Conflicts of interest are part and parcel of living in a social group, yet actual conflict can be rare in established groups. Within limits, individuals can maximize the benefits of group living by resolving conflict with other group members. Thus, understanding what causes conflict, what determines its outcome, and how it is resolved holds the key to understanding the evolution and maintenance of sociality. Here, we investigate these questions using the clown anemonefish Amphiprion percula. Clownfish live in groups composed of a breeding pair and zero to four non-breeders that queue for breeding positions. Within groups, there is potential conflict over rank yet actual conflict is very rare. We staged contests in aquaria between pairs of non-breeding individuals over access to a key resource (an anemone), analogous to contests that would occur at the onset of group formation in the wild. The initial size ratio between individuals tended to predict the intensity, and predicted the outcome and resolution of conflict: conflict intensity was greater when individuals were more similar in size; the probability of the smaller individual winning was greater when individuals were more similar in size; and the loser of the contest grew less than the winner when individuals were more similar in size. These results provide a critical test of foundational assumptions upon which our understanding of clownfish and other fish societies has been built. More generally, the results show that one of the simplest and most effective ways for animals to resolve conflict is to modify the phenotype that triggers conflict.