Are good leaders truly good?

This paper offers a new insight on the Condorcet Jury Theorem (CJT) in the theory of epistemic democracy. This theorem states that democratic decision-making leads us to correct outcomes under certain assumptions. One key assumption is the 'independence condition', which requires that voters form their beliefs independently when they vote. This paper examines the role of an opinion leader as an informational source, which potentially violates independence. We demonstrate that voters' beliefs may be correlated in the presence of the leader, and that the CJT can fail if the leader's opinions are reliable. This leads us to the following paradoxical observation: for epistemic democracy, good leaders may be bad, while bad leaders may be good.