Measure of Morality: A Mathematical Theory of Egalitarian Ethics

[2503.00039] Measure of Morality: A Mathematical Theory of Egalitarian Ethics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Economics > General Economics arXiv:2503.00039 (econ) [Submitted on 25 Feb 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: Measure of Morality: A Mathematical Theory of Egalitarian Ethics Authors: Shuang Wei View a PDF of the paper titled Measure of Morality: A Mathematical Theory of Egalitarian Ethics, by Shuang Wei View PDF HTML (experimental) Abstract: This paper develops a rigorous mathematical framework for egalitarian ethics by integrating formal tools from economics and mathematics. We motivate the formalism by investigating the limitations of conventional informal approaches by constructing examples such as probabilistic variant of the trolley dilemma and comparisons of unequal distributions. Our formal model, based on canonical welfare economics, simultaneously accounts for total utility and the distribution of outcomes. The analysis reveals deficiencies in traditional statistical measures and establishes impossibility theorems for rank-weighted approaches. We derive representation theorems that axiomatize key inequality measures including the Gini coefficient and a generalized Atkinson index, providing a coherent, axiomatic foundation for normative philosophy. Comments: Fix the errors in the proofs of the last version, and also add more counterexamples to the previously established results in the literature Subjects: General Economics (econ.GN) Cite as: arXiv:2503.00039 [econ.GN] (or arXiv:2503.00039v2 [econ.GN] for this version) https://doi.org/10.48550/arXiv.2503.00039 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shuang Wei [ view email ] [v1] Tue, 25 Feb 2025 10:00:43 UTC (30 KB) [v2] Sat, 11 Apr 2026 07:11:51 UTC (107 KB) Full-text links: Access Paper: View a PDF of the paper titled Measure of Morality: A Mathematical Theory of Egalitarian Ethics, by Shuang Wei View PDF HTML (experimental) TeX Source view license Current browse context: econ.GN < prev | next > new | recent | 2025-03 Change to browse by: econ q-fin q-fin.EC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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