The round-robin is the circle in which the men sign their names before they're going to start a mutiny. They sign it that way so no one person can be held responsible. Here's Captain Jaggery's take:
"A round-robin," he said. "The men sign it this way so no name shall appear on top, or bottom. How typical of them not to accept responsibility for their own wayward actions. It's a kind of pact." (5.71)
Captain Jaggery sees the round-robin as a symbol of not taking responsibility, but it's clear that the men see it as a representation of egalitarianism (that means they're all equal). Why? Because there's no hierarchy in a circle.