Approval Voting without Faithfulness

In this short paper, we analyze the implications of dropping the axiom of faithfulness in the axiomatization of approval voting, due to P. C. Fishburn. We show that a ballot aggregation function satisfies the remaining axioms (neutrality, consistency and cancellation) if and only if it is either a function that chooses the whole set of alternatives, or an approval voting, or a function that chooses the least approved alternatives.