= ∑ v∈R yv 5 return S, λ 6 Function FairDecomposition(G, L, R) 7 k = 0 8 L′, R′ = L,R 9 while L′ 6= ∅ do 10 X, λ′ = SmallestRatioSet(G, L′, R′) 11 L′ = L′ \X 12 if k = 0 or λ′ 6= λ then /* Create new block [...] b2), (a3, b1)}. The distribution F1 choosing from among M1,M2,M4 and M5 with probability 1 3 , 1 6 , 1 6 , 1 3 , respectively, is maxmin-fair. The satisfaction probabilities of a0, a1, a2 and a3 are then [...] are equivalent: (1) D is maxmin- fair; (2) D is minmax-Pareto; (3) D is Pareto-efficient and D↓ 6= E↓ 6= for all Pareto-efficient distributions E over S. The proof may be found in Appendix A. Note that …