Abstract
This is the last of four chapters on belief democracy, and discusses how to rationalize persistent opposition in the light of Wollheim's paradox, and Bayesian considerations that make it utterly irrational for anyone ever to continue disagreeing once everyone has voted. The first section demonstrates that none of the easy and obvious ways of extending the Bayesian framework rationalize majoritarianism without derationalizing ongoing opposition. Next, various ways of moving beyond Bayes to overcome the paradox of persisting opposition are put forward; these include repudiating Bayesian reasoning altogether, assuming that disagreement betokens unreliability, assuming that smaller groups are inherently more reliable, and assuming that each election is different; none of these produce the required result. Finally, political arguments are put forward more explicitly to see whether they can rationalize ongoing opposition; these include the crucial role of opposition in democratic politics, proceduralism, denying propositional content, biased perception, strategic voting, segmented information pools, and different interests. In the light of what has been presented overall, the author puts forward his own explanation, which suggests that what is wrong with Bayesian models that ask us to update our beliefs in the light of others’ votes is that those votes mix facts and values, and only one of these can reasonably be taken into account in updating our beliefs; thus, it is the epistemic power of majorities when dealing with shared facts that underwrites the rationality of majority rule, but their lack of epistemic authority when it comes to matters of evaluations that underwrites the rationality of persisting opposition.