Christian Klamler’s ”A distance measure for choice functions” [Social Choice and Welfare 30 (2008) 419–425]: a correction
指出Klamler关于选择函数距离度量的公理化结果存在反例,通过修改公理给出正确刻画,并发现其中一条公理是冗余的。
Abstract 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.