This essay is a review of Ronald Dworkin's recent essay on equality of resources. Many of the ideas discussed by Dworkin have also been examined by economists with, I believe, considerable insight. Unfortunately, economists tend to write for economists, not for philosophers, and their insights are seldom communicated properly to noneconomists. Of course, the same criticism can be levied on philosophers! But perhaps legal theorists are less subject to this criticism. One of the great contributions of Dworkin is that he (...) is very readable; and the quality of his exposition makes these ideas accessible to a wide audience of philosophers, lawyers, and social scientists in general. (shrink)

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.

I state and prove formal versions of the claim that the Nash bargaining solution creates a compromise between egalitarianism and utilitarianism, but that this compromise is “biased”: the Nash solution puts more emphasis on utilitarianism than it puts on egalitarianism. I also extend the bargaining model by assuming that utility can be transferred between the players at some cost ; I use the extended model to better understand the connections between egalitarianism and utilitarianism.

Suppose it is possible to make approximate interpersonal comparisons of welfare gains and losses. Thus, if w\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w$$\end{document}, x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}, y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y$$\end{document} and z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z$$\end{document} are personal states, then it is sometimes possible to say “The welfare gain of the state change w⇝x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w\leadsto x$$\end{document} is greater than the welfare gain of the state change y⇝z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y\leadsto z$$\end{document}”. We can represent this by the formula “⪰\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\succeq $$\end{document}”, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} is a difference preorder: an incomplete preorder on the space of all possible personal state changes. A social state change is a bundle of personal state changes. A social difference preorder is an incomplete preorder on the space of social state changes, which satisfies Pareto and Anonymity axioms. We characterize a family of SDPs which are roughly utilitarian in nature. We also apply the model to redistributive taxation. (shrink)

Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.

This paper provides an ethical intepretation of the Nash choice rule. In a setting in which (cardinal) utilities are interpersonally comparable, this procedure is characterised by an impartiality requirement and by the assumption that choices are not responsive to the agents' relative ability to convert resources into utility.

The purpose of the article is to draw comparisons between the major normative rules of distributive justice. This comparison is based on a kind of distribution of goods which is sometimes called the problem of pure distribution, i.e. the distribution of a homogeneous, infinitely distributable good in a situation when claims of different persons on the distributed good were in no way differentiated. This problem is defined against the background of typology of problems of goods distribution. Normative rules of distributive (...) Justice are defined formally as social welfare functionals. Eight rules of justice are distinguished: the rule of the utilitarian, Rawls’s maximin rule, Rawls’s lexicographical maximin rule, the maximax rule of the conservatives, the rule of lexicographical maximax of the conservatives, Nash’s rule, and two rules advanced by egalitarianists which differ by the meaning attributed to equality of distribution. Premises underlying the construction of these rules of justice and which indicate the measurement of preferences and possibilities of interpersonal comparisons are discussed. The same justice rules are also presented graphically. The method of the comparison amounts to examining if a certain set of ethical postulates is fulfilled by the rules under consideration. Several ethical postulates concerning the distribution of goods are formulated. Some of them define conditions any method of evaluating inequality of distribution of goods should fulfil. The remaining postulates involve more general requirements put to methods of making social decisions. Theorems about the fulfilment or nonfulfilment by individual rules of distributive justice of the considered ethical postulates are presented in a recapitulating table. The author demonstrates that almost a1l justice rules fulfil general postulates put to methods of social decision making. Nash’s rule and the two rules of the egalitarians are the exceptions, as they do not fulfil the postulate of separability with respect to unconcerned individuals. Besides, the two rules of the egalitarians do not fulfil the Pareto optimality principle. Significant differences between rules of distributive justice become manifest only when you compare way they fulfil ethical postulates concerning the manner of evaluating the inequality of the distribution. With regard to this set of postulates, they can be arranged along a definite continuum, with Rawls’s lexicographical maximin — the radical egalitarian rule, and the lexicographical maximax of the conservatives – the radical conservative rule as the extreme points of this continuum. (shrink)

According to the person-affecting view, the ethics of welfare should be cashed out in terms of how the individuals are affected. While the narrow version fails to solve the non-identity problem, the wide version is subject to the repugnant conclusion. A middle view promises to do better – the Interpersonal Comparative View of Welfare (ICV). It modifies the narrow view by abstracting away from individuals’ identities to account for interpersonal gains and losses. The paper assesses ICV’s merits and flaws. ICV (...) solves the non-identity problem, avoids the repugnant conclusion, and seems to accommodate the person-affecting intuition. But it cuts too many things along the way: ICV obstructs the advantage of the wide view to account for all future individuals’ welfare, abandons the intuitions that underlie the narrow view, and even violates its own presuppositions by turning out to be merely pseudo person-affecting. (shrink)

Arrow’s impossibility result not only had a profound influence on welfare economics, but was, as this paper shows, also widely discussed in philosophy of science and in the engineering design literature.

This paper discusses justice-constrained libertarian claims that were proposed as a way to circumvent the impossibility of the Paretian liberal. Since most of the results are negative in character, we suggest an alternative route: A requirement on the structure of individual orderings should be combined with the idea that under particular circumstances individual decisiveness should be controlled by higher-order principles.

In this paper, I present the suggestion that a suitable theory of “justice as fairness” could offer a consistent path for solving many issues related to the actual crisis of the classical liberal model of economy and democracy, by substituting the abstract “equality” principle, with the concrete “equity” one in the notion of justice. After a short discussion of some main characters of the present worldwide crisis of the classical liberal model, I present two main theories of justice as fairness. (...) John Rawls’ theory in political philosophy that emphasizes how really equitable judgements must overcome the equalitarianism of the Classical Liberalism, by considering the real possibilities of individuals and groups of accessing and enjoying commodities and utilities, as well as, the “basic liberties” defining the citizen equal dignity in the Modern State. Rawls propose, therefore, a notion of fairness compliant with the Kantian normativism, and a notion of fair distributive justice based on the ethical principle of the maximin, as a criterion for judging the righteousness of the State Institutions. The other theory of justice as fairness I discuss in this paper is an evolution of Rawls’ in the direction of the development of a “comparative distributive justice”, without any normativism. This theory is developed in the context of the newborn discipline of the “social choice theory”, formalizing social decision processes, with applications in economic, social, and political sciences. What characterizes Sen’s theory is its original synthesis between the Aristotelian notion of fairness, based on the “personal flourishing”, and Adam Smith’s ethical principle of the “extended sympathy”, by which making comparable different approaches to pursue the personal flourishing, i.e., for achieving “valued and valuable ways of being and of doing”, compliant with, and respectful of, different value systems. (shrink)

Ramsey famously condemned discounting “future enjoyments” as “ethically indefensible”. Suppes enunciated an equity criterion which, when social choice is utilitarian, implies giving equal weight to all individuals’ utilities. By contrast, Arrow accepted, perhaps reluctantly, what he called Koopmans’ :287–309, 1960) “strong argument” implying that no equitable preference ordering exists for a sufficiently unrestricted domain of infinite utility streams. Here we derive an equitable utilitarian objective for a finite population based on a version of the Vickrey–Harsanyi original position, where there is (...) an equal probability of becoming each person. For a potentially infinite population facing an exogenous stochastic process of extinction, an equitable extinction biased original position requires equal conditional probabilities, given that the individual’s generation survives the extinction process. Such a position is well-defined if and only if survival probabilities decline fast enough for the expected total number of individuals who can ever live to be finite. Then, provided that each individual’s utility is bounded both above and below, maximizing expected “extinction discounted” total utility—as advocated, inter alia, by the Stern Review on climate change—provides a coherent and dynamically consistent equitable objective, even when the population size of each generation can be chosen. (shrink)

Abstract:Standard lessons from economics tell us that an externality creates inefficiency, and that this inefficiency can be removed by internalizing the externality. This papers considers how successfully these lessons can be extended to intergenerational externalities such as emissions of greenhouse gas. For intergenerational externalities, the standard lessons involve comparisons between states whose populations of people differ, either in their identities or their numbers. Common notions of efficiency break down in these comparisons. This paper supplies a new notion of efficiency that (...) allows the lessons to survive, but at the cost of reducing their practical significance. (shrink)

This article illustrates how axiomatic social choice theory can be used in the evaluation of measures of group fitness for a biological hierarchy, thereby contributing to the dialogue between the philosophy of biology and social choice theory. It provides an axiomatic characterization of the ordering underlying the MichodSolariNedelcu index of group fitness for a multicellular organism. The MVSHN index has been used to analyse the germ-soma specialization and the fitness decoupling between the cell and organism levels that takes place during (...) the evolutionary transition to multicellularity. It is argued that some of the axioms satisfied by the MVSHN group fitness ordering are not appropriate for all stages in this transition. (shrink)

According to the Maximin principle of distributive justice, one outcome is more just than another if the worst off individual in the first outcome is better off than the worst off individual in the second. This is often interpreted as a highly egalitarian principle, and, more specifically, as a highly egalitarian way of balancing a concern with equality against a concern with efficiency. But this interpretation faces a challenge: why should a concern with efficiency and equality lead us to a (...) concern only for the very worst off? Egalitarian proponents of Maximin tend to meet this challenge by showing that it possible to formally derive Maximin from surprisingly weak conditions relating efficiency and equality to justice. But in this paper, I argue that this reply fails. The issue is not that the proofs are invalid, but instead that every existing proof of Maximin transforms into an impossibility result as soon as we realize that any reasonable conception of equality must satisfy a certain formal property. The upshot is that even if it is possible to defend Maximin on other grounds, there is no known way to defend it on the grounds that it balances a concern with equality against a concern for efficiency. Further, more general implications of this result for egalitarian theories of distributive justice are also explored. (shrink)

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, independence (...) conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (shrink)

Ramsey famously pronounced that discounting “future enjoyments” would be ethically indefensible. Suppes enunciated an equity criterion implying that all individuals’ welfare should be treated equally. By contrast, Arrow accepted, perhaps rather reluctantly, the logical force of Koopmans’ argument that no satisfactory preference ordering on a sufficiently unrestricted domain of infinite utility streams satisfies equal treatment. In this paper, we first derive an equitable utilitarian objective based on a version of the Vickrey–Harsanyi original position, extended to allow a variable and uncertain (...) population with no finite bound. Following the work of Chichilnisky and others on sustainability, slightly weakening the conditions of Koopmans and co-authors allows intergenerational equity to be satisfied. In fact, assuming that the expected total number of individuals who ever live is finite, and that each individual’s utility is bounded both above and below, there is a coherent equitable objective based on expected total utility. Moreover, it implies the “extinction discounting rule” advocated by, inter alia, the Stern Review on climate change. (shrink)