Social conflict is defined operationally as occurring when the behavior of two (or more) individuals indicates that their motivational priorities are incompatible: they seek the same thing of different things, and both cannot be satisfied. Social dominance is defined as consistent winning at points of social conflict, regardless of the tactic used. Four problems generated by many current uses of the social dominance concept are critically reviewed here. (1) Dominance is sometimes equated with and is sometimes operationally defined as priority of access to resources. It is argued that dominance functions to resolve many kinds of social conflict, and not just those involving resources. (2) A tendency to describe all conflict resolution by using the dominance/subordination paradigm obstructs consideration of other relationships, specifically egalitarian ones. Egalitarian relationships are defined. (3) A Tendency to link dominance and aggression causes non-aggressive patterns of dominance(e.g., passive refusal to cooperate, manipulation) to be neglected. (4) When dominance is used as an intervening variable to define a dyadic relationship in many contexts, investigators may overlook important exceptions. Since costs and benefits of winning a given conflict are context-dependent, a dyad member may be dominant in one context but not in others (the "spheres-of-dominance" phenomenon). Social dominance can be based on aggresion (primary social dominance) or on leverate (secondary social dominance). Leverage is discussed and illustrated. Since social dominance is defined as consistent winning, regardless of what tactic is used, a smaller or weaker individual can sometimes be socially dominant to a larger or stronger one, often because of a leverage advantage. Both dominance/subordination and egalitarian relationships are phenotypes. Game theory can clarify the conditions under which particular phenotypes emerge; a model (Parker and Rubenstein, 1981) is presented, modified to account for leverage costs, that predicts the conditions under which various phenotypes should occur and when individuals with less resource-holding potential (RPH) should be socially equal or dominant to others with great RPH. Finally, the aggression of larger dyad members may be suppressed or modulated in some conflict contexts by means of affiliative social bonds (pair-bonds, parent-offspring bonds, or friendships).