等级聚合问题中的平均主义：民主的新维度
Egalitarianism in the rank aggregation problem: a new dimension for democracy
摘要：
在两名候选人之间的选举中，以多数选出获胜者是唯一符合民主原则的规则。相反，当候选人有三个或更多，选民按偏好对候选人进行排名时，选择获胜（共识）排名没有明确的标准，结果显然取决于所采用的规则。在十八世纪孔多塞理论的基础上，其思想是最大限度地提高总选民的满意度，我们在这里建议增加一个新的基本原则（维度）来指导选择：满意度应该尽可能平等地分布在选民中。有了这个新的标准，我们确定了一组最佳的排名。它们的范围从孔多塞的解决方案，以一个是最平等的尊重选民。我们表明，高度平等的排名具有重要的属性是更稳定的波动和经典的共识排名（科普兰，Tideman，舒尔茨）往往被证明是非最优的。新的方面，我们已经介绍了，当使用与孔多塞，一个明确的分类所有可能的排名。通过提高选择共识排名的意识，我们的方法可能会导致社会的选择，这是更平等主义相比，目前可用的投票系统。
英文摘要：
Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no univocal criteria for the selection of the winning (consensus) ranking and the outcome is known to depend sensibly on the adopted rule. Building upon XVIII century Condorcet theory, whose idea was to maximize total voter satisfaction, we propose here the addition of a new basic principle (dimension) to guide the selection: satisfaction should be distributed among voters as equally as possible. With this new criterion we identify an optimal set of rankings. They range from the Condorcet solution to the one which is the most egalitarian with respect to the voters. We show that highly egalitarian rankings have the important property to be more stable with respect to fluctuations and that classical consensus rankings (Copeland, Tideman, Schulze) often turn out to be non optimal. The new dimension we have introduced provides, when used together with that of Condorcet, a clear classification of all the possible rankings. By increasing awareness in selecting a consensus ranking our method may lead to social choices which are more egalitarian compared to those achieved by presently available voting systems.
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