Axiomatization of plurality refinements

Plurality rule uniquely satisfies anonymity, monotonicity, neutrality, and tops-onlyness. However, it is not always able to produce resolute outcomes. We study singleton-valued refinements of plurality rule that satisfy all but one of these four axioms. Monotonicity is preserved by all refinements of plurality, whereas no refinement satisfies the remaining three except for a very limited case. We explore what dropping one of the three remaining axioms brings about towards singleton-valued refinements.