We present a class of orderings L for which there exists a profile u of preferences for a fixed odd number of individuals such that Bordas rule maps u to L.
The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to investigate t
he dimension of the partial order. We provide a characterization of a partial order having dimension n in general.
