Non-dominance and potential optimality for partial preference relations

•The paper investigates the choice of single or several best objects.•Decision maker’s preferences are expressed by means of binary relations.•The notions of potential optimality and non-dominance are equivalent.

In this paper we obtain new theoretical results relating the notions of potential optimality and non-dominance without an assumption that a value function exists. In particular, we investigate a decision problem involving the choice of single or multiple best objects. Our results show that the notions of potential optimality and non-dominance are equivalent in a special case of preferences of the decision maker expressed by partial quasi-orders.