This is a huge question and the answer to it formed a large part of my doctoral thesis, particularly chapter 2.

In legitimate early-modern seafaring there existed two distinct chains of command: within the ship (the internal chain) the captain held sway, with command passing down through the ship's officers; but in almost every instance there also existed a higher chain of command outside the ship (the external chain), consisting of the vessel's owners, in the case of merchant or privateer ships, or the in the case of Navy ships, the higher chain of commodores and Admirals, extending ultimately to the government and the monarch via the Lords of the Admiralty.

However, pirate ships faced the problem of not having any form of external command to direct things like the appointment of officers or the course of actions the ship took. De facto ownership of the pirate ship fell to the crew themselves, effectively placing the external command hierarchy uniquely within the confines of the ship. This created an intriguing dichotomy whereby the captain held command over the crew on internal matters, but was subservient to the crew on external matters. Or, put a different way, as members of the crew the rank-and-file pirates were at the bottom of the chain of command, but as de facto owners of the vessel they were also at the top of the chain.

So, for example, the crew might choose the captain of their ship in their position as owners, just as the owners of a legitimate vessel would, but having chosen him generally had to obey his commands in their position as crew, just as the crew of a legitimate vessel would.

Thus, on the face of it, pirate crews appeared to be highly democratic.

But here's the kicker. On very few pirate vessels were the entire crew considered to be owners.

Much has been made of the clause in Bartholomew Roberts' articles that states 'Every man shall have a vote in affairs of the moment', but of all the surviving articles Roberts' is the only one to contain such a clause, and there is strong evidence that 'every man' did not actually include every man bound by the articles. Roberts' company included a large number of slaves, a few boys, and a number of forced conscripts, none of whom were probably allowed to vote. Former soldiers in the company were looked down upon and only given a quarter share in any proceeds, which, while not evidence that they couldn't vote, does suggest that not all men were equal. Thomas Davis, a forced man in Bellamy's company, gave evidence at trial that sheds light on the extent of the franchise in practice:

When the company was called together to Consuls, and each Man to give his Vote, they would not allow the forced men to have a Vote. There were one hundred and thirty forced Men in all, and Eighty of the Old company; and this examinate being a forced Man had no opportunity to discover his Mind.

That is to say, only 38% of Bellamy's company had the right to vote. In colonial Massachusetts the right to vote was extended to anywhere between 28.4% and 77.6% of the adult male population, so pirate companies begin to look less and less like beacons of democracy. On p. 132 of my thesis (linked above) there is a table showing the extent of the franchise in 14 pirates companies, 1704-1724, in which the number of voters ranges from 18-87%, in an analysis which is likely to overestimate the number of voters rather than underestimate.

In some companies, like John Gow's, there is no evidence of any formal voting taking place at all. John Philips was described as 'so arbitrary as to be hated by his own crew,' and one of Gow's articles states,

That every Man shall obey his Commander in all Respects, as if the Ship was his own, and we under Monthly Pay

Perhaps one of the biggest issues is that even when a vote was taken, there was no guarantee that it would be adhered to. For example, the company of a pirate ship commanded by William Mason in the Atlantic voted on whether to sail East for the Indian Ocean or West for the Pacific. The officers all voted for the East and the men (the larger party) voted West, but since everyone capable of navigating had voted for the East, that was the course they took.

The status of both women and black men on pirate ships of the 'golden age' could easily fill a whole post each: here's the short version. Only four women are known to have been members of pirate companies in the period, and while three of them seem to have been more or less 'equal', that's a statistically insignificant number. The status of black men varied enormously: those who were useful and spoke English might well become free members of the company, though I've yet to find an example of a black man receiving a share of the profit; the rest were generally treated as slaves, to be put to work on the arduous tasks like pumping or sold for profit.