Extend the impossibility-domain correspondence to supportiveness

Extend the correspondence between Φ-triviality and impossibility domains from unanimity to supportiveness for predicates over finite product domains.

Background

The paper proves that, under a permutation assumption on Φ and unary Φ-triviality, Φ-triviality for all arities is equivalent to being an impossibility domain with respect to unanimity.

Supportiveness is another standard generalization of Pareto efficiency to arbitrary finite alphabets, but the paper does not establish an analogous equivalence for it. The authors explicitly list this extension as an open question.