Dwarves live under a weird government. Like England, they have an official monarch, but he's more of a figurehead than anything. There are nobles who are allowed to mandate things and have some small power in government (such as taxes and law), but like the king they don't actually run things.
Dwarf colonies start under a theocratic utopian government. Everyone does what work is assigned without complaint (or rather, they don't complain about the work, only the conditions) and partakes freely of what they need. The only things dwarves truly "own" are bedrooms and clothing. As this scales up, a small form of government emerges, but mostly it remains true to early utopian societies until the arrival of the baron and implementation of the economy.
The dwarf economy most closely resembles that of a communist state. The government assigns jobs and gives arbitrary pay for completion of any task given. Goods are taken from the state and resold to the population, but all is owned by the state (ok, technically not true, but if you want something a dwarf has, possession is just a magma bath away). However, there is no official ruling body. No dwarf is "more equal" than another, at least officially. All dwarves simply obey a divine will.
So dwarves currently live under a seemingly monarchic but really theocratic communist state. A really frikin complicated government if you ask me.