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

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

Indices - better off - worse off - nothing changed

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

References Aleskerov, F.T., Yakuba, V.I., 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., A method for threshold aggregation of three-grade rankings. Doklady Mathematics 75, Aleskerov, F., Chistyakov V., Kaliyagin V. The threshold aggregation, Economic Letters, 107, 2010, Aleskerov, F., Yakuba, V., Yuzbashev, D., A `threshold aggregation' of three-graded rankings. Mathematical Social Sciences 53, Aleskerov, F.T., Yuzbashev, D.A., Yakuba, V.I., Threshold aggregation of three-graded rankings. Automation and Remote Control 1, Chistyakov, V.V., Kalyagin, V.A., A model of noncompensatory aggregation with an arbitrary collection of grades. Doklady Mathematics 78, Chistyakov V.V., Kalyagin V.A An axiomatic model of noncompensatory aggregation. Working paper WP7/2009/01. State University -- Higher School of Economics, Moscow, 2009, 1-76 (in Russian). 16

Thank you 17