On the Utility Function Representability of Lexicographic Preferences

The paper examines the utility function representability of the lexicographic preferences over multiple attributes. A sufficient and necessary condition is provided: a lexicographic preference is utility function representable if and only if there is at most one attribute with uncountable levels and when such an attribute exists, it is the least important one. An auxiliary result of independent interest for general rational preferences is proved stating that the class of utility function representable sets is closed in countable unions under some mild condition.