A reference-dependent choice function is a generalization of a standard choice function where chosen alternatives may depend on a reference alternative in addition to the set of feasible options. Such a function is non-deteriorating if there exists an ordering over the universal set of...

Consistency of a binary relation requires any preference cycle to involve indifference only. It has been shown that consistency is necessary and sufficient for the existence of an ordering extension of a binary relation. It is therefore of interest to examine the rationalizability of choice...