Tokyo University of Science, Noda, Japan.
PLoS One. 2024 Jan 2;19(1):e0296351. doi: 10.1371/journal.pone.0296351. eCollection 2024.
This paper proposes a new class of efficient and equitable social welfare orderings, a generalized leximin rule that includes rank-weighted utilitarianism, leximin, and their lexicographic compositions. While the famous Deschamps and Gevers' joint characterization theorem shows that a Paretian, anonymous, separable social welfare ordering must be either weak utilitarianism, leximin, or leximax under the assumption of cardinal full comparability, this study provides a new joint characterization theorem in which imposing rank-separability, instead of separability, enables acceptable social welfare ordering to be the generalized leximin rule. This result is proven by an intuitive and easy-to-understand method, which also helps show the mechanism by which a class of Paretian, anonymous, and separable social welfare orderings is limited to weak utilitarianism and leximin.
本文提出了一类新的有效且公平的社会福利排序，即广义的 Leximin 规则，它包含了等级加权功利主义、Leximin 和它们的词典序组合。虽然著名的 Deschamps 和 Gevers 的联合特征定理表明，在基数完全可比较性的假设下，一个帕累托、匿名、可分离的社会福利排序必须是弱功利主义、Leximin 或 Leximax，但本研究提供了一个新的联合特征定理，其中施加等级可分离性，而不是可分离性，使得可接受的社会福利排序成为广义的 Leximin 规则。这一结果是通过一种直观且易于理解的方法证明的，该方法还有助于展示一类帕累托、匿名和可分离的社会福利排序仅限于弱功利主义和 Leximin 的机制。
