In opposite to the common belief, pirate captains never were indefeasible, totalitarian "masters next God", like Navy mates.
They had been elected by the crew, and excepting during battle they didn't get any special rights. If a captain didn't please his crew, they elected easily a new one. If they hated their old cap'n, he was marooned or killed.

Well, if there were two equal liked candidates, or someone wanted to prove he would be a better captain, they dueled, if possible on some beach, never aboard.

Michel de Grammont took about ten "electional" duels. Alone three after he lost his eye. This pic shows his eight, against Black Murphy on Rhode Island...He is the one with the french hat.