Hello. Not discouraging anyone from providing additional information, but do check out this answer by u/davidAOP.

You should check out the FAQ if you like to know more about pirates.

Hello, I am a historian who graduated from SIUE who wrote on the Golden Age of Piracy. I do not have much time so I will keep it brief and come back to this later if I can! The answer this question is "yes, however..."

We'll look at the most prominent primary source on the Golden Age of Piracy, which is also a secondary source, a book published in 1724, General History of the Robberies & Murders of the Most Notorious Pyrates by Captain Charles Johnson. "Captain Charles Johnson" is a pen name and Arne Bialuschewski has identified the most likely author, journalist Nathaniel Mist.(1) This book covers the Golden Age of Piracy by covering the pirates themselves. In a chapter on Bartholomew Roberts, Johnson writes on Roberts' articles for conduct detailing the rights of the crew, stating “Every man has a vote in affairs of the moment; has equal title to the fresh provisions, or strong liquors, at any time seized and use them at pleasure, unless a scarcity make it necessary, for the good of all, to vote a retrenchment."(2) You'll find other articles for pirate ships held similar codes for voting, however, not all did. There was a second volume written years later, The History of the Pyrates: VOL II, which also gives further insight into the democracies of pirates. You'll find each ship held its own codes and rules, as if each ship was its own small nation. Giving equal share and vote is a common theme among them. A desire to have what is due as well as some power.

David Cordingly also touches on this subject in his book Under the Black Flag: The Romance and Reality of Life Among the Pirates. Pirates ran their ships on democracy, and Cordingly states, “The captain was elected by the votes of the majority of the crew and he could be deposed if the crew were not happy with his performance.”(3) The captain’s power was also limited, and Cordingly states, “The crew, and not the captain, decided the destination of each voyage and whether or not to attack a particular ship or raid a coastal village.”(3)

It is not strange to think pirate crews would be democratic. The Golden Age of Piracy ends where the Age of Enlightenment begins. Some privateers and pirates, like William Dampier, were educated men. Dampier wrote somewhat scientific books during his travels. Made up of sailors who have built hatred of the top down power structure of military and merchant sailing life. They held little say until they struck out on their own in criminal ways. A few were ex slaves or natives who had been freed experienced freedom under piracy, although, many were simply captured and sold as slaves. People who would normally be mortal enemies based on their nationality instead came to cooperate. Colin Woodard wrote that “pirate vessels frequently joined forces and came to one another’s aid, even when one crew was largely French and the other dominated by their traditional enemies, the English."(4) Piracy was an oddly united and progressive movement, but via violent criminal action. Not to say all pirates held good morals or progressive ideals, simply that the movement itself was heavily influenced by progressive ideals such as gay marriage, healthcare, equal rights, and democracy. Robert’s also listed a form of healthcare within his articles, which stated, “any man should lose a limb, or become a cripple in their service, he was to have eight hundred dollars, out of the public stock, and for lesser hurts, proportionately.” (5) A form of union between two men called "matelotage" was practiced among pirates and often functioned like marriage. (6) Pirates needed each other to survive. They worked together and this meant sharing equal prize and equal vote. This was fueled by many factors. New progressive ideals, sailors looking for a new life with freedoms, wars ending, privateers out of work, and the growing slave trade/colonization of the new world. A perfect storm for "progressive" pirates.

Sources:

(1) Woodard, The Republic of Pirates, 325.

(2) Charles Johnson, General History of the Robberies & Murders of the Most Notorious Pyrates, 230.

(4) Woodard, The Republic of Pirates, 2.

(3) Cordingly, Under the Black Flag, 96.

(5) Johnson, General History of the Robberies & Murders of the Most Notorious Pyrates, 232.

(6) Anna Livia and Kira Hall, Queerly Phrased: Language, Gender, and Sexuality, 139.

I study the history of constitutions, not the history of piracy, but perhaps I might have a go. Twice a year I open my first lecture of a course on comparative constitutions with a picture of a pirate ship (and also a poster of The Godfather and a copy of the Laws of Cricket) to demonstrate how constitutions and constitutionalism occur in a range of contexts, including outside the state.

There is evidence that at least some pirate ships had documents approximating modern constitutions, by which their ship-borne communities were governed.

People familiar with the American constitutional tradition tend to think of constitutions primarily as instruments for the protection of rights, but that's only one of their functions. Another key functions - which are equally applicable on a pirate ship - include: (1) establishing legitimate authority (making it clear who can decide on what); (2) reducing conflict by creating reasonable shared expectations of how others must act; (3) sharing resources.

The 'Pirate constitutions' I've seen deal with a lot of the ordinary things that in a modern ship would by dealt with by Queen's Regulations and Admiralty Instructions (or equivalent) or by Captain's Standing Orders. Lots of things about when lights must be extinguished, when you can and can't drink alcohol, avoiding fighting on the lower deck, that sort of thing. They are rules that keep the ship and its crew safe.

But they also include mechanisms to determine who has the power to decide. This may include the election by the crew of the captain; in some cases, the captain might appoint a Sailing Master, who will be in actual charge of sailing the ship. This is very interesting, because it replicates the modern division in a state between politicians and civil servants: the Sailing Master can't be elected, because he needs technical skills that have to be selected for on merit, not popularity.

There might also be a separately elected Quarter Master, in addition to the Captain, who would be responsible for enforcing the rules - a sort of primitive 'separation of the powers': if the Captain violates the rules, you can appeal to the Quarter Master.

There might also be rules for the removal of a Captain who does not prove equal to the duties of his office. That looks like it puts the Captain in a weaker positions, but really it doesn't - if there is an established procedure, then any attempt at removal outside that procedure (by assassination, duel etc) is illegitimate. Rules empower as well as constrain.

Next to the question of 'who is in charge', the question of 'who gets what' is often a cause of conflict. In a pirate ship, this concerns the distribution of booty. Last thing you want, after having captured a treasure ship, is to fall to fighting amongst yourselves about how to divy it up. Having rules written in advance prevents this sort of thing (how effectively, in practice, I do not know).

So, yes, some pirate ships definitely did have governing documents that were at least quasi-constitutional in character, and these did have elements of 'democracy', at least in terms of choosing and removing captains and quartermasters.

Pirates joining a crew would be required to sign or subscribe to this pseudo-constitutional documents (often called, the 'Articles', in imitation of the terms of engagement on a merchant ship). Changes to the rules may also have required the general consent of the crew, or the major part thereof.

What I do not know, and here others might answer, is how widespread this was. Just because we have some surviving examples of these documents doesn't mean every pirate ship had them - although when we look at it practically and functionally, we can see it as a sensible idea, to make sure the ship had a legitimate leadership and internal order in a community otherwise prone to violence.

A good introductory source is 'Criminal Constitutions' by Peter T. Leeson and David B. Skarbek. Peter Leeson is really the go-to-guy for this:

Leeson, Peter T. 2007a. “An-arrgh-chy: The Law and Economics of Pirate Organization.” Journal of Political Economy 115(6): 1049-1094.

Leeson, Peter T. 2009a. “The Calculus of Piratical Consent: The Myth of the Myth of Social Contract” Public Choice 139(3-4): 443-459.