Strong sequences and their consequences in social choice

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).