Efficiency in the Degree of Compromise: A New Axiom for Social Choice

We introduce a social choice axiom called efficiency in the degree of compromise. Our axiom is based on the trade-off between the quantity and quality of support that an alternative receives. What we mean by the quantity of support is the number of voters behind an alternative, while the quality of support is about the definition of being behind depending on the rank of an alternative in voters' preference orderings. Naturally, one can increase the quantity of support of an alternative to the expense of giving up from its quality. We say that an alternative is an efficient compromise if there exists no other alternative with at least an equal quantity of support with a higher quality. Our efficient compromise axiom is based on not choosing inefficient compromises. We introduce it and show that many standard social choice rules of the literature, such as Condorcet-consistent rules, plurality with a runoff, the Borda count and the single transferable vote, may choose inefficient compromises.