The golden age of piracy came early in the 1700s, around the time span from 1716 to 1726. This was also the time of the Enlightenment. Studying pirate societies gives us some insight into the social order that was emerging from the Enlightenment.
Among other things, the Enlightenment stressed rational approaches to human problems. This is why it was opposed to monarchy. It saw monarchy as an irrational way to order human affairs.
Instead, the Enlightenment tended to promote the idea of democracy. This can be seen in pirate societies since they tended to elect their own leaders and split up their loot in egalitarian ways. They also set up their societies in ways that were clearly different from the autocratic and brutal ways of most ships in those days.
But there was also an anarchistic side to the pirates that reveals something of a tension in Enlightenment thought. It could be argued that democracy, taken to its extreme form, is the same as anarchy. The struggle between the need to have some order and the desire to break down irrational forms of order was one that caused tension in Enlightenment times. This tension can be seen in pirate societies.