Committees with leaks

We analyze the quality (informativeness and efficiency) of advice obtained from a committee of careerist experts where voting is secret but voting profiles are ‘leaked’ with an exogenously given probability. We show that fully informative voting is achievable only when the common prior is not too informative, the committee uses the unanimity rule and faces random leakage. It is then shown that informativeness and efficiency are mutually exclusive properties of committees with careerist experts.