Aggregation with Many Effective Voters

McGarveys’s theorem [6] shows that majority aggregation of a profile of linear orders generates any complete binary relation. Kalai [5] proved that the same is true for any neutral monotone SWF defined by a strong simple game where the power of every voter is sufficiently small, which implies that there are many effective voters. In this paper we study neutral monotone SWFs with many effective voters with no restriction on voter power. We give bounds on the minimal number of relations generated by such SWFs.