A note on the redundancy of an axiom in the Pattanaik-Peleg characterization of the lexicographic maximin extension

P. K. Pattanaik and B. Peleg have provided an axiomatic characterization of the lexicographic maximin extension of an ordering over a finite set to an ordering over the set of all non-empty subsets of that set. This note shows that one of their axioms, namely the Union axiom, is redundant, thus obtaining a more economical characterization composed of the remaining four axioms (which are independent by virtue of the examples given by Pattanaik and Peleg).