Rube Goldberg Political Machine

In the 12th century, the Republic of Venice had a problem.  The office of the Doge (sort of like an elected duke) was always in danger of becoming a hereditary office, as the Doges came from powerful families and sought to pass the title to their sons.

Normally, you could solve this with a simple election, to ensure that everyone had a say in the matter and no one family could monopolize the title.  But Venice was full of wealthy, scheming bastards who were more than willing to place a few bribes to get the right man on the throne.  To combat this, they came up with a slightly complicated system to make sure it was difficult to buy your way to the top.

Starting in 1172, a new Doge would be elected as follows.  First, four members of the Great Council (sort of like congress) would be selected at random.  These four would then agree on a committee of forty (late increased to 41 after a vote ended in a tie) who would then vote for the Doge.  This way, it was difficult to know in advance who you needed to bribe.  Problem solved, right?

Wrong.  This plan severely underestimated the lengths to which the Venetian families would go in order to game the system.  So they did the only sensible thing and made it way more complicated.  Starting in 1268, the new system worked like this:  First, draw lots to select thirty random members of the Great Council.  Next, a second drawing of lots reduced the group to nine.  These nine were then tasked with agreeing on a group of forty.  In order for a group to be approved, seven of the nine had to agree on it.  After that, the chosen forty drew lots and were reduced to twelve.

At this point, you might think it'd be time to have a vote for Doge.  You'd be wrong.  The twelve then selected a group of twenty-five.   This time nine of the twelve had to agree for the twenty-five to be approved.  Once they had that, the twenty-five again drew lots to reduce the group back to nine.  This new group of nine would have to agree on a group of forty-five, requiring the approval of seven of the nine.  At this point, presumably, it'd be time for nap.

After a good long nap, the forty-five would draw some more lots (of course), and be reduced to eleven.  These eleven would then have to come up with a new group of forty-one, requiring nine of the eleven to agree on it.  Finally, these forty-one would actually vote on who the next Doge should be, with a super-majority of twenty-five out of forty-one being required to win.  By then, of course, everyone had completely lost interest in the whole process, and were quite happy just to have it over with.