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Competition for social influence is a major force shaping societies. But should one align with competitors when striving for maximum social influence, or strategically misalign? Applying game theory to a scenario where two advisers compete for a client, we find that the rational solution for advisers is to report truthfully when favored by the client, but to exaggerate or blatantly lie when ignored. Across seven experiments, such a strategic adviser was consistently able to sway human voters, outcompeting an honest adviser. The game-theoretic strategy trumped truth-telling in swaying individual voters, the majority vote in anonymously voting groups, and the consensus vote in communicating groups. Our results suggest that strategical misalignment is a powerful approach to gain social influence, which can help explain the success of political movements thriving on disinformation, vocal underdog politicians with no credible program, and overnight social media celebrities.