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Social threshold aggregations

Social threshold aggregations. Fuad T. Aleskerov, Vyacheslav V. Chistyakov, Valery A. Kalyagin Higher School of Economics. Examples. Apartments Three students – whom we hire Refereeing process in journals. - alternatives ,

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Social threshold aggregations

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  1. Social threshold aggregations Fuad T. Aleskerov, Vyacheslav V. Chistyakov, Valery A. Kalyagin Higher School of Economics

  2. Examples • Apartments • Three students – whom we hire • Refereeing process in journals

  3. - alternatives , , - agents, - set of ordered grades with . An evaluation procedure assigns to and a grade , i.e., where for each is the set of all -dimentional vectors with components from

  4. We assume , so the number of grades in the vector Note that Let

  5. Social decision function Social decision function on satisfying (a) iff is socially (strictly) more preferable than , and (b) iff and are socially indifferent

  6. Axioms

  7. The binary relation on is said to be the lexicographic ordering if, given and from , we have: in iff there exists an such that for all (with no condition if ) and Construction of social ordering – threshold rule compare vectors and

  8. Theorem: A social decision function on X satisfies the axioms Pairwise Compensation, Pareto Domination, Noncompensatory Threshold and Contraction iff its range is the set of binary relations on X generated by the threshold rule.

  9. Let be a set of three different alternatives, a set of voters and the set of grades (i.e., ).

  10. The dual threshold aggregation

  11. Manipulability of Threshold Rule • ComputationalExperiments • Multiple Choice Case • Several Indices of Manipulability

  12. Indices - better off - worse off - nothing changed

  13. Applications • Development of Civil Society in Russia • Performance of Regional Administrations in Implementation of Administrative Reform

  14. References • Aleskerov, F.T., Yakuba, V.I., 2003. A method for aggregation of rankings of special form. Abstracts of the 2nd International Conference on Control Problems, IPU RAN, Moscow, Russia. • Aleskerov, F.T., Yakuba, V.I., 2007. A method for threshold aggregation of three-grade rankings. Doklady Mathematics 75, 322--324. • Aleskerov, F., Chistyakov V., Kaliyagin V. The threshold aggregation, Economic Letters, 107, 2010, 261-262 • Aleskerov, F., Yakuba, V., Yuzbashev, D., 2007. A `threshold aggregation' of three-graded rankings. Mathematical Social Sciences 53, 106--110. • Aleskerov, F.T., Yuzbashev, D.A., Yakuba, V.I., 2007. Threshold aggregation of three-graded rankings. Automation and Remote Control 1, 147--152. • Chistyakov, V.V., Kalyagin, V.A., 2008. A model of noncompensatory aggregation with an arbitrary collection of grades. Doklady Mathematics 78, 617--620. • Chistyakov V.V., Kalyagin V.A. 2009. An axiomatic model of noncompensatory aggregation. Working paper WP7/2009/01. State University -- Higher School of Economics, Moscow, 2009, 1-76 (in Russian).

  15. Thank you

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