Equitable, neutral, and efficient voting rules

In the context of voting, Moulin (1980) establishes that anonymity, neutrality, and efficiency are often incompatible unless one accepts indecision (i.e. ties). We show that versions of this incompatibility continue to hold for a natural weakening of anonymity proposed by Bartholdi et al. (2021) called equity . As equity is a relatively weak fairness requirement, the tension between fairness and efficiency in voting is deeper than previously established.