Generalize Arrow’s theorem to arbitrary finite alphabets

Generalize the stated Mossel-type Arrow theorem from the Boolean predicate $P_{\mathrm{3NAE}}$ to predicates over arbitrary finite alphabets, characterizing the resulting dictatorial, anti-dictatorial, certificate, or other allowable polymorphism types.

Background

The paper studies the Boolean three-candidate predicate representing consistent preference orderings and recalls Mossel’s classification of its polymorphisms as dictators, anti-dictators, or certificates.

Although related work treated unanimous or supportive polymorphisms over arbitrary finite alphabets, the paper explicitly leaves open the corresponding generalization of the non-unanimous Arrow theorem in its setting.