This paper explores lexicographically additive representations of mult
i-attribute preferences on finite sets. Lexicographic additivity combi
nes a lexicographic feature with local value tradeoffs. Tradeoff struc
tures are governed by either transitive or nontransitive additive conj
oint measurement. Alternatives are locally traded off when they are cl
ose enough within threshold associated with a dominant subset of attri
butes.