Genetic studies of social behaviour have currently received new impetus from models including indirect genetic effects (IGEs) of social partners. This study aimed at investigating the contribution of conspecifics in social dominance, considered as response of dyadic interaction that is, winning (dominant individual) or losing (subordinate). A genetic correlation of −1 is expected between the attitude to win and the attitude to loose, and because a population always accounts for half winners and half losers, the heritability of the dominant status should be close to zero. Specifically, social dominance was studied in Aosta Chestnut and Aosta Black Pied (Bos taurus) breeds, alpine rustic cattle famous for traditional tournaments where pairs of cows assess dominant status in bloodless fights. The outcomes of 25 590 dyadic interactions performed by 8159 individuals in 11 years were analysed by applying a classical quantitative model and models including indirect effects. Data were analysed via Bayesian approach on a threshold trait. The assessment of variances revealed a genetic correlation of −0.976 between direct and indirect genetic components. The heritability measured on a liability scale was 0.122 for direct phenotype, but decreased to 0.014 when the total heritable variance (TBV) was considered. The trend of estimated breeding values showed that the total TBV was constant over the years, even though its direct component increased and the indirect part decreased. This result confirms the relevance of IGEs on social behaviour and the assumption that the mean individual social dominance cannot evolve within a population, due to the evolutionary constraints imposed by the ‘social environment’.