Note on lexicographic-order preservation and stochastic dominance

This note concerns two issues left unresolved in our study of lexicographic-order preservation and stochastic dominance in settings where preferences are represented by utility vectors, ordered lexicographically, and judgements emerge as matrices that premultiply utility vectors in expected utility sums. First, a generalization of the ‘Conjecture Σ’, which implied transitivity of a stochastic dominance relation under non-vacuous resolution-level information, is proved. Second, this paper comments on using resolution-level information in higher as well as in first degree stochastic dominanace analysis.