Information disclosure with many alternatives

We consider two-stage collective decision problems where some agents have private information about alternatives and others don’t. In the first stage informed agents (experts) may or may not disclose their private information, thus eventually influencing the preferences of those initially uninformed. In the second stage the resulting preferences of all agents after disclosure are aggregated by a social choice function. We provide general conditions on social choice functions guaranteeing that the collective outcome will be the same that would obtain if all agents shared all the information available in society. Experts should be granted a coalitional veto power: changes in the social outcome that are due to changes in the preferences of other agents after information disclosure should not harm all the experts at the same time. We then specialize our general results. When the set of experts is a priori determined, we characterize those strategy-proof rules defined on single-peaked or separable preference domains that ensure that desired level of information disclosure. We also prove that, when the set of experts is unknown, no voting rule can fully achieve this goal, but majority voting provides a unique second best solution when preference profiles are single-peaked.