Six studies explored the hypothesis that third parties are averse to resolving preference disputes with winner-take-all solutions when disputing factions belong to different social categories (e.g. gender, nationality, firms, etc.) versus the same social category. Studies 1-3 showed that third parties’ aversion to winner-take-all solutions, even when they are based on the unbiased toss of a coin, is greater when the disputed preferences correlate with social category membership than when they do not. Studies 4-6 suggested that reluctance to resolve inter-category disputes in a winner-take-all manner is motivated by a desire to minimize the affective disparity—the hedonic gap—between the winning and losing sides. The implication is that winner-take-all outcomes, even those that satisfy conditions of procedural fairness, become unacceptable when disputed preferences cleave along social category lines.