Divided majorities can effectively harmonize their votes by the means of algorithmic coordinators: mechanisms that aggregate reported preferences and issue voting recommendations. We focus on incentive-compatible coordinators, and study their effect on social welfare. While some of them are highly efficient, contrary to common wisdom, some others are welfare reducing, even compared to when no coordinator exists. We conduct a laboratory investigation that provides strong support for these theoretical predictions: when bad coordinators are available, subjects are trapped in following their advice, and inferior outcomes prevail. These findings qualify the appeal of centralized coordination and issue caveats regarding its use.