<p>Communities frequently experience belief polarization, even in the face of overwhelming scientific evidence supporting one side of the debate. Current explanations for this phenomenon, which we define as <i>bad polarization</i>, attribute its emergence to the influence of social incentives on belief formation. However, these explanations presuppose the existence of a fragmented community in which opposing groups develop different beliefs. Here, we provide a model of belief formation in which social incentives bring about bad polarization even in structurally cohesive communities. We assume agents to distribute a finite amount of social support among their like-minded neighbors and to sample evidence partially in order to form the belief that grants them the highest possible support. Accordingly, we show that bad polarization emerges more frequently when communities are highly connected, and that bad believers, individuals holding unsupported beliefs, are consistently a minority. Bad polarization is driven by the competition for social support: bad believers form a minority because this allows them to gain a higher amount of support than if they adhered to the majority view.</p>