By determining access to limited resources, social dominance is often an important determinant of fitness. Thus, if heritable, standard theory predicts mean dominance should evolve. However, dominance is usually inferred from the tendency to win contests, and given one winner and one loser in any dyadic contest, the mean proportion won will always equal 0.5. Here, we argue that the apparent conflict between quantitative genetic theory and common sense is resolved by recognition of indirect genetic effects (IGEs). We estimate selection on, and genetic (co)variance structures for, social dominance, in a wild population of red deer Cervus elaphus, on the Scottish island of Rum. While dominance is heritable and positively correlated with lifetime fitness, contest outcomes depend as much on the genes carried by an opponent as on the genotype of a focal individual. We show how this dependency imposes an absolute evolutionary constraint on the phenotypic mean, thus reconciling theoretical predictions with common sense. More generally, we argue that IGEs likely provide a widespread but poorly recognized source of evolutionary constraint for traits influenced by competition.