Christian Klamler’s ”A distance measure for choice functions” [Social Choice and Welfare 30 (2008) 419–425]: a correction

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 A1–A5. We provide counterexamples to Klamler’s result, suggest a slight modification of axioms A4 and A5 to obtain a correct characterization, and finally observe that axiom A4 is redundant.