How the Republic of Venice chose its Doge: Lot-based elections and supermajority rule

We study a family of voting rules inspired by the peculiar protocol used for over 500 years by the Republic of Venice to elect its Doge. Such lot-based indirect elections have two main features: a pool of delegates is chosen by lot out of a general assembly, and then they vote in a single winner election with qualified majority. Under the assumption that the assembly is divided in two factions, we characterise the win probability of the minority and study how it varies with the electoral college size and the winning threshold. We argue that these features promoted a more equitable allocation of political representation and thus may have contributed to the political stability of the Republic of Venice.