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

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

3. 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. 4 We assume, so the number of grades in the vector Note that Let

5. 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. 6 Axioms

7. 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. 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. 9 Let be a set of three different alternatives, a set of voters and the set of grades (i.e., ).

10. 10 The dual threshold aggregation

11. Manipulability of Threshold Rule Computational Experiments Multiple Choice Case Several Indices of Manipulability 11

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

15. Applications Development of Civil Society in Russia Performance of Regional Administrations in Implementation of Administrative Reform 15

16. 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). 16

17. Thank you 17