A characterization of lexicographic preferences

This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: a weaker notion of continuity called 'mild continuity' (strict preference order between any two alternatives that are different with respect to every attribute is preserved around their small neighborhoods) and an 'unhappy set' (any alternative outside such a set is preferred to all alternatives inside). Three key aspects of our characterization are: (i) use of continuity arguments, (ii) the stepwise approach of looking at two attributes at a time and (iii) in contrast with the previous literature, we do not impose noncompensation on the preference and consider an alternative weaker condition.