Comment on the Kannai-Peleg impossibility theorem for extending orders

Recent work by Y. Kannai and B. Peleg shows that two appealing axioms for extending a linear order on a set of six or more elements to a weak order on the family of non-empty subsets of that set are mutually incompatible. This comment shows that a modest restriction of their monotonicity axiom is compatible for extension with a generalization of their other axiom provided that the linear order on the basic set is a well ordering.