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Using Similarity and Dissimilarity Measures of Binary Patterns for the Comparison of Voting Procedures

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Granular, Soft and Fuzzy Approaches for Intelligent Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 344))

Abstract

An interesting and important problem of how similar and/or dissimilar voting procedures (social choice functions) are dealt with. We extend our previous qualitative type analysis based on rough sets theory which make it possible to partition the set of voting procedures considered into some subsets within which the voting procedures are indistinguishable, i.e. (very) similar. Then, we propose an extension of those analyses towards a quantitative evaluation via the use of degrees of similarity and dissimilarity, not necessarily metrics and dual (in the sense of summing up to 1). We consider the amendment, Copeland, Dodgson, max-min, plurality, Borda, approval, runoff, and Nanson, voting procedures, and the Condorcet winner, Condorcet loser, majority winner, monotonicity, weak Pareto winner, consistency, and heritage criteria. The satisfaction or dissatisfaction of the particular criteria by the particular voting procedures are represented as binary vectors. We use the Jaccard–Needham, Dice, Correlation, Yule, Russell–Rao, Sockal–Michener, Rodgers–Tanimoto, and Kulczyński measures of similarity and dissimilarity. This makes it possible to gain much insight into the similarity/dissimilarity of voting procedures.

To Ron, Professor Ronald R. Yager, whose highly original and ground breaking ideas, and vision, have shaped and changed research interests of so many of us for years.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk & Sławomir Zadrożny

  2. Warsaw School of Information Technology (WIT), Ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk & Sławomir Zadrożny

  3. Department of Political Science, University of Turku, 20014, Turku, Finland

    Hannu Nurmi

Authors
  1. Janusz Kacprzyk
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  2. Hannu Nurmi
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  3. Sławomir Zadrożny
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Correspondence to Janusz Kacprzyk .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Research and Innovation Center, Ford Motor Company, Dearborn, Michigan, USA

    Dimitar Filev

  3. Deakin University, Burwood, Victoria, Australia

    Gleb Beliakov

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Kacprzyk, J., Nurmi, H., Zadrożny, S. (2017). Using Similarity and Dissimilarity Measures of Binary Patterns for the Comparison of Voting Procedures. In: Kacprzyk, J., Filev, D., Beliakov, G. (eds) Granular, Soft and Fuzzy Approaches for Intelligent Systems. Studies in Fuzziness and Soft Computing, vol 344. Springer, Cham. https://doi.org/10.1007/978-3-319-40314-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-40314-4_8

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