&gt; &quot;...no pirate has an incentive to deviate unilaterally (one vote can&#x27;t change the voting outcome)...&quot;<p>I would strongly challenge that assumption as having any realism (even for perfectly rational agents and no communication): if an agent decided to vote, he could assume all other perfectly rational agents (another usual assumption) would also take the same decision (by symmetry), so he can safely vote yes. This symmetry could only be broken if the agents have access to randomness.