Abstract
An additive-across-states decomposition of lexicographic linear utility is easily obtained under a mild structural assumption concerning sufficient richness of acts in the domain of preference assessment, but the vectorial nature of lexicographic utility introduces two complexities absent in the real-valued case. First, the concept of state nullity becomes lexicographic rather than binary; and second, a standard construction for obtaining subjective probabilities from real-valued, state-dependent utilities produces matrices instead of nonnegative real numbers in the lexicographic setting.
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Lavalle, I.H., Fishburn, P.C. Lexicographic state-dependent subjective expected utility. J Risk Uncertainty 4, 251–269 (1991). https://doi.org/10.1007/BF00114156
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DOI: https://doi.org/10.1007/BF00114156