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An extensive choice over X is a function assigning to any subset S of X a possibly empty subset of S . Klamler (Soc Choice Welf 30:419–425, 2008) shows that the operation of symmetric difference induces a metric on the family of extensive choices over X , and this metric is characterized by five axioms –. We provide counterexamples to Klamler’s result, suggest a slight modification of axioms and to obtain a correct characterization, and finally observe that axiom is redundant.
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Carpentiere et al. (2024) studied this question.
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