Rawls and Bentham reconciled

The paper deals with the characterization of a class of social welfare orderings. The social evaluation functions which represent these orderings are separable in the components of the ordered utility vector. The characterization is based on the Strong Pareto Property, Co-cardinality, Continuity and a new Independence Property. Since this class encompasses the utilitarian rule and since there are members of this family which almost coincide with the rules of rank dictatorship this family bridges the gap between pure utilitarianism and rank dictatorship.     

On games under expected utility with rank dependent probabilities

Expected utility with rank dependent probabilities is a generalization of expected utility. If such preference representations are used for the payoffs in the mixed extension of a finite game, Nash equilibrium may fail to exist. Set-valued solutions, however, do exist even for those more general utility functions. But some set-valued solutions may have certain conceptual shortcomings. The paper thus proposes a new set-valued solution concept, called fixed sets under the best reply correspondence. All set-valued solution concepts are robust to perturbations of the expected utility hypothesis.     

Utility Functions for Wealth

We specify all utility functions on wealth implied by four special conditions on preferences between risky prospects in four theories of utility, under the presumption that preference increases in wealth. The theories are von Neumann-Morgenstern expected utility (EU), rank dependent utility (RDU), weighted linear utility (WLU), and skew-symmetric bilinear utility (SSBU). The special conditions are a weak version of risk neutrality, Pfanzagl's consistency axiom, Bell's one-switch condition, and a contextual uncertainty condition. Previous research has identified the functional forms for utility of wealth for all four conditions under EU, and for risk neutrality and Pfanzagl's consistency axiom under WLU and SSBU. The functional forms for the other condition-theory combinations are derived in this paper.     

Comparative statics for rank-dependent expected utility theory

Recently, a number of generalizations of the expected utility (EU) model have been proposed. In order to make such generalizations useful, it is necessary that they should yield sharp comparative static results, like those obtained using EU theory. In this article, rank dependent expected utility (RDEU) theory, a generalization of EU theory based on the concept of probability weighting, is examined. A number of methods of extending results from EU to RDEU are considered. It is shown that a major class of comparative static results can be extended to the RDEU model, but not to the case of general smooth preferences. This is because RDEU maintains the separation between probabilities and utilities that is abandoned in the general case.     

Mean utility preserving increases in risk for state dependent utility functions

This paper defines the concept of a mean utility preserving spread across states (MUPSAS) for state dependent utility functions and analyzes the behavioural impact of shifts in the probability distribution of wealth across states such that overall mean utility is preserved. The main result provides an alternative way of ranking state dependent utility functions according to their degree of risk aversion (thus extending Kami's theorem of comparative risk aversion) and establishes a link between increases in risk and risk aversion for state dependent preferences. In a portfolio problem where preferences and the rate of return of the risky venture are state dependent, we find sufficient conditions to determine the impact of a MUPSAS on the optimal share of the portfolio invested in the risky asset.

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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.     

Lottery Dependent Utility: a Reexamination

In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. The goal of this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science.     

The Lovász Extension of Market Games

The multilinear extension of a cooperative game was introduced by Owen in 1972. In this contribution we study the Lovász extension for cooperative games by using the marginal worth vectors and the dividends. First, we prove a formula for the marginal worth vectors with respect to compatible orderings. Next, we consider the direct market generated by a game. This model of utility function, proposed by Shapley and Shubik in 1969, is the concave biconjugate extension of the game. Then we obtain the following characterization: The utility function of a market game is the Lovász extension of the game if and only if the market game is supermodular. Finally, we present some preliminary problems about the relationship between cooperative games and combinatorial optimization.     

Losers and losers: Some demographics of medical malpractice tort reforms

Our research examines how recent reforms have affected a key aspect of patients?? implicit insurance present in medical malpractice torts. Specifically, we estimate how non-economic damages caps affected pre-trial settlement speed and settlement amounts. Maximum entropy (most likely) quantile regressions emphasize that the post-reform settlement effects most informative for policy evaluation differ greatly from OLS (mean) estimates and clarify the conclusion emerging. In particular, the effect of the tort reform here can best be thought of as a 25% tax on the asset value of settlements that exempts settlements involving infants. The social welfare effects of tort reform are less clear than the asset reduction effects due to likely health state dependent utility.     

A characterization of the maximin rule in the context of voting

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule.     

Reference Wealth Effects in Sequential Choice

It is argued that in order to accommodate experimentally-observed choice patterns, it is not enough to model the utility function as being dependent on changes from a reference wealth point. Instead, individuals should be modeled as treating decisions as part of an identifiable sequence of decisions, and utility should be a function of reference wealth, income so far from the sequence, and payoffs from the current decision. The three-argument utility function allows for risk aversion over gains and risk seeking over losses for the first choice in the sequence, and for the house money and break-even effects in later decisions.     

Discounting health and money: New evidence using a more robust method

This study compares discounting for money and health in a field study. We applied the direct method, which measures discounting independent of utility, in a representative French sample, interviewed at home by professional interviewers. We found more discounting for money than for health. The median discount rates (6.5% for money and 2.2% for health) were close to market interest rates, suggesting that at the aggregate level the direct method solves the puzzle of unrealistically high discount rates typically observed in applied economics. Constant discounting fitted the data better than the hyperbolic discounting models that we considered. The substantial individual heterogeneity in discounting was correlated with age and occupation.     

Moment characterization of higher-order risk preferences

This article presents a characterization of higher-order risk preferences such as prudence or temperance in terms of statistical moments. Our results, which are generalizations of Roger (Theory Decis, 70(1):27–44, 2011) and Ekern (Econ Lett, 6(4), 329–333, 1980), give a better understanding of how higher-order risk preferences relate to skewness preference and kurtosis aversion. While they are not based on expected utility theory, an implication within that theory is that all commonly used utility functions exhibit skewness preference and kurtosis aversion.     

Stronger utility

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model.     

Poverty and Pediatric Palliative Care: What Can We Do?

It has been recognized that families of children with life-limiting health conditions struggle with significant financial demands, yet may not have awareness of resources available to them. Additionally, health care providers may not be aware of the socioeconomic needs of families they care for. This article describes a mixed-methods study examining the content validity and utility for health care providers of a poverty screening tool and companion resource guide for the pediatric palliative care population. The study found high relevance and validity of the tool. Significant barriers to implementing the screening tool in clinical practice were described by participants, including: concerns regarding time required, roles and responsibilities, and discomfort in asking about income. Implications for practice and suggestions for improving the tool are discussed. Screening and attention to the social determinants of health lie within the scope of practice of all health care providers. Social workers can play a leadership role in this work.     

Towards a more precise decision framework

The terms negative utility of gambling and risk aversion conflate three things: