The paper deals with voting rules that require voters to rate the candidates on a finite evaluation scale and then elect a candidate whose median grade is maximum. These rules differ by the way they choose among candidates with the same median grade. Call proponents (resp. opponents) of a candidate the voters who rate this candidate strictly above (resp. strictly below) her median grade. A simple rule, called the typical judgment, orders tied candidates by the difference between their share of proponents and opponents. An appealing rule, called the usual judgment, divides this difference by the share of median votes. An alternative rule, called the central judgment, compares the relative shares of proponents and opponents. The usual judgment is continuous with respect to these shares. The majority judgment of Balinski and Laraki (Proce Natl Acad Sci 104(21):8720–8725, 2007) considers the largest of these shares and loses continuity. A result in Balinski and Laraki (Oper Res 62(3):483–511, 2014) aims to characterize the majority judgment and states that only a certain class of functions share some valuable characteristics, like monotonicity. We relativize this result, by emphasizing that it only holds true for non-discrete scales of grades. Properties remaining specific to the majority judgment in the discrete case are idiosyncratic features rather than universally sought criteria, and other median-based rules exist that are both monotonic and continuous.

本文涉及投票规则，该规则要求选民在有限的评估等级上对候选人进行评级，然后选出中位成绩最高的候选人。这些规则因他们在中位成绩相同的候选人中选择的方式而异。将候选人的支持者（反对者）称为选民，他们对该候选人的评分严格高于（平均严格低于）其中位数。一个简单的规则，称为典型判断，通过候选人在支持者和反对者之间的差异来命令候选人。一个有吸引力的规则，即通常的判断，将这种差异除以中位数选票的份额。另一种称为中心判断的规则比较了支持者和反对者的相对份额。对于这些股份，通常的判断是连续的。Balinski和Laraki的多数判决（Proce Natl Acad Sci 104（21）：8720–8725，2007）认为这些份额中的最大份额并失去了连续性。Balinski和Laraki的结果（Oper Res 62（3）：483–511，2014）旨在描述多数判断的特征，并指出仅某些功能类具有某些有价值的特征，例如单调性。我们通过强调该结果仅适用于非离散等级量表来相对化此结果。在离散情况下，多数判断仍具有特定的属性是特有的特征，而不是普遍寻求的标准，并且存在其他基于中位数的规则，这些规则既是单调的又是连续的。2014年）旨在描述多数判断，并指出只有某些功能类别具有一些有价值的特征，例如单调性。我们通过强调该结果仅适用于非离散等级量表来相对化此结果。在离散情况下，多数判断仍具有特定的属性是特有的特征，而不是普遍寻求的标准，并且存在其他基于中位数的规则，这些规则既是单调的又是连续的。2014年）旨在描述多数判断的特征，并指出只有一类功能具有某些有价值的特征，例如单调性。我们通过强调该结果仅适用于非离散等级量表来相对化此结果。在离散情况下，多数判断仍具有特定的属性是特有的特征，而不是普遍寻求的标准，并且存在其他基于中位数的规则，这些规则既是单调的又是连续的。