When to defer to supermajority testimony — and when not

Abstract
Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. Here I identify the conditions under which deference to supermajority testimony ensures consistency, and those under which it does not. I also introduce the new concept of ‘consistency of degree k’, which is weaker than full consistency by ruling out only ‘blatant’ inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while supermajoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense
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