And Democracies and Republics. The majority of all governments in other words.
Ok, so the proper breakdown is this:
Loses dukeship when elected: Monarchy, Republic, (Democracy?)
Cannot reappoint self as duke: Monarchy, (Democracy? I doubt it though. Seems like being ruler isn't a condition to prevent one from running, but, I guess that covers "election" Hang on...)
Cannot be reelected as duke: Monarchy, (Democracy?)
So to recap, the government types in which you absolutely cannot become duke after becoming ruler are the following: Monarchy, and possibly Democracy
The following government types allow you to become dukes after becoming ruler, although in the case of Republics, people might get annoyed at you: Republic, Theocracy, Tyranny.
Note that Democracy is still a wild card. In Fontan 2007-08 I recall seeing the Chancellor as Duke before, so I have a hunch that the ruler can still run for duke.
So actually...If we want to be strict about it, I was correct in what I said. Only in monarchies is the ruler actually barred from becoming duke, unless democracies have the same rule. So no, not the majority of government types.