What question did this study set out to answer?

This work aims to enumerate subclasses of resolute decision rules based on the number of voters involved.

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March 16, 2026Open Access

On the enumeration of resolute majority rules

Key Points

This work aims to enumerate subclasses of resolute decision rules based on the number of voters involved.
Examined resolute decision rules allowing 'yes', 'no', and 'abstain' votes.
Focused on properties such as monotonicity and anonymity.
Compared different subclasses of the decision rules from an axiomatic perspective.
Identified various subclasses of resolute decision rules.
Demonstrated how these rules change as the number of voters increases.

Abstract

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.

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