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.     

Linear Aggregation of SSB Utility Functionals

A necessary and sufficient condition for linear aggregation of SSB utility functionals is presented. Harsanyi's social aggregation theorem for von Neumann–Morgenstern utility functions is shown to be a corollary to this result. Two generalizations of Fishburn and Gehrlein's conditional linear aggregation theorem for SSB utility functionals are also established.     

Characteristic properties of FPTP systems

In this article, we model FPTP systems as social preference rules and give two characterizations. We show that a social preference rule is an FPTP system if, and only if, it satisfies the axioms of subset consistency, district consistency, subset cancellation, and district cancellation. The second characterization consists of the axioms of subset consistency, subset anonymity, neutrality, topsonlyness, Pareto optimality, district consistency and district cancellation. The characterizations give us an opportunity to compare the characteristic properties of FPTP systems to the characteristic properties that we found for list systems of proportional representation (list PR systems) in Hout et al. (Social Choice and Welfare, 27:459–475, 2006), where we modelled those systems also as social preference rules. We find that consistency and anonymity distinguish list PR systems from FPTP systems. On the other hand, it is district cancellation that distinguishes FPTP systems from list PR systems.     

Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.     

Bargaining Solutions as Social Compromises

A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized.     

How to combine pareto optimality with liberty considerations

I argue that the liberty condition of Sen's important impossibility of a Paretian liberal result is not a condition that liberals (or libertarians) would accept. The problem is that an appropriate liberty condition must be formulated in terms of consent - not in terms of preference. To formulate an adequate condition the framework needs to expand from collective choice rules (which only take information about preferences as input) to rights-based social choice rules (which also take as input information about which options have been consented to and which would violate someone's rights). I formulate a more adequate liberty condition based on the notion of consent that is acceptable to liberals, and then show that Pareto optimality is incompatible even with that condition. I then show how the liberty condition can be weakened in a plausible manner, and describe an interesting class of theories - rights-based Paretian theories - that satisfy the Pareto optimality requirement while being sensitive to liberty considerations.     

The arguments of utility: Preference reversals in expected utility of income models

There is a debate in the literature about the arguments of utility in expected utility theory. Some implicitly assume utility is defined on final wealth whereas others argue it may be defined on initial wealth and income separately. I argue that making income and wealth separate arguments of utility has important implications that may not be widely recognized. A framework is presented that allows the unified treatment of expected utility models and anomalies. I show that expected utility of income models can predict framing induced preference reversals, a willingness to pay-willingness to accept gap for lotteries, and choice-value preference reversals. The main contribution is a theorem. It is proved that for all utility functions where initial wealth and income enter separately, either there will be preference reversals or preferences can be represented by a utility function defined on final wealth alone.     

Social Structure,Economic Performance and Pareto Optimality

This paper shows that, if the performance of the economy is independent of the identities of individuals, then many welfare criteria yield sets of optimal social states that are equal to the Pareto optimal set. This result is proved for income distributions and extended to more general social choice problems. If the independence condition holds, then the set of optimal states is invariant to the adoption of an anonymity axiom, and to the utility information available.     

The impossibility of the Paretian liberal and its relevance to welfare economics

The purpose of this study is to analyse the implications of Sen's impossibility result, the liberal paradox, for orthodox welfare economics. Because the rather special format of social choice theory makes it a little difficult to be sure of the relevance of this result, the whole dilemma is posed here in terms of a rather informal analysis of information al patterns.On the one hand, it is argued that the traditional approach to welfare economics, including both utilitarianism and Paretian ordinalism, contains severe informational constraints eliminating the use of all kinds of independent non-utility information in the social evaluation process. This property, called welfarism, is also present in the weak Pareto principle, which conflicts with even minimal requirements of personal liberty according to Sen's result.On the other hand, it is argued that there is in fact little to be resolved in this problem in spite of several attempts to circumvent the conflict. These studies are argued to be mainly ad hoc solutions to the formal problem and relevant only to the extent they indicate how severe restrictions are needed to avoid the paradox. The analogy with the prisoner's dilemma does not work either. Since liberal values are intrinsically non-welfaristic, the liberal paradox can be interpreted as only one, but a rather powerful, example of the informational deficiency of the orthodox approach.Finally, it is argued that the liberal paradox has striking implications for both the concept of preference and social optimum as well as empirical research on social welfare. This means that if the impossibility is to be taken seriously we need to revalue both the status of utility information and the role of the Pareto principle in social welfare analysis.The author is grateful to Professor Amartya Sen and Matti Tuomala for helpful comments and suggestions.     

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.     

Ordered sum and tensor product of linear utility structures

Measurement-theoretic behavior of the category of social utility models is studied in terms of ordered sums and tensor products of mixture spaces. Necessary and sufficient conditions are given for the existence of individual utility functions and a social utility function (being a weighted average, and in another case a product, of the individual utilities) in terms of individual and social preference rankings.Part of the research presented here was supported by the NSF Grant GS-2936.I am deeply indebted to Richard C. Jeffrey for his stimulation and advice, and to Duncan Luce for many valuable discussions on related topics of measurement theory.     

For whom does social comparison induce risk-taking?

A ‘bonus culture’ among financial traders has been blamed for the excessive risk-taking in the run-up to the latest financial crisis. I show that when individuals are more social gain seeking than social loss averse (i.e. gloating is stronger than envy), social comparison predicts more risk-taking as well as a preference for negatively correlated gambles. Testing these two joint propositions in a laboratory experiment, I find that preference for positively or negatively correlated outcomes is highly correlated with risk-taking in a social risky investment task. While only a third of subjects prefer negatively correlated outcomes in a peer comparison setting, in line with relatively stronger social gain seeking, those subjects invest on average 50 % more in a risky gamble in their peer comparison setting than a reference group that made the same decision in an isolated individual setting. Subjects with a preference for positively correlated outcomes, in line with relatively stronger social loss aversion, do not show a higher propensity to invest in a risky gamble compared to the individual reference group.     

Multiple motives of pro-social behavior: evidence from the solidarity game

The article analyses experimental “solidarity games” with two benefactors and one beneficiary. Depending on their motive for giving—e.g., warm glow, altruism, or guilt—the benefactors’ response functions are either constant, decreasing, or increasing. If motives interact, or if envy is a concern, then more complex (unimodal) shapes may emerge. Controlling for random utility perturbations, we determine which and how many motives affect individual decision making. The main findings are that the motives of about 75% of the subjects can be identified fairly sharply, that all of the motives discussed in the literature co-exist in the population, and that for any given individual no more than two motives (out of six motives considered overall) are identified. We conclude that a unifying motive for solidarity cannot be derived even when we allow for individually heterogeneous parameterization: different subjects give for different reasons and all existing social preference theories are partially correct.     

Intradimensional Single-Peakedness and the Multidimensional Arrow Problem

Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an impossibility theorem, highlighting not only the threat of dictatorship of a single individual, but also the threat of dominance of a single dimension. In particular, even if preferences are single-peaked across individuals within each dimension – a situation called intradimensional single-peakedness – any aggregation procedure satisfying Arrow-type conditions will make one dimension dominant. I introduce lexicographic hierarchies of dimensions as a class of possible aggregation procedures under intradimensional single-peakedness. The interpretation of the results is discussed.     

Pareto utility

In searching for an appropriate utility function in the expected utility framework, we formulate four properties that we want the utility function to satisfy. We conduct a search for such a function, and we identify Pareto utility as a function satisfying all four desired properties. Pareto utility is a flexible yet simple and parsimonious two-parameter family. It exhibits decreasing absolute risk aversion and increasing but bounded relative risk aversion. It is applicable irrespective of the probability distribution relevant to the prospect to be evaluated. Pareto utility is therefore particularly suited for catastrophic risk analysis. A new and related class of generalized exponential (gexpo) utility functions is also studied. This class is particularly relevant in situations where absolute risk tolerance is thought to be concave rather than linear.     

On the definition of risk aversion

Two definitions of risk aversion have recently been proposed for non-expected utility theories of choice under uncertainty: the former refers the measure of risk aversion (Montesano 1985, 1986 and 1988) directly to the risk premium (i.e. to the difference between the expected value of the action under consideration and its certainty equivalent); the latter defines risk aversion as a decreasing preference for an increasing risk (introduced as mean preserving spreads) (Chew, Karni and Safra 1987, Machina 1987, Röell 1987, Yaari 1987).When the von Neumann-Morgenstern utility function exists both these definitions indicate an agent as a risk averter if his or her utility function is concave. Consequently, the two definitions are equivalent. However, they are no longer equivalent when the von Neumann-Morgenstern utility function does not exist and a non-expected utility theory is assumed. Examples can be given which show how the risk aversion of the one definition can coexist with the risk attraction of the other. Indeed the two definitions consider two different questions: the risk premium definition specifically concerns risk aversion, while the mean preserving spreads definition concerns the increasing (with risk) risk aversion.The mean preserving spreads definition of risk aversion, i.e. the increasing (with risk) risk aversion, requires a special kind of concavity for the preference function (that the derivatives with respect to probabilities are concave in the respective consequences). The risk premium definition of local risk aversion requires that the probability distribution dominates on the average the distribution of the derivatives of the preference function with respect to consequences. Besides, when the local measure of the first order is zero, there is risk aversion according to the measure of the second order if the preference function is concave with respect to consequences.Yaari's (1969) measure of risk aversion is closely linked to the r.p. measure of the second order. Its sign does not indicate risk aversion (if positive) or attraction (if negative) when the measure of the first order is not zero (i.e., in Yaari's language, when subjective odds differ from the market odds).     

Bare preference and interpersonal utility comparisons

From time to time it has been proposed to use just noticeable preference intervals as standard intervals upon which to base interpersonal utility comparisons. Such proposals have met with a number of difficulties due especially to the discovery that such intervals are difficult to take as representing equal differences in utility even for one individual.In this paper I suggest conditions upon individual utility functions which, if satisfied, would make such bare preference intervals useful as a basis for interpersonal utility comparisons even if the intervals are not interpreted as representing equal utility differences for any single individual.     

The real foundations of the alleged errors in Allais' Impossibility Theorem: Unceasingly repeated errors or contradictions of mark machina

1.-The Impossibility Theorem rests on five fundamental properties. On each of them Machina has confirmed his agreement over and over again between 1984 and 1986. The proof of the Impossibility Theorem is mathematically and rigorously correct.2.- The alleged Machina's demonstration of the Allais' two errorsis indeed only grounded on a series of errors and it isin total contradiction with the interpretationsexplicitly given by Machina from 1982 to 1986 of his local utility theory in the discrete case, especially in his letters.3.1 In fact one cannot but ask if Machina really understands the meaning and the implications of his formulation of the local utility, and what is really in question.In any case it would he without any doubt eminently desirable that before hastily concluding that the others are making mistakes, Machina should begin by seriously asking himself if he is not himself into error.     

Buying and selling price for risky lotteries and expected utility theory with gambling wealth

I analyze two expected utility models which abandon the consequentialist assumption of terminal wealth positions. In the expected utility of gambling wealth model, in which initial wealth is allowed to be small, I show that a large WTA/WTP gap is possible and the (Rabin in Econometrica, 68(5), 1281–1292, 2000) paradox may be resolved. Within the same model the classical preference reversal which allows arbitrage is not possible, whereas preference reversal (involving buying prices in place of selling prices), which does not allow arbitrage, is possible. In the expected utility of wealth changes model, in which there is no initial wealth, I show that both a WTA/WTP gap as well as the classical preference reversal are possible due to loss aversion, both in its general as well as some specific forms.     

Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division

In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we show that there exists a partition in which each player receives either more than, less than, or exactly his or her entitlement (according to his or her measure), in any desired combination, provided that the measures are not all equal.