No Testimonial Route to Consensus

The standard image of how consensus can be achieved is by pooling evidence and reducing if not eliminating disagreements. But rather than just pooling substantive evidence on a certain question, why not also take into account the formal, testimonial evidence provided by the fact that a majority of the group adopt a particular answer? Shouldn't we be reinforced by the discovery that we are on that majority side, and undermined by the discovery that we are not? Shouldn't this be so, in particular, when Condorcet's jury theorem applies? It turns out not. There are serious problems attending any strategy of majoritarian deference.