This just hit me, the Shichibukai can each represent a different type of ruler or power either political or social. I want to examine each pirate one by one.
Hancock: She is an empress. Plain and simple. An empire can be different than a kingdom. An empire usually means more than one country, ironic since she just has power over Amazon Lily.
Mihawk: He is a bit of a vigilante (like Batman). He followed Krieg and slashed him to a pulp simply because he was bored. He seems to do as he pleases. He showed up in Marijois because he felt like it.
Crocodile: Mafia don. This should be fairly obvious. He screams mafioso. He sat in the shadows and gave orders directly to his subordinates. Also, like the mafia, Baroque Works had a chain of command. Think of what he did in Alubarna as a form of "protection."
Kuma: As his epithet suggests, he would be a tyrannical ruler, autocratic and oppressive. While he does not display his tendencies as much as the other Shichibukai, we don't know the specifics of what he did to earn the nickname "Tyrant." It probably wasn't pretty.
Jinbe: Yakuza. His outfit (like Crocodile's) is very suggestive of a stereotypical yakuza. While he has not been seen actually doing any pirating, if Arlong is any suggestion of how Jinbe worked, it is very much like a mafia.
Moriah: Triads. This one is a bit of a stretch, but I believe Moria would be representative of a triad leader. The fact that he has three other people working directly under him could be a pun on the "tri" part of "triad." That, or the Mysterious Four could be representative of a triad high council. Again, a bit of a stretch. Also (just realized), shadow government. The people on Thriller Bark could more or less do what they wanted, as long as they didn't mess with the secretive and reclusive ruler. There were his supporters and those who disliked him (think communist Russia).
Teach: If anything, he would be part vigilante and part autocrat. He does what he wants and his crew doesn't have too much of a say in their activities. Teach broke the animal theme and he broke this one too.
Doflamingo: I saved the best for last. Doflamingo was the one who inspired me to do this. His sunglasses and powers should tell it all. He is representative of a puppet government, a government where the person acting as leader is actually receiving orders from someone else. The best example would be France in World War II. The Nazi's made a puppet government with Philipe Petain at the end of the strings. Petain acted as a ruler and also as a curtain (like sunglasses) to what the Nazi's were really doing. Doflamingo's named after a French hero. Also, coincidentally, Philipe Petain, Donquixote Doflamingo. Both begin their first and last names with the same letter.
That's my revelation. If I've blown your minds, let me know. Actually, just let me know regardless.