Let B denote a set of bicolorings of [n], where each bicoloring is a mapping of the points in [n] to {−1,+1}. For each B∈B, let YB=(B(1),…,B(n)). For each A⊆[n], let XA∈{0,1}n denote the incidence vector of A. A non-empty set A is said to be an ‘unbiased representative’ for a bicoloring B∈B if XA,YB=0. Given a set B of bicolorings, we study the minimum cardinality of a family A consisting of subsets of [n] such that every bicoloring in B has an unbiased representative in A. © 2019 Elsevier B.V.