Special majority rules and the existence of voting equilibria

This paper is concerned with voting rules in which one alternative defeats a second alternative if and only if it is preferred to the second alternative by a pre-specified proportion of the individuals who have strict preferences on the pair. In particular, the paper focuses on the potential of two alternative lower bounds (for the proportion used) as tools for studying the existence of voting equilibria (i.e., for studying the existence of alternatives which cannot be defeated). It establishes that there are certain important contexts where one of the two bounds does not directly reveal whether any voting equilibria exist, but the other one does.