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).
Intransitive, incomplete and discontinuous preferences are not always irrational but may be based on quite reasonable considerations. Hence, we pursue the possibility of building a theory of social choice on an alternative foundation, viz. on individual preference tournaments. Tournaments have been studied for a long time independently of rankings and a number of results are therefore just waiting to be applied in social choice. Our focus is on Slater’s rule. A new interpretation of the rule is provided.
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