Yep, the Directorate is 4 seats held by the high priests of the city, 1 seat held by the dean of the city university, and 10 for which anybody can run. But to quote,
"While the seats held by the priests and the university are permanent, the ten chairs held by the merchant houses are supposedly open to any member of the Burgerhof, rich or poor. Since the time of Magnus, though, these seats have been reserved in all but name for the merchant houses. By informal agreement, the heads of the ten wealthiest families win election at the start of each two-year term, their liberal patronage ensuring that they have the necessary votes."
(Pardon the cursed old PDF spacing.)
The whole government is democratic in theory - Sold Down The River kinda emphasizes how Marienburg is sort of the birthplace of what'd we consider recognizably "modern" democracy in the Warhammer world, with a lower chamber of legislators elected to represent different regional constituencies and so on. There's also some discussion about how it could be hypothetically possible for someone to overcome the biases of the system, and people pushing for reform to make that more feasible.