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AbstractA theory of additive utilities is discussed for cases where the set X, on which an individual's preference‐indifference relation is defined, is a subset of the Cartesian product of n finite sets. A number of potential applications of additive utilities in decision making are presented.

AbstractThis article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment‐type constraints along with other constraints. Several unresolved questions of a number‐theoretic nature are mentioned at the conclusion of the article.

ABSTRACTThirty empirically assessed utility functions on changes in wealth or return on investment were examined for general features and susceptability to fits by linear, power, and exponential functions. Separate fits were made to below‐target data and above‐target data. The usual "target" was the no‐change point.The majority of below‐target functions were risk seeking; the majority of above‐target functions were risk averse; and the most common composite shape was convex‐concave, or risk seeking in losses and risk averse in gains. The least common composite was concave‐concave. Below‐target utility was generally steeper than above‐target utility with a median below‐to‐above slope ratio of about 4.8. The power and exponential fits were substantially better than the linear fits. Power functions gave the best fits in the majority of convex below‐target and concave above‐target cases, and exponential functions gave the best fits in the majority of concave below‐target and convex above‐target cases. Several implications of these results for decision making under risk are mentioned.

"Approval Voting" proposes a compelling way to elect some 500,000 officials in public elections. Under this system voters may vote for, or approve of, as many candidates as they like in multicandidate elections. Among the many benefits of approval voting are its propensity to elect the majority candidate (rather than the strongest minority candidate, as often occurs under plurality voting), its relative invulnerability to insincere or strategic voting, and - by offering voters the opportunity to influence election outcomes more equitably - a probable increase in voter turnout. Since