Value superiority

Abstract

Value superiority encompasses two distinct non-Archimedean relations: strong superiority, where any amount of a higher good outranks any amount of a lower good, and weak superiority, where a sufficient amount of a higher good outranks any amount of a lower good. These relations are frequently invoked in welfare aggregation and population ethics to circumvent the Repugnant Conclusion and resolve intrapersonal value trade-offs. While strong superiority between the endpoints of a finite decreasing sequence does not logically necessitate strong superiority between adjacent elements, this flexibility is lost if the betterness ordering satisfies the condition of independence. Under such a condition, weak superiority collapses into strong superiority, and abrupt breaks in value become unavoidable. Conversely, weak superiority is shown to be a strict weak order; if it holds between the first and last elements of a finite sequence, it must necessarily obtain between at least one pair of adjacent elements. This finding implies a dilemma for value theory: one must either reject the existence of superiorities or concede that weak superiority can exist between goods that differ only marginally. The structural features of these relations demonstrate that superiority does not require infinite value differences but does necessitate the rejection of value additivity and independent contributive value. – AI-generated abstract.