Abstract: We spent two winters studying the social behaviour of wild woodland caribou (Rangifer tarandus caribou) at a time when their main food (ground lichens; Cladina sp.) is available only at snow craters dug by the animals. The competition for access to such craters was severe, the animals constantly trying to take over the craters of others. During a two-month period when a group maintained a constant size (20) and composition (all age-sex classes represented), we could rank the animals in a rather linear dominance hierarchy (Landau's index = 0.87). Rank was correlated with access to resources, percent of time spent active, and percent of time feeding in craters. It was also correlated with age and antler size. However, rank is not an attribute of individuals, but of a relationship between individuals. As such it is only an intervening variable between physical attributes and access to resources, a variable whose value has meaning only within a given group. Among the three attributes studied (age, sex, antler size), the latter was by far the best predictor of the occurrence and outcome of interactions. Between two individuals within any of the three age-sex classes studied (adult and yearling males and adult females), the one with larger antlers initiated significantly more often, escalated its aggression (to the point of hitting the target) less often, and enjoyed a higher success rate in obtaining resources. When their antlers were larger than those of an adult male target (i.e. males that had shed their antlers), adult females won almost all their interactions with adult males even though they escalated only one fourth of them. This clarifies the long-standing speculation that female caribou have antlers and shed them later than males, in order to overcome their sexual handicap in competition for food in the winter. We conclude that the link between rank and dominance of an individual on one hand, and some of its attributes on the other (e.g. sex, age, weight, antler size) is fundamentally realized by the animal itself through its active preference for targets it is likely to beat, i.e. targets with smaller antlers.