Venetian Elections and Lot-based Voting Rules

Between 1268 and 1797, the Venetian Republic used a complicated voting system that appears designed to resist manipulation. The system starts with randomly drawing voters, followed by 8 rounds of a complicated addition and elimination of voters before the approval voting rule is finally used to select the winner, the new Doge. In this paper, we study a family of voting rules inspired by this Venetian election system, which we call lot-based voting rules. Such rules have two steps: in the first step, k votes are selected by a lottery, then in the second round (the runoff), a voting rule is applied to select the winner based on these k votes. We study some normative properties of such lot-based rules. We also investigate the computational complexity of computing the winner with weighted and unweighted votes, and of computing manipulations. Finally, we propose an efficient sampling technique for generating the k runoff voters non-uniformly.