Cardinal Utility Research Articles

Epsilon-Nash implementation

This paper provides necessary and sufficient conditions for a social choice correspondence to be implementable via epsilon-Nash equilibrium when agents' preferences can be represented by cardinal utilities. Our results also display robustness of Maskin's seminal result on Nash implementation.

Introduction to the Conference on Law and Happiness

Economists who make normative proposals traditionally assume that policy should advance “efficiency,” usually in the Kaldor or Hicks sense, which defines efficiency in terms of whether the project’s winners can hypothetically compensate the project’s losers. A compensation criterion is used because it can be based on ordinal utilities, which puts a smaller information burden on the decision maker than cardinal utilities do. Ordinal utilities, unlike cardinal utilities, can (in principle) be inferred from observations of consumer behavior. By seeing how people trade off goods, willingness-to-pay (or willingness-to-accept) amounts can be derived and summed, so that alternative policy outcomes can be easily compared. This approach has received a great deal of criticism over the decades, but it has survived mainly because no alternative method has commanded widespread agreement. In recent years, however, a small group of economists and psychologists have argued that an alternative method is available. This method, often called the “happiness approach,” relies on surveys that ask people to rate their happiness on a scale. Econometric analysis then finds correlations between ratings on the scale and various characteristics or experiences of the survey respondents—wealth, income, family relationships, and so forth. Though still regarded with skepticism in many quarters, the happiness approach has scored some notable successes. The various factors that are correlated with happiness appear to be robust: they recur in different surveys and are correlated

Risk Attitudes: Cardinal Utility Theory (Actitudes Hacia El Riesgo: Teoría De La Utilidad Cardinal. Slides)

This is a teaching material (slides) accompanying the book in Spanish Decisiones Empresariales bajo Riesgo e Incertidumbre (Managerial Decision Making under Risk and Uncertainty). In this material we present the basic ideas of the cardinal utility theory, it uses, applications and limitations.

Fuzzy set solutions for optimal maintenance strategy selection

Selecting optimal maintenance strategy under fuzzy environment is not a trivial task. This paper presents an illustration of multi-criteria maintenance strategy selection under fuzzy environment. Three most common maintenance strategies and eight maintenance decision criteria have been considered and most appropriate/ optimal strategy selection process is demonstrated using three different techniques/ methods. Fuzzy linguistic terms have been used to rate and weigh the maintenance decision criteria. Linguistic terms/ variables are represented by triangular fuzzy sets/ number and fuzzy set operations have been carried out using α– cut method. The basic technique used is rating and ranking method using fuzzy set theory wherein ratings of alternatives/ strategies is determined first and then ranking is carried out to decide the optimal strategy. Other methods i.e. ranking fuzzy sets using cardinal utilities and by maximizing and minimizing sets are also established to confirm our choice of optimal maintenance strategy.

On Ordinal Utility, Cardinal Utility and Random Utility

Though the Random Utility Model (RUM) was conceived entirely in terms of ordinal utility, the apparatus through which it is widely practised exhibits properties of cardinal utility. The adoption of cardinal utility as a working operation of ordinal is perfectly valid, provided interpretations drawn from that operation remain faithful to ordinal utility. The article considers whether the latter requirement holds true for several measurements commonly derived from RUM. In particular it is found that measurements of consumer surplus change may depart from ordinal utility, and exploit the cardinality inherent in the practical apparatus.

Risk Attitudes (Actitudes Hacia El Riesgo)

This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers. In this fifth chapter we deal with the attitudes toward risk. We present the classical cardinal utility theory and illustrate the three well know cases of attitudes toward risk: averse toward risk, indifferent toward risk and propense toward risk. We also present the concept of certainty equivalent. We mention the limitations of the cardinal utility theory. We include a short reference to the prospect theory by Kahneman and Tversky. We illustrate the concept of risk aversion with a real life lottery example.

Perspectives from the Happiness Literature and the Role of New Instruments for Policy Analysis

After having been ignored for a long time by economists, happiness is becoming an object of serious research in 21st century economics. In Section 2 we sketch the present status of happiness economics. In Section 3 we consider the practical applicability of happiness economics, retaining the assumption of ordinal individual utilities. In Section 4 we introduce a cardinal utility concept, which seems to us the natural consequence of the happiness economics methodology. In Section 5 we sketch how this approach can lead to a normative approach to policy problems that is admissible from a positivist point of view. Section 6 concludes.

An analytical framework for aggregating multiattribute utility functions

This paper proposes a procedure for aggregating individual cardinal utility functions into a social utility function that represents the preferences of all the individuals as a whole. The procedure is non-interactive and is based upon the determination of the utility consensus values. This is accomplished by minimizing a distance function model that is transformed into an Archimedean goal programming problem. The procedure is applied to a general group multilinear utility function.

Reconciling introspective utility with revealed preference: Experimental arguments based on prospect theory

In an experiment, choice-based (revealed-preference) utility of money is derived from choices under risk, and choiceless (non-revealed-preference) utility from introspective strength-of-preference judgments. The well-known inconsistencies of risky utility under expected utility are resolved under prospect theory, yielding one consistent cardinal utility index for risky choice. Remarkably, however, this cardinal index also agrees well with the choiceless utilities, suggesting a relation between a choice-based and a choiceless concept. Such a relation implies that introspective judgments can provide useful data for economics, and can reinforce the revealed-preference paradigm. This finding sheds new light on the classical debate on ordinal versus cardinal utility.

Neuroeconomics: Cardinal Utility in the Orbitofrontal Cortex?

Modern economics no longer uses the concept of cardinal utility, which describes the value of a good independently of a comparison with another good. New electrophysiological recordings in primates performing economic choices suggest a neurological substrate for cardinal utility, a finding that economists should perhaps take note of.

Strategy-proof Cardinal Decision Schemes

This paper analyses strategy-proof mechanisms or decision schemes which map profiles of cardinal utility functions to lotteries over a finite set of outcomes. We provide a new proof of Hylland’s theorem which shows that the only strategy-proof cardinal decision scheme satisfying a weak unanimity property is the random dictatorship. Our proof technique assumes a framework where individuals can discern utility differences only if the difference is at least some fixed number which we call the grid size. We also prove a limit random dictatorship result which shows that any sequence of strategy-proof and unanimous decision schemes defined on a sequence of decreasing grid sizes approaching zero must converge to a random dictatorship.

Decision Making Under Risk and Uncertainty (Slides in Spanish)

This is a course material (slides in pdf format) from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversion. Para la valoracion financiera de proyectos y empresas. Chapter 12 studies the problem of making decisions under risk and uncertainty. We present basic ideas on sensitivity analysis for one and several variables, game theory, decision trees, cardinal utility theory and Montecarlo simulation. We include some new subjects such as the Analytical Hierarchical Process, AHP and the Analytic Network Process, ANP, methods Developer by professor Thomas L. Saaty and a very short introduction to financial and real options.

12 Decision Making Under Uncertainty

This is a course material from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversion. Para la valoracion financiera de proyectos y empresas. Chapter 12 studies the problem of making decisions under risk and uncertainty. We present basic ideas on sensitivity analysis for one and several variables, game theory, decision trees, cardinal utility theory and Montecarlo simulation. We include some new subjects such as the Analytical Hierarchical Process, AHP and the Analytic Network Process, ANP, methods Developer by professor Thomas L. Saaty and a very short introduction to financial and real options.

Strength of preference and cardinal utility

This paper provides simpler and more general preference foundations for difference representations than known before and shows how to obtain cardinal utility from those difference representations. In addition, this paper unifies all earlier derivations of cardinal utility by showing that they are implied as direct corollaries.

A contribution to duality theory, applied to the measurement of risk aversion

This paper determines the precise connection between the curvature properties of an objective function and the ray-curvature properties of its dual. When the objective function is interpreted as a Bernoulli or cardinal utility function, our results characterize the relationship between an agent’s attitude towards income risks and her attitude towards risks in the underlying consumption space. We obtain these results by developing and applying a number of representation theorems for concave functions.

Measurement theory and the foundations of utilitarianism

This article reconsiders the Harsanyi–Sen debate concerning whether Harsanyi is justified in interpreting his Aggregation and Impartial Observer Theorems as providing axiomatizations of utilitarianism. Sen's criticism and its formalization by Weymark are based on the claim that von Neumann–Morgenstern utility theory is ordinal, whereas Harsanyi's utilitarian conclusions require cardinal utility. Proposals for overcoming Sen's objection that appeal to formal measurement theory are considered. It is argued that one of these proposals due to Broome and Risse rightly points to a feature of expected utility theory that was ignored by Sen and Weymark, but that this proposal does not provide a normatively compelling justification for cardinal utility. The other proposal due to Broome is shown to make use of a strength of preference relation in addition to the axioms of expected utility theory.

Representation of subjective preferences under ambiguity

The objective of this paper is to show how potentially incomplete preferences of a decision maker (DM) on acts can be modelled formally in a subjective ambiguity perspective. We identify acts as functions from a state space Ω to bounded support (finitely additive) probabilities over a set X of prizes. Then, we characterize preferences over equibounded acts a which have a numerical representation by the family of functionals { J π ( a ) = ∫ Ω [ ∫ X u ( x ) a ( ω ) ( dx ) ] π ( d ω ) ; π ∈ Π } , where u is a cardinal utility on X (representing the risk attitude of the DM) and Π is a unique pointwise closed convex set of probabilities on all events in Ω (representing the ambiguity perceived by the DM). To this end, in addition to the usual independence and continuity assumptions, we add completeness and dominance for preferences restricted to constant acts; moreover, we consider two other properties (subjective monotonicity and coherence) related with the preferences of a DM who is not able, owing to his partial knowledge, to evaluate any event in Ω .

A simple axiomatization of risk-averse expected utility

An agent's preferences exhibit risk aversion with respect to some probabilities of states of the world if she prefers deterministic outcome equal to the expected value of a state-contingent outcome under these probabilities to the state-contingent outcome itself. We show that if preferences exhibit risk aversion with respect to some probabilities and satisfy the independence axiom (sure thing principle), then they have an expected utility representation with respect to these probabilities. Since the independence axiom is necessary and sufficient for state-separable utility representation [Debreu, G., 1959. Topological methods in cardinal utility theory. In: Arrow, K., Karlin, S., Suppes, P. (Eds.), Mathematical Methods in Social Sciences. Standford University Press], our result shows that, given separable utility representation, expected utility follows from risk aversion.

A model for ordinally constructing additive objective functions

We investigate a method for constructing piecewise-linear approximations of an additive (called also separable) objective function in n target variables from a few indifference points in two-dimensional planes. It is shown that (a) the data used by the method are ordinal, simplest, and minimal; (b) the limit ordinal preference is independent of the cardinal utility scale used in intermediate computations, since the accuracy of the approximations is estimated in the Hausdorff metric on the space of binary relations. The method is illustrated with an example of constructing an additive objective function of German economic policy in four target variables: Inflation, Unemployment, GNP Growth, and Increase in Public Debt. We provide some modifications of the model aimed at user's convenience.

Petrohradský paradox a kardinální funkce užitku

The St Petersburg paradox could be used as an extreme demonstration of the utility function cardinalisation in case of stochastic utility. In this article we reassume the von Neumann and Mongernstern explanation to this paradox based on the risk aversion expressed by the strict concavity of the expected utility function. We suggest the utility function derived from the Pareto distribution of the probability of downfall of the subject in danger. Our cardinal utility function is based on the economically reasonable economic assumption. In contrast to the other often used cardinal utility functions it does not need the specification of its parameters ad hoc. Other advantage of our utility function is its explanation of the difference in decision making of different "players" in the St Petersburg casino, based on their wealth (including the explanation of the situational risk seeking behaviour of players under the boundary of survival).