A note on Marshallian and von Neumann-Morgenstern utility

The curvature of a decision maker's utility function is often used to measure his risk preference. In order to comprehensively describe an individual's decision making behaviour, however, it would also seem desirable to measure the gain in utility from an increase in wealth or income before accounting for risk. If a small increase in wealth leads to a large utility gain, then it could be said that the individual's aspiration to achieve the wealth increase would be high. This aspiration, however, may be more than offset by the risk involved in obtaining this extra wealth and the individual's attitude towards risk. In the following paper it is shown how the marginal utility of Marshall can be used in a measure of aspiration with this measure then combined with the usual measure of risk preference to explain the shape of any individuals utility curve. Using these measures, a general utility curve for all income or wealth classes is postulated.The author would like to thank Professor I. Horowitz for providing the inspiration that led to his note. Any errors are the responsibility of the author.     

A note on Savage's theorem with a finite number of states

This article gives a preference-based characterization of subjective expected utility for the general equilibrium model with a finite number of states. The characterization follows Savage (1954) as closely as possible but has to abandon his axiom (P6), atomlessness of events, since this requires an infinite state space. To introduce continuity we replace (P6) with a continuity assumption on the set of consequences and assume the preferences are smooth. Then we apply Savage's sure-thing principle and his state-independence axiom to get an additively separable utility representation. Finally, to separate subjective probabilities from basic tastes, we apply a new axiom, which states that for each pair of states the marginal rate of substitution is constant along the certainty line.     

A note on the prisoner's dilemma

This paper clarifies some basic concepts or assumptions of the prisoner's dilemma, asserts the independence between the two agentsA andB, and advocates the application of the dominance principle of decision theory to the prisoner's dilemma. It discusses several versions of the prisoner's dilemma, including the one-shot and repeated cases of a noncooperative game from a purely egoistic point of view. The main part of this paper, however, is a study of the problem from a moral point of view through a special decision-theoretic approach. Morality is taken into account by incorporating the utility of the feeling of moral satisfaction for the agent, as a part of the total utility for the agent, into the decision-theoretic model. In this way the problem will appear as a purely technical decision problem, and the conflicts between various assumptions, or the dilemma caused by the problem, will no longer exist. It is also pointed out that in a more general case, for some values of the coefficient of moralityk, dominance will not exist so that the dominance principle will not be applicable.     

A note on negativity bias and framing response asymmetry

An “unprocessed risk” is a collection of simple lotteries with a reduction-rule that describes the actual-payoff to the decision-maker as a function of realized lottery outcomes. Experiments reveal that the willingness to pay for unprocessed risks is consistently biased toward the payoff-level in the unprocessed representation. The “anchoring-to-frame” bias in cases of positive framing is significantly weaker than in cases of negative framing suggesting that rational “negativity bias” may reflect in asymmetric violations of rationality.     

A note on Abraham Lincoln in probabilityland

Abraham Lincoln's dictum that you may fool all of the people some of the time; and some of the people all of the time; but you can't fool all of the people all of the time, is interpreted in terms of a simple binomial model, and potential ambiguities in Lincoln's assertion are clarified.     

A note on Chichilnisky's social choice paradox

One of the main results in topological social choice states the non-existence of a continuous, anonymous, and unanimous aggregation rule on spheres. This note provides a proof based upon simple methods such as integration.     

A note on the permutationally convex games

If marginal worth vector of a game for an ordering is in the core, the game does not have to be a p.c. game.     

A note on the median voter theory and voter alienation

This note explores the consequences of movement of candidates toward the center of the political distribution. Uniform and normal distributions are considered. Movement toward the center of the political distribution can increase or decrease the number of votes received by a candidate. However, even if the candidate loses votes by such a move, as long as the distribution is denser in the center than in the tails, the candidate will benefit relative to his/her opponent. If both the candidate and his/her opponent move toward the center, the individual who makes the greater move benefits at the expense of the other individual.     

A note on manipulability of large voting schemes

A voting system is a rule which assigns to every possible combination of votes (by any number of individuals) an alternative. We define the notion of asymptotic nonmanipulability for voting systems, and prove that every representable positionalist voting system is asymptotically nonmanipulable. Various aspects of manipulation of large voting schemes and several examples are also discussed.     

A note on the two person exchange game

The two person exchange game is analysed using core theory, the Nash solution and the competitive equilibrium. It is shown for specific utility functions that relative to the other trader, the less wealthy trader does better under the Nash solution than he would under the competitive solution. Conversely, the trader with the lower initial utility level does better under the competitive solution than he would under the Nash solution. If traders have disparate initial endowments, it is argued that outcomes should be restricted to a reduced core containing the Nash and competitive solutions as endpoints.     

Remarks of a Polish praxiologist on the subject of a paper by C. Gutiérrez

Most theories of human action investigated primarily with respect to its efficiency, which came into existence during the last nearly 100 years (some of which have been christened by their authors praxeology or praxiology) are empirical ones. Prof. Gutiérrez' elegant critique of the extraordinary claim of praxeology to have an aprioristic character should be thus limited to v. Mises' (exceptional among other praxeologists) aprioristic approach. In any case that critique does not apply to the Polish school of Praxeology founded by T. Kotarbiski.     

Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly

This paper deals with the equilibria of games when the agents have multiple objectives and, therefore, their utilities cannot be represented by a single value, but by a vector containing the various dimensions of the utility. Our approach allows the incorporation of partial information about the preferences of the agents into the model, and permits the identification of the set of equilibria in accordance with this information. We also propose an additional conservative criterion which can be applied in this framework in order to predict the results of interaction. The potential application of the theoretical results is shown with an analysis of a mixed oligopoly in which the agents value additional objectives other than their own benefit. These objectives are related to social welfare and to the profit of the industry. The flexibility of our approach provides a general theoretical framework for the analysis of a wide range of strategic economic models.     

Violence: recent books on a not-so-recent epidemic

Violence, like the poor, may always be with us. Recent events, however, have italicized the ubiquity and importance of violence, and the difficulty of coming to terms with it. Although relatively few social scientists are experts in violence, they are often called upon to function in that capacity. Accordingly, a review of approaches to the topic seems most timely.