On the enumeration of resolute majority rules

Abstract

This paper considers resolute decision rules in which each voter may vote “yes", “abstain" or vote “no", and the outcome is “yes" or “no". The model we consider is more general than that of simple games since the input admits abstention or indecision, but it is more specialized since it assumes the properties of monotonicity and anonymity. Many subclasses of these resolute decision rules have been studied in the literature from an axiomatic point of view. The purpose of this work is to enumerate these subclasses as a function of the number of voters.