Group living increases the likelihood of inter-individual conflicts, necessitating effective conflict resolution. While institutions and social structures play an important role in resolving conflicts, societies which emphasize egalitarianism often prioritize individual autonomy and lack strong socio-political institutions. Existing scholarship highlights the critical role of leaders in facilitating conflict resolution, particularly in the maintenance of group cohesion under egalitarianism. Here we investigate the association of peer-rated conflict resolution skills with 11 peer-rated psycho-social traits linked to leadership in a sample of 60 individuals from a Chabu community, a relatively egalitarian population of forest-dwelling Ethiopian forager-horticulturalists. We employ network-based methods and Bayesian multi-level modeling to identify trait clustering, trait-based linkages, and the key predictors of conflict resolution skills. We found that conflict resolution skills cluster with decision-making abilities, intelligence, social alliances, and expertise, while attributes such as being respected and liked constitute another distinct cluster. Conversely, traits like aggressiveness, being feared, and farming productivity align within a third separate cluster. After accounting for inter-rater variation, sound decision-making and intelligence (i.e., neural capital) as well as social alliances were positive predictors of conflict resolution skills, while aggressiveness was a negative predictor. Our results also reveal an overlap in similarity networks between women and men. These findings suggest that, when it comes to effective conflict resolution, it is neither better to be feared nor loved. Instead, in this egalitarian social context, well-connected individuals equipped with high levels of neural capital emerge as the most effective conflict mediators. Our results shed light on leadership phenotypes associated with conflict resolution under egalitarianism. Additionally, they carry implications for the evolution of group living among humans by highlighting the pivotal role of neural capital in promoting effective conflict mediation in more close-knit social contexts.