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1 Introduction -- 2 Linear Utility on Mixture Sets -- 3 Expected Utility for Probability Measures -- 4 Lexicographic Quasilinear Utility -- 5 Linear Utility for Partially Ordered Preferences -- 6 Linear Utilities on Product Sets -- 7 Multilinear Utility on Products of Mixture Sets -- 8 Multilinear Utility for Probability Measures -- 9 Subjective Linear Utility on Products Of Mixture Sets -- 10 Subjective Expected Utility for Arbitrary State Sets -- 11 Subjective Linear Utility for Partially Ordered Preferences -- 12 Subjective Linear Utility with Conditional Preference Comparisons -- References.

AbstractA self‐reflecting signed order is a preference relation that compares relative likes and dislikes for items in a set X by jointly ordering X and a disjoint copy of X. If you would like Jones but not Smith appointed to a committee, and also think it more important to exclude Smith than include Jones, your self‐reflecting signed order records this information. We review basic representational theory for signed orders, then examine them when X is multiattributed. Axioms for additive measurement of multiattribute self‐reflecting signed orders are specified for several X‐structures.