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In each round, Balancer first claims \\(p\\) previously unclaimed vertices, and then Unbalancer claims \\(q\\) previously unclaimed vertices. Let \\(B\\) and \\(U\\) be the final sets of vertices claimed by Balancer and Unbalancer, respectively. For an edge \\(e\\in\\mathcal E\\), define $D_e = q|B\\cap e|-p|U\\cap e|\n  = (p+q)|B\\cap e|-p|e|$. Thus \\(D_e\\) measures the deviation of Balancer's share of \\(e\\) from the density \\(p/(p+q)\\). 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