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. 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 into two factions, we characterise the win probability of the minority and show that these features promote a more equitable allocation of political representation, striking a balance between protecting the minority and giving proper recognition to the majority. We then consider this family of voting procedures from a constitutional perspective: we analyse how the electoral result varies with the college size and the winning threshold in order to understand how these two parameters can be tuned when drawing up electoral law. We find that minorities are better off with larger majority thresholds. The role of the college size, on the other hand, is ambiguous: a smaller college size offers more protection to sparse minorities; for more sizeable ones, it depends instead on the qualified majority required for the election.

中文翻译：

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威尼斯共和国如何选择其总督：抽签选举和绝对多数统治

我们研究了一系列投票规则，其灵感来自威尼斯共和国 500 多年来用于选举总督的特殊协议。基于抽签的间接选举有两个主要特点：从大会中抽签选出一组代表，然后他们以合格的多数票在单一获胜者选举中投票。在议会分为两个派系的假设下，我们描述了少数派获胜的概率，并表明这些特征促进了政治代表的更公平分配，在保护少数派和适当承认多数派之间取得了平衡。然后我们从宪法的角度考虑这一系列的投票程序：我们分析了选举结果如何随大学规模和获胜门槛而变化，以了解在制定选举法时如何调整这两个参数。我们发现少数群体的情况更好，多数阈值越大。另一方面，大学规模的作用是模棱两可的：规模较小的大学可以为稀疏的少数族裔提供更多保护；对于规模较大的选举，则取决于选举所需的合格多数。