Symmetric majority social choice functions.

Under the assumption that individual preferences are linear orders on the set of alternatives, we study the social choice functions which satisfy suitable symmetries and obey the majority principle. In particular, supposing that individuals and alternatives are exogenously partitioned into subcommittees and subclasses, we provide necessary and sufficient conditions for the existence of reversal symmetric majority social choice functions that are anonymous and neutral with respect to the considered partitions. We also determine a general method for constructing and counting all those functions.