The authors study the phenomenon of strategic group polarization, in which members take more extreme actions than their preferences. The analysis is relevant for a broad range of formal and informal group settings, including social media, online platforms, sales teams, corporate and academic committees, and political action committees. In the model, agents with private preferences choose a public action (voice opinions), and the mean of their actions represents the group’s realized outcome. The agents face a trade-off between influencing the group decision and truth-telling. In a simultaneous-move game, agents strategically shade their actions toward the extreme. The strategic group influence motive can create substantial polarization in actions and group decisions even when the preferences are relatively moderate. Compared with a simultaneous game, a randomized-sequential-actions game lowers polarization when agents’ preferences are relatively similar. Sequential actions can even lead to moderation if the later agents have moderate preferences. Endogenizing the order of moves (through a first-price sealed-bid auction) always increases polarization, but it is also welfare enhancing. These findings can help group leaders, firms, and platforms design mechanisms that moderate polarization, such as the choice of speaking order, the group size, and the knowledge members have of others’ preferences and actions.