By enriching the set of acts deemed available at least as objects of assessment, the authors obtain a significant tightening of the linear lexicographic representation described in I. LaValle and P. Fishburn (1991). Under the state-independent assumption that every outcome is available in every state, each state must be either completely null or completely essential (rather than lexicographically essential), and the matrices characterizing subjective probabilities of the states must be square and lower triangular with positive diagonal entries. It follows that there are straightforward generalizations of real-valued-probability relationships such as Bayes' theorem. Even in the tighter case, the matrix probabilities cannot be reduced to scalar matrices or even fully diagonal matrices. Nevertheless, they are easy to work with and permit fully consequentialist decision analysis of problems in which preferences are non-Archimedean. Copyright 1992 by Kluwer Academic Publishers
