The Republic of Florence had their own selection system, from about 1115 to 1434, movement to restore in 1465. Corrupted by the Medici family during much of its later history.

Florentine system (From ChrisB)

Florence was governed by a council called the signoria, which consisted of nine men. The head of the signoria was the gonfaloniere, who was chosen every two months in a lottery, as was his signoria. To be eligible, one had to have sound finances, no arrears or bankruptcies, he had to be older than thirty, had to be a member of Florence’s seven main guilds (merchant traders, bankers, two clothe guilds, and judges). The roster of names in the lottery were replaced every five years.
The main organs of government were known as the the maggiori. They were: the twelve good men, the standard bearers of the gonfaloniere, and the signoria. The first two debated and ratified proposed legislation, but could not introduce it. To hold an elective office, one had to be of a family that had previously held office.

From Wikipedia (May, 2016)

In order to reconcile the warring factions and families, a complex electoral system was developed as mechanism for sharing power.[3] Incumbent officers and appointees carried out a secret ballot every three or four years. They committed the names of all those elected into a series of bags, one for each sesto, or sixth, of the city. One name was drawn from each bag every two months to form the highest executive of the city, the Signoria. The selection scheme was controlled to ensure that no two members of the same family ended up in the same batch of six names.

This lot arrangement organized the political structure of Florence until 1434 when the Medici family took power. To maintain control, the Medici undermined the selection process by introducing a system of elected committees they could effectively manipulate by fear and favour. Civic lotteries still took place but actual power rested with the Medicis. In 1465, a movement to reintroduce civic lotteries was halted by an extraordinary commission packed with Medici supporters.[4]

The Florentine republic example shows how the process of sortition can be used as a check on arbitrary power and patronage through the anonymous and impartial selection of political office holders.