This paper proves a rigidity theorem characterizing the Gini-type Lorenz-area ordering under general decision-theoretic constraints together with weak Lorenz dominance, thereby resolving the characterization problem pursued in this line of research on egalitarianism. This does not, of course, bring the broader inquiry to an end. In a certain sense, it may instead mark a step beyond the infancy of our attempt to connect social choice theory, welfare economics, and formal moral philosophy through a common mathematical language. The main proof strategy was originally obtained by the author's own hand, though 5.6sol and Astra could effortlessly reproduce it without any additional hint.
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