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Non-Contradictory Aggregation of Strict Order Relations

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Abstract

We study the problem of collective choice. The profile of individual preferences of experts is defined by relations of strict order. A non-contradictory aggregate preference relation is based on the weighted majority graph that characterizes the degree of superiority of one alternative over another. The aggregate relation also defines a strict order and satisfies requirements to group decisions, namely, the monotony, the preservation of the Pareto relation, the minimality of the distance to expert preferences.

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References

  1. Arrow, K. J. Social Choice and Individual Values (Wiley, 1951; GU-VShE, Moscow, 2004).

    MATH  Google Scholar 

  2. Mirkin, B. G. The Group Choice Problem (Nauka, Moscow, 1974) [in Russian].

    MATH  Google Scholar 

  3. Vol’skii, V. I. and Lezina, Z. M. Voting in Small Groups: Procedures and Comparative Analysis Methods (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  4. Osipova, V. A., Podinovskii, V. V. and Yashina, N. P. “On Non-Contradictory Extension of Preference Relations inDecision-Making Problems”, U.S.S.R.Comput. Math.Math. Phys. 24, No. 3, 128–134 (1984).

    Article  MATH  Google Scholar 

  5. Aleskerov, F. and Monjardet, B. Utility Maximization. Choice and Preference (Springer, Berlin, 2002.)

    Book  MATH  Google Scholar 

  6. “Social Choice Theory. The Stanford Encyclopedia”, First published Dec. 18, 2013. https://plato.stanford.edu/entries/social-choice/

  7. Osipova, V. A. A Course inDiscrete Mathematics (Forum, Moscow, 2013) [in Russian].

    Google Scholar 

  8. Smerchinskaya, S. O. and Yashina, N. P. “Construction of the Aggregate Preference Relation on the Base of aWeighted Majority Graph”, Electronic Journal Tr.MAI 39 (2010) [in Russian].

  9. Shreider, Yu. A. Equality, Resemblance, and Order (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  10. Smerchinskaya, S. O. and Yashina, N. P. “The Analysis of Expert Competencies in Group Choice Problems”, Informatsyonnye i Telekommunikatsionnye Tekhnologii 15, 103–115 (2012) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4., Moscow, 125993, Russia

    V. N. Nefyodov, V. A. Osipova, S. O. Smerchinskaya & N. P. Yashina

Authors
  1. V. N. Nefyodov
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  2. V. A. Osipova
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  3. S. O. Smerchinskaya
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  4. N. P. Yashina
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Corresponding author

Correspondence to V. N. Nefyodov.

Additional information

Original Russian Text © V.N. Nefyodov, V.A. Osipova, S.O. Smerchinskaya, N.P. Yasina, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 5, pp. 71–85.

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Nefyodov, V.N., Osipova, V.A., Smerchinskaya, S.O. et al. Non-Contradictory Aggregation of Strict Order Relations. Russ Math. 62, 61–73 (2018). https://doi.org/10.3103/S1066369X18050092

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  • DOI: https://doi.org/10.3103/S1066369X18050092

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