Abstract
We look for classes of hypergraphs H in which any partition of V (H) can be represented almost fairly by some edge. We show that this is true when H is the set of independent sets in a path, and conjecture that it is true when H is the set of matchings in K_n, n.
We prove that partitions of E(K_n, n) into three sets can be represented almost fairly. The methods of proofs are topological.