Since you specifically mentioned Chinese pirates, let me talk a bit about the most famous Chinese pirate, Zheng Yisao (aka Ching Shih and other aliases). She and her husband, Zheng yi - Zheng Yisao literally meaning "Zheng Yi's Wife" - were amongst the most successful pirates in modern history. This is particularly true for Zheng Yisao. She not only commanded hundreds of ships and tens of thousands of men, but also managed to retire rather gracefully.

Zheng Yisao took over a giant pirate fleet from her husband when he died. She then managed to both get accepted by the crews and also impose her own set of rules and organisation on the pirates under her command. In her fleet, a code of rules was successfully enforced, including regulation of plundering, and harsh punishment against the mistreatment of women when raiding or who were in captivity. It's debatable whether she or her adoptive son and lover (yes, it's complicated) actually set these rules. Regardless, they were in effect amongst the ships of the fleet they led together.

As far as the democratic elements are concerned, I don't think the few sources we have mention a particularly democratic conduct. Zheng Yisao's rise to leadership was a combination of her being the previous leaders wife and managing to gain the favour of other pirate leaders together with her adoptive son and lover. From what I have read, it seems like they imposed the rules on the pirates, though in reality it is hard to tell whether this was a mutual agreement. In comparison to Carribean pirates like Bartholomew Roberts, I would certainly say that organisation under Zheng Yisao was not as democratic as Carribean pirates voting for their leaders and for important decisions.

Unfortunately, I don't know whether other Chinese pirates were organized similarly.

The answer to this question might be of interest to you:

Did Asia experience any Golden Age of Piracy?

Part 3 gives the details of how raids were organised by the Iranun pirates.