Transitivity and Non-Transitivity of Majorities

Abstract

A committee makes decisions: it arrives at the decision a _h say, instead of a _k or a _l. It does not make valuations. Yet there is some natural tendency to regard it, in these circumstances, as valuing a _h as being preferable to a _k and a _k as preferable to a _l, in somewhat the same way as does the individual. Again the preferences and choice-making of the individual are usually taken as being transitive. So, the feeling is, the ‘preferences’ of the committee will also be transitive: if a _h can get a majority against a _k and a _k against a _l, then a _h will be able to get a majority against a _l.