Nonimposition For each set of candidates C and each k-element subset W of C, there is an election E = (C, V ) such that R(E, k) ={W }. The next three axioms—consistency, homogeneity, and monotonicity—are adapted from the single-winner setting. For the first two, the adaptation is straightforward. Consistency For every pair of elections E 1 = (C, V 1 ), E 2 = (C, V 2 ) over a candidate set C and each k ∈[ C ],ifR(E 1 , k) ∩ R(E 2 , k) =∅then R(E 1 + E 2 , k) = R(E 1 , k) ∩ R(E 2 , k). Homogeneity For every election E = (C, V ), each k ∈[ C ], and each t ∈ N it holds that R(tE, k) = R(E, k).