Quality & Quantity

, Volume 51, Issue 1, pp 285–306 | Cite as

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

  • José Carlos R. Alcantud
  • María José M. Torrecillas


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.


Consensus measure Diversity index Political consensus 



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).


  1. Alcalde, J., Vorsatz, M.: Measuring the cohesiveness of preferences: an axiomatic analysis. Soc. Choice Welf. 41, 965–988 (2013)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. Alcantud, J.C.R., de Andrés Calle, R., Cascón, J.M.: Pairwise dichotomous cohesiveness measures. Group Decis. Negot. 24, 833–854 (2015)CrossRefGoogle Scholar
  4. Alesina, A., Devleeschauwer, A., Easterly, W., Kurlat, S., Wacziarg, R.: Fractionalization. J. Econ. Growth 8, 155–194 (2003)CrossRefGoogle Scholar
  5. Bosch, R.: Characterizations of voting rules and consensus measures. Ph.D. thesis, Tilburg University (2005)Google Scholar
  6. 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)CrossRefGoogle Scholar
  7. Gehrlein, W., Lepelley, D.: Refining measures of group mutual coherence. Qual. Quant. 1–26 (2015). doi: 10.1007/s11135-015-0241-x
  8. Herfindahl, O.: Concentration in the steel industry. Ph.D. dissertation, Columbia University (1950)Google Scholar
  9. Hirschman, A.: National Power and the Structure of Foreign Trade. University of California Press, Berkeley (1945)Google Scholar
  10. Hirschman, A.O.: The paternity of an index. Am. Econ. Rev. 54, 761–762 (1964)Google Scholar
  11. 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
  12. Linder, W., Iff, A.: The political system in Switzerland. Technical report, Federal Department of Foreign Affairs, Presence Switzerland (2011)Google Scholar
  13. Rhoades, S.: Market share inequality, the HHI, and other measures of the firm-composition of a market. Rev. Ind. Organ. 10, 657–674 (1995)CrossRefGoogle Scholar
  14. Shannon, C.: A mathematical theory of communication. AT & T Tech. J. 27, 379–423, 623–656 (1948)Google Scholar
  15. Simpson, E.: Measurement of diversity. Nature 163, 688 (1949)CrossRefGoogle Scholar
  16. Szpiro, G.G.: Hirschman versus Herfindahl: some topological properties for the use of concentration indexes. Math. Soc. Sci. 14(3), 299–302 (1987)CrossRefGoogle Scholar
  17. Vergottini, G.D.: Diritto Costituzionale, 5th edn. Cedam, Padova (2006)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • José Carlos R. Alcantud
    • 1
  • María José M. Torrecillas
    • 2
  1. 1.BORDA Research Unit and IMEUniversidad de SalamancaSalamancaSpain
  2. 2.Facultad de CC Económicas y EmpresarialesUniversidad de AlmeríaAlmeríaSpain

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