Criminal sanctions are usually public, stable and predictable. In contrast, the practices governing the determination of the probability of detection and conviction reinforce uncertainty. We invoke psychological insights to illustrate that criminals prefer a scheme in which the size of the sentence is uncertain while the probability of detection and conviction is certain. Consequently, the choice to increase certainty with respect to the size of the sentence and to decrease certainty with respect to the probability of detection and conviction can be justified on the grounds that such a scheme is disfavored by criminals and consequently has better deterrent effects.

This paper provides characterization theorems for preferences that can be represented by the minimum, the maximum, and the sum of components, or combinations of these forms. It contains a discussion of applications to social choice.

This paper assumes that in addition to the conventional (selfish) preferences over outcomes, players in a strategic environment have preferences over strategies. In the context of two-player games, it provides conditions under which a player's preferences over strategies can be represented as a weighted average of the individual's selfish payoffs and the selfish payoffs of the opponent. The weight one player places on the opponent's selfish utility depends on the opponent's behavior. In this way, the framework is rich enough to describe the behavior of individuals who repay kindness with kindness and meanness with meanness. The paper assumes that each player has an ordering over his opponent's strategies that describes the niceness of these strategies. It introduces a condition that insures that the weight on opponent's utility increases if and only if the opponent chooses a nicer strategy.

This paper studies a game-theoretic model in which players have preferences over their strategies. These preferences vary with the strategic context. The paper further assumes that each player has an ordering over an opponent's strategies that describes the niceness of these strategies. It introduces a condition that insures that the weight on an opponent's utility increases if and only if the opponent chooses a nicer strategy.

This paper assumes that in addition to conventional preferences over outcomes, players in a strategic environment have preferences over strategies. It provides conditions under which a player's preferences over strategies can be represented as a weighted average of the utility from outcomes of the individual and his opponents. The weight one player places on an opponent's utility from outcomes depends on the players' joint behavior. In this way, the framework is rich enough to describe the behavior of individuals who repay kindness with kindness and meanness with meanness. The paper identifies restrictions that the theory places on rational behavior. (C) 2006 Elsevier Inc. All rights reserved.