If everyone votes &quot;yes&quot;, one pirate deciding to vote &quot;no&quot; doesn&#x27;t affect their expected return. Therefore everyone voting &quot;yes&quot; is a subgame-perfect equilibrium.<p>Ideas like Nash equilibria and subgame-perfect equilibria are the only known formalizations of rational behavior in multiplayer games. I&#x27;m not obfuscating, I just don&#x27;t know any other kind of math that would work...