A model of group decision-making is studied, in which one of two alternatives must be chosen. While group members differ in their valuations of the alternatives, everybody prefers some alternative to disagreement. Our model is distinguished by three features: private information regarding valuations, varying intensities in the preference for one outcome over the other, and the option to declare neutrality in order to avoid disagreement. We uncover a variant on the "tyranny of the majority": there is always an equilibrium in which the majority is more aggressive in pushing its alternative, thus enforcing their will via both numbers and voice. However, under very general conditions an aggressive minority equilibrium inevitably makes an appearance, provided that the group is large enough. This equilibrium displays a "tyranny of the minority": it is always true that the increased aggression of the minority more than compensates for smaller number, leading to the minority outcome being implemented with larger probability than the majority alternative. In all cases the option to remain neutral ensures that the probability of disagreement is bounded away from one (as group size changes), regardless of the supermajority value needed for agreement, as long as it is not unanimity.