Article  Google Scholar 

  • Gehrlein, W., Lepelley, D.: Refining measures of group mutual coherence. Qual. Quant. 1–26 (2015). doi:10.1007/s11135-015-0241-x

  • Herfindahl, O.: Concentration in the steel industry. Ph.D. dissertation, Columbia University (1950)

  • Hirschman, A.: National Power and the Structure of Foreign Trade. University of California Press, Berkeley (1945)

    Google Scholar 

  • Hirschman, A.O.: The paternity of an index. Am. Econ. Rev. 54, 761–762 (1964)

    Google Scholar 

  • Hunter, P., Gaston, M.: Numerical index of the discriminatory ability of typing systems: an application of Simpson’s index of diversity. J. Clin. Microbiol. 26, 2465–2466 (1988)

    Google Scholar 

  • Linder, W., Iff, A.: The political system in Switzerland. Technical report, Federal Department of Foreign Affairs, Presence Switzerland (2011)

  • Rhoades, S.: Market share inequality, the HHI, and other measures of the firm-composition of a market. Rev. Ind. Organ. 10, 657–674 (1995)

    Article  Google Scholar 

  • Shannon, C.: A mathematical theory of communication. AT & T Tech. J. 27, 379–423, 623–656 (1948)

  • Simpson, E.: Measurement of diversity. Nature 163, 688 (1949)

    Article  Google Scholar 

  • Szpiro, G.G.: Hirschman versus Herfindahl: some topological properties for the use of concentration indexes. Math. Soc. Sci. 14(3), 299–302 (1987)

    Article  Google Scholar 

  • Vergottini, G.D.: Diritto Costituzionale, 5th edn. Cedam, Padova (2006)

    Google Scholar 

Download references

Acknowledgments

The authors express their gratitude for the perceptive comments from an anonymous reviewer. The authors are grateful to Rocío de Andrés Calle, José Manuel Cascón Barbero, Susana Ruiz Tarrías, and the participants at the 2013 Annual Conference of the Spanish Association of Law and Economics and the 2013 International Meeting of the Association for Public Economic Theory for helpful conversations. J. C. R. Alcantud acknowledges financial support by the Spanish Ministerio de Economía y Competitividad (Project ECO2015-66797-P). M. J. M. Torrecillas acknowledges financial support by the Junta de Andalucía (Project P09-SEJ-05404).

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Authors and Affiliations

  1. BORDA Research Unit and IME, Universidad de Salamanca, 37007, Salamanca, Spain

    José Carlos R. Alcantud

  2. Facultad de CC Económicas y Empresariales, Universidad de Almería, La Cañada de San Urbano s.n., 04120, Almería, Spain

    María José M. Torrecillas

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  1. José Carlos R. Alcantud
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  2. María José M. Torrecillas
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Correspondence to José Carlos R. Alcantud.

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Alcantud, J.C.R., Torrecillas, M.J.M. Consensus measures for various informational bases. Three new proposals and two case studies from political science. Qual Quant 51, 285–306 (2017). https://doi.org/10.1007/s11135-015-0305-y

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