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Strong sequences and their consequences in social choice

Jureczko J.

Silesian Journal of Pure and Applied Mathematics

2016

Vol. 6, iss. 1

49--58

One of the most famous theorems in social choice theory – Arrow impossibility theorem – was published in 1951. Since Arrowian paper most researchers tried to ﬁnd diﬀerent versions of this theorem not only for ﬁnite but also for inﬁnite sets of alternative and individuals, where one can treat this situation as anticipation for future social behaviour. The aim of this paper is to ﬁnd some results concerning social voting for inﬁnite sets using one of the combinatorial methods of set theory – strong sequences method. This method was introduced by Eﬁmov in 1965 for proving wellknown theorems in dyadic spaces, (i.e. continuous images of the Cantor cube).