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Relational concepts in social choice. (English) Zbl 1364.91051

Kahl, Wolfram (ed.) et al., Relational and algebraic methods in computer science. 13th international conference, RAMiCS 2012, Cambridge, UK, September 17–20, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-33313-2/pbk). Lecture Notes in Computer Science 7560, 278-293 (2012).
Summary: What now is called social choice theory has ever since attracted mathematicians – not least several Nobel laureates – who try to capture the comparison relations expressed and to aggregate them. Their results are often referred to nowadays. The purpose of this paper is to make point-free relation-algebraic mathematics available as a tool for the study of social choice. Thus, we provide simplification, additional systematics, more compact relation-algebraic proofs and also an access to solving such problems with programs in the language TituRel – at least for the medium sized cases.
For the entire collection see [Zbl 1246.68043].

MSC:

91B14 Social choice
03G15 Cylindric and polyadic algebras; relation algebras
06A15 Galois correspondences, closure operators (in relation to ordered sets)
18B35 Preorders, orders, domains and lattices (viewed as categories)

Software:

TituRel
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References:

[1] Schmidt, G.: Relational Mathematics. Encyclopedia of Mathematics and its Applications, vol. 132. 584 pages. Cambridge University Press (2011) ISBN 978-0-521-76268-7
[2] Sen, A.K.: Collective choice and social welfare. Mathematical Economics Texts, vol. 5. Holden-Day, San Francisco (1970) · Zbl 0227.90011
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[4] Schmidt, G., Ströhlein, T.: Relations and Graphs – Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoretical Computer Science. Springer (1993) ISBN 3-540-56254-0, ISBN 0-387-56254-0 · Zbl 0900.68328
[5] Suzumura, K.: Rational choice, collective decisions, and social welfare. Cambridge University Press (1983), Reprinted 2009
[6] Wriglesworth, J.L.: Libertarian conflicts in social choice. Cambridge University Press (1985)
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