Aggregation of voting designs

 
PIIS042473880010524-5-1
DOI10.31857/S042473880010524-5
Publication type Article
Status Published
Authors
Occupation: Principal Scientific Researcher
Affiliation: Central Economics and Matthematics Institute, Russian Academy of Sciences
Address: Moscow, Russian Federation
Occupation: Chief scientific researcher
Affiliation: Central Economics and Mathematics Institute, Russian Academy of Sciences
Address: Russia
Affiliation: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
Address: Russia
Journal nameEkonomika i matematicheskie metody
EditionVolume 56 Issue 3
Pages103-112
Abstract

A Condorcet domain (a domain of linear orders where the majority rule does not violate the transitivity) can be considered as a ground (or design) of organizing a voting procedure. In the present paper we make a next step, namely, we discuss an organization of choices among designs. Here we restrict ourselves by considering those Condorcet domains that are produced with the help of rhombus tilings. Our main result asserts that the majority rule correctly aggregates designs which are produced by use of cubillages, which are three-dimensional generalizations of rhombus tilings. More precisely, to every cubillage  we associate a superdomain  of designs and give an aggregation rule  on this superdomain. We show that the resulting aggregated tiling (design) always belongs to the same superdomain. Also we show that such rules  are agreeable within the intersection of superdomains.

Keywordsrhombus tiling, Condorcet domain, median, cubillage, zonotope, majority rule.
AcknowledgmentThis study was supported by the Russian Foundation for Basic Research (project 20-010-00569-А).
Received02.09.2020
Publication date04.09.2020
Number of characters31950
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1. Black D. (1948). On the rationale of group decision-making. Journal of Political Economy, 56, 23–34.

2. Chameni-Nembua C. (1989). Regle majoritaire et distributivite dans le permutoedre. Math. Inform. Sci. Hum., 108, 5–22.

3. Danilov V.I., Karzanov A.V., Koshevoy G.A. (2010a). Systems of separated sets and their geometric models. Uspekhi Matematicheskikh Nauk (Russian Mathematical Surveys), 65, 4 (394), 67–152.

4. Danilov V.I., Karzanov A.V., Koshevoy G.A. (2019). Cubillages of cyclical zonotopes. Uspekhi Matematicheskikh Nauk (Russian Mathematical Surveys), 74, 6 (450), 181–244 (in Russian).

5. Danilov V.I., Karzanov A.V., Koshevoy G.A. (2010b). Condorcet domains and rhombus tilings. Economics and Mathematical Methods, 46, ¹ 4, 55–68 (in Russian).

6. Danilov V.I., Koshevoy G.A. (2013). Maximal Condorcet domains. Order, 30, 1, 181–194.

7. Felsner S., Ziegler G.M. (2001). Zonotopes associated with higher Bruhat orders. Discrete Mathematics, 241, 301–312.

8. Fishburn P. (1997). Acyclic sets of linear orders. Soc. Choice Welf., 14, 113–124.

9. Manin Yu.I., Shekhtman V.V. (1986). Higher Bruhat orders related to the symmetric group. Functional Analysis and Its Applications, 20, 2, 74–75 (in Russian).

10. Monjardet B. (2009). Acyclic domains of linear orders: a survey. In: S. Brans, W. Gehrlein, F. Roberts (eds.). The mathematics of preferebce, choice and order, 136–160. Berlin: Springer.

11. Puppe C. (2018). The single-peaked domain revisited: A simple global characterization. J. Econ. Theory, 176, 55–80.

12. Puppe C., Slinko A. (2019). Condorcet domains, median graphs and the single-crossing property. Economic Theory, 67, 285–318.

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