Whom do people prefer to have serve as leaders and how does the answer depend on social context? Despite prior research suggesting a preference for dominant leaders during times of war, six experiments suggest that people prefer prestige-based leaders (those relying on knowledge and expertise to govern) over dominant leaders (those relying on assertiveness, intimidation, and formal authority as a means of influencing others), even in contexts of intergroup conflict such as war. This preference for prestige-based leaders was explained by perceptions of their trustworthiness, tendency to encourage cooperation, consideration of input from group members, and skillful decision making. However, preference for dominance and prestige did shift in response to social context. Dominant leaders consistently received a boost in support in contexts involving intergroup conflict, whereas prestige-based leaders saw a drop in support. This pattern was specific to intergroup threat and did not generalize to contexts involving a high need for social coordination (e.g., within-group conflict, COVID-19 pandemic). The boost in support for dominant leaders was mediated by perceptions of their ability to enforce collective action (e.g., by punishing free-riders) and to defeat rival groups. The drop in support for prestige-based leaders was mediated by beliefs that their desire for popularity and their strong tendency to prioritize input from group members might undermine their performance and ability to make decisions. These studies provide new insight into why people prefer particular types of leaders, as well as how and why leadership preferences change based on social context.