A note on the redundancy of an axiom in the Pattanaik-Peleg characterization of the lexicographic maximin extension (Q1059537)

\textit{P. K. Pattanaik} and \textit{B. Peleg} [ibid. 1, 113-122 (1984; Zbl 0549.90007)] 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).