A principal and $n\ge 2$ agents can launch a project if the principal proposes it and at least $k$ agents accept. Their individual payoffs from the project depend on an ex ante unknown state. The principal can conduct a test to learn about the state and then communicate her findings to the agents via cheap talk. This paper focuses on comparing two communication regimes: public and private messaging. We show that public messaging is weakly dominant: any outcome implementable under private messaging can also be implemented under public messaging. Moreover, in a canonical environment with linear payoffs, we characterize the principal's optimal test in each regime and show that public messaging can be strictly dominant if and only if there exist two agents who are the principal's conflicting allies.

翻译：一个委托人和 $n\ge 2$ 个代理人可以启动一个项目，前提是委托人提出该项目且至少 $k$ 个代理人接受。他们从项目中获得的个人收益取决于事前未知的状态。委托人可以进行一项测试以了解状态，然后通过廉价交谈将她的发现传达给代理人。本文侧重于比较两种沟通机制：公开信息和私人信息传递。我们证明，公开信息传递是弱占优的：任何在私人信息传递下可实施的结果也可以在公开信息传递下实施。此外，在线性收益的标准环境中，我们刻画了每种机制下委托人的最优测试，并证明公开信息传递是严格占优的当且仅当存在两个作为委托人冲突盟友的代理人。