Abstract: We introduce assessment to the analysis of dominance hierarchies by exploring the effect of an evolutionarily stable fighting rule when there is variation in resource holding potential (RHP) and RHP is not a perfectly reliable predictor of the outcome of a fight. With assessment, the probability of a linear hierarchy decreases with group size but can remain appreciable for groups of up to seven or eight individuals, whereas it decreases virtually to zero if there is no assessment. The probability of a hierarchy that correlates perfectly with RHP is low unless group size is small.