Cardinality versus Ordinality: A Suggested Compromise
通过将效用函数集合作为原始概念，定义了一个衡量效用函数测量要求的排序，发现基数与序数假设之间存在中间层次，并论证了凹性假设可作为两者之间的折中，同时指出Arrow-Koopmans解释实际上依赖基数测量类。
By taking sets of utility functions as primitive, we define an ordering over assumptions on utility functions that gauges their measurement requirements. Cardinal and ordinal assumptions constitute two levels of measurability, but other assumptions lie between these extremes. We apply the ordering to explanations of why preferences should be convex. The assumption that utility is concave qualifies as a compromise between cardinality and ordinality, while the Arrow-Koopmans explanation, supposedly an ordinal theory, relies on utilities in the cardinal measurement class. In social choice theory, a concavity compromise between ordinality and cardinality is also possible and rationalizes the core utilitarian policies.