Exponential Health Utility: A Characterization and Comments on a Paper by Happich and Mühlbacher.

In a recent paper Happich and Mühlbacher [Eur J Health Econom (2003) 4:292-294] proposed an axiom of constant absolute trade-off in life years, and studied the family of QALY models satisfying this axiom under expected utility and mutual utility independence between life years and health state. In this paper, we provide a complete characterization of the above-mentioned family of QALY models. This family should not be mistaken for the family of multiplicative expo-nential QALY models; in particular, it violates the zero-condition.

QALYs, Person Trade-Offs, and the Pareto Principle.

A considerable literature seems to argue the use of person trade-offs to estimate the quality-adjustment factor in Quality-Adjusted Life Years (QALY) models. A similar practise is followed by the WHO to estimate the disability weights used in calculation of Disability-Adjusted Life Years (DALY) for assessment of region- and disease-specific burden of disease. In this note we show that QALY (and DALY) models based on person trade-off scores generally violate the Pareto principle.person trade-off; QALY; DALY; Pareto principle; social welfare

Merging and Splitting in Cooperative Games: Some (Im-)Possibility Results

Solutions for cooperative games with side-payments can be manipulated by merging a coalition of players into a single player, or, conversely, splitting a player into a number of smaller players. This paper establishes some (im-)possibility results concerning merging- or splitting-proofness of core solutions of balanced and convex games.cooperative games; manipulation; Dutta-Ray solution

Preferences Between Continuous Streams of Events

Cost-benefit and health policy studies often model a consequence occurring over time as a continuous stream of events. Such a consequence is measured by the rates at which events occur or by the states that occur, and the value of the consequence is measured by an integral. This paper presents a foundation for such models. It defines conditions on preferences between consequences that are equivalent to an integral value function having a discounting function and an intertemporal equity function.discounting; equity; continuous time; value function; evaluation

Integral-Value Models for Outcomes over Continuous Time

Models of preferences between outcomes over continuous time are important for individual, corporate, and social decision making, e.g., medical treatment, infrastructure development, and environmental regulation. This paper presents a foundation for such models. It shows that conditions on preferences between real- or vector-valued outcomes over continuous time are satisfied if and only if the preferences are represented by a value function having an integral form.continuous time; discounting; ordinal utility scale; value function; integral

Multivariate Discrete First Order Stochastic Dominance

This paper characterizes the principle of first order stochastic dominance in a multivariate discrete setting. We show that a distribution f first order stochastic dominates distribution g if and only if f can be obtained from g by iteratively shifting density from one outcome to another that is better. For the bivariate case, we develop the theoretical basis for an algorithmic dominance test that is easy to implement.multidimensional first degree distributional dominance; robust poverty gap dominance; majorization; generalized equivalence result

Cardinal Scales for Public Health Evaluation

Policy studies often evaluate health for a population by summing the individuals’ health as measured by a scale that is ordinal or that depends on risk attitudes. We develop a method using a different type of preferences, called preference intensity or cardinal preferences, to construct scales that measure changes in health. The method is based on a social welfare model that relates preferences between changes in an individual’s health to preferences between changes in health for a population.public health evaluation; social welfare; preference intensity; health state

Forming and Dissolving Partnerships in Cooperative Game Situations

A group of players in a cooperative game are partners (e.g., as in the form of a union or a joint ownership) if the prospects for cooperation are restricted such that cooperation with players outside the partnership requires the accept of all the partners. The formation of such partnerships through binding agreements may change the game implying that players could have incentives to manipulate a game by forming or dissolving partnerships. The present paper seeks to explore the existence of allocation rules that are immune to this type of manipulation. An allocation rule that distributes the worth of the grand coalition among players, is called partnership formation-proof if it ensures that it is never jointly profitable for any group of players to form a partnership and partnership dissolution-proof if no group can ever profit from dissolving a partnership. The paper provides results on the existence of such allocation rules for general classes of games as well as more specific results concerning well known allocation rules.cooperative games; partnerships; partnership formation-proof; partnership dissolution-proof

Discounting Models for Outcomes over Continuous Time

Events that occur over a period of time can be described either as sequences of outcomes at discrete times or as functions of outcomes in an interval of time. This paper presents discounting models for events of the latter type. Conditions on preferences are shown to be satisfied if and only if the preferences are represented by a function that is an integral of a discounting function times a scale defined on outcomes at instants of time.continuous time; integral discounting; integral value or utility function

Inequality Preserving Rationing

The present paper considers rationing problems interpreted as e.g. bankruptcy problems or taxation problems. We demonstrate that among the continuous and order-preserving rationing methods, theproportional method is the only rationing method that preserves inequality in both gains and losses.rationing; inequality preservation; taxation; manipulation; proportional method