We axiomatically define a cardinal social inefficiency function, which, given a set of alternatives and individuals' vNM preferences over the alternatives, assigns a unique number -- the social inefficiency -- to each alternative. These numbers -- and not only their order -- are uniquely defined by our axioms despite no exogenously given interpersonal comparison, outside option, or disagreement point. We interpret these numbers as per capita losses in endogenously normalized utility. We apply our social inefficiency function to a setting in which interpersonal comparison is notoriously hard to justify -- object allocation without money -- leveraging techniques from computer science to prove an approximate-efficiency result for the Random Serial Dictatorship mechanism.

翻译：我们通过公理化方法定义了一个基数社会无效率函数。给定一组备选方案以及个体对这些方案的冯·诺依曼-摩根斯坦偏好，该函数为每个备选方案分配一个唯一数值——即社会无效率值。尽管没有外生给定的人际比较、外部选项或分歧点，这些数值（而不仅仅是其排序）由我们的公理唯一确定。我们将这些数值解释为内生标准化效用的人均损失。我们将社会无效率函数应用于一个众所周知难以论证人际比较的设定——无货币条件下的物品分配，并借助计算机科学技术证明了随机序列独裁机制的一个近似效率结果。