Uniformly bounded sufficient sets and quasitransitive social choice

► The feasible set is infinite. IIA is not imposed. Social preference is quasitransitive. ► The following uniform boundedness condition is imposed: There is an integer β such that every pair of alternatives has a sufficient set with at most β members. ► Embedded in any rule satisfying the above conditions is a sub-rule that offers the following stark trade-off: Veto power can be reduced only by reducing responsiveness to individual preference.