This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Voting: algebra and topology

### From Mathematics Is A Science

The social choice results presented in Topology Illustrated are reworked and expanded here.

**References**

- Kenneth Joseph Arrow (1951), Social Choice and Individual Values (1st ed.). Wiley.
- Yuliy M. Baryshnikov, Topological and discrete social choice: in a search of a theory, Topological social choice. Soc. Choice Welf. 14 (1997), no. 2, 199–209.
- G. Chichilnisky, Intersecting families of sets and the topology of cones in economics, Bull. AMS 29 (1993), 189-207.
- B. Eckmann, R~iume mit Mittelbildungen, Comment. Math. Helv. 28 (1954), 329-340.
- B. Eckmann, T. Ganea, P.J. Hilton, Generalized means, Studies in Mathematical Analysis, Stanford University Press (1962), 82-92.
- B. Eckmann, Social Choice and Topology, A Case of Pure and Applied Mathematics, Expo. Math. 22 (2004): 385-393.
- C.D. Horvath, On the topological social choice problem, Soc.Choice Welfare 18 (2001), 227-250.
- Alan P. Kirman and Dieter Sondermann, Arrow's Theorem, many agents, and invisible dictators, CORE Discussion Paper 7142 (1971/72).
- A. Kolmogorov, Sur la notion de moyenne, Rendiconti Acad. dei Lincei 12(1930), 388-391.
- P. Saveliev, Topology Illustrated, 2016.
- S. Weinberger, On the topological social choice model, 2003, Soc. Choice Welfare.