Interpersonal comparison necessary for Arrovian aggregation

4 - SIMPLICITY: IMPOSSIBILITY THEOREMS

Chapter 3 - First-Best and Second-Best Analyses and the Political Economy of Public Sector Economics

Chapter 3 - First-Best and Second-Best Analyses and the Political Economy of Public Sector Economics

Arrow’s Impossibility Theorem inspired subjective image quality assessment approach

Mas-Colell and Sonnenschein [1972] have proved a well-known impossibility theorem for acyclic social preference. They showed that if social preference is acyclic for each configuration of individual preferences, and if the mapping between individual and social preferences satisfies the Pareto axiom, the independence of irrelevant alternatives, and May’s positive responsiveness axiom, then there must be an individual i such that for any x and y, xP_iy ⇒ xRy. This individual might be considered a “vetoer.”

The social welfare function (SWF) framework is a powerful tool for evaluating governmental policies in light of human well-being. The framework originates in theoretical welfare economics and is widely used in contemporary economic scholarship, although not (yet) in governmental practice. This book is intended to provide an accessible, yet reasonably rigorous overview of the SWF approach. The framework has three components: an interpersonally comparable measure of well-being, which functions to translate outcomes into lists (“vectors”) of well-being numbers, one for each person in the population; a rule (the SWF) for ranking well-being vectors, such as the utilitarian SWF (which simply adds up well-being numbers), a continuous-prioritarian SWF (which gives greater weight to the worse off), or some other; and a procedure for ranking policies, understood as probability distributions across outcomes. Each component of the SWF framework is reviewed in detail; in doing so, the book engages both the economic literature on SWFs and philosophical scholarship regarding individual well-being, ethics, and distributive justice. The book also clarifies the difference between the SWF approach and cost-benefit analysis (CBA), which uses money rather than an interpersonally well-being measure as the scale for quantifying policy impacts. The book includes a detailed case study of risk regulation—illustrating how the SWF framework can be used in practice and how it contrasts with CBA. The book is written to be accessible to readers without much mathematical training, but is backed up by an extensive mathematical appendix.

Utility independence versus IIA property in independent probit models

This chapter provides a synopsis of the social welfare function (SWF) framework. It presents the key components of the framework, which are then developed in greater detail in subsequent chapters: an interpersonally comparable measure of well-being, which converts each outcome into a list (“vector”) of well-being numbers, one for each person in the population; a rule (the SWF) for ranking well-being vectors, such as the utilitarian SWF or a continuous-prioritarian SWF; and a procedure for ranking policies, understood as probability distributions across outcomes. The chapter then discusses the relation between the SWF methodology and ethics. This framework provides an ethical evaluation of governmental policies—an evaluation that is consequentialist and, specifically, welfarist. Finally, the chapter contrasts the SWF framework with cost-benefit analysis (CBA); and explains how the framework succeeds in producing a well-behaved ranking of outcomes and policies, notwithstanding Arrow’s theorem.

Giving for development provides an interesting case study in the application of welfare economics. Giving for development is modest in total amount, but it is one of the few direct ways in which individuals reveal information relevant to the properties of the social welfare function to be applied to global redistribution. Where individuals themselves are willing to make transfers, how should this be taken into account in the social welfare function? The chapter first examines individual motives for giving, turning to the specific purpose of development in the second section. It then considers how far these motives are welfarist. The fourth section examines the implications for the social welfare function of individual altruism towards people in poor countries. If individuals are non-welfarist in their concerns, should the state continue to adopt a welfarist social welfare function? The final section addresses explicitly the geographical dimension, and the fact that the social welfare is a national social welfare function, which has to take into account the limited ‘sphere of control’ of national governments.

It is argued that Bayesian decision theory is a solution of an important philosophical problem, viz. the problem of how to define rational behavior under risk and uncertainty. The author has shown in earlier papers that if we take the Bayesian rationality postulates seriously, and take an individualistic point of view about social welfare, then our social welfare function must be a linear function of individual utilities: indeed, it must be their arithmetic mean. The present paper criticizes Diamond’s and Sen’s contention that one of the Bayesian postulates (viz. the sure-thing principle) does not apply to social decisions, even though it may apply to individual decisions. It also criticizes Sen’s proposal of making social welfare a nonlinear function of individual utilities. The social welfare function proposed by the author depends on interpersonal utility comparisons. The use of such comparisons is defended. It is also argued that anybody who feels that the utilitarian (i.e., linear) form of the social welfare function is not egalitarian enough, should reject the author’s individualism axiom, instead of trying to reject the Bayesian rationality axioms. However, this would be equivalent to giving egalitarian considerations a priority in many cases over humanitarian considerations. Finally, the paper discusses the reasons why even full agreement on the mathematical form of the social welfare function would not give rise to a Utopian state of moral consensus: moral controversies arising from disagreements about what predictions to make about future empirical facts would still remain.

The use of natural resource revenues for achievement of development has been a challenging issue for resource abundant countries. These challenges stem from the fact that incomes from natural resources are non-durable, unpredictable and uncertain. Different countries have pursued various approaches and tools for managing these revenues to avoid economic fluctuations. The international organizations and economic experts propose a diversification in the use of resource revenues through different approaches of public investment. Maximizing the social welfare function has become a common guideline for resource revenue management in resource-rich countries. This article investigates the effect of public investment approaches and their impacts on intergenerational social welfare function of Iran. To this end, the impact of two public investment approaches, namely Permanent Income Hypothesis (PIH) and Bird In Hand (BIH), was examined and compared on a certainty equivalent of social welfare function. Results of the simulation with Iran's economic data indicated substantial positive loss in welfare if switching to the BIH approach. Calculations show that the certainty equivalent of social welfare function for PIH and BIH is 786.3 and 444.3, respectively. PIH provides a higher welfare level for the Iranian economy.

This paper examines the normative foundations of fiscal equalization – an issue handled, apparently decisively, in a classic paper by James Buchanan (1950). Contrary to Buchanan's claims, we argue that fiscal equalization requires extremely strong value judgements – at least in the case where fiscal differences arise from the interaction of public goods provision under different population size – effectively committing one to a Rawlsian maximin rule. Much weaker forms of the 'social welfare function' in this public goods case will generate the requirement that private consumption levels be equalized, but specifically not public consumption levels – in which sense private goods equalization seems normatively weaker than public goods equalization, If this is so, the hope of justifying federal fiscal equalization on the basis of relatively uncontroversial individualistic norms seems illusory.

On the (Near) Equivalence of Welfarist and Extra-Welfarist Methods to Value Healthcare With Implications for Assessing Equity

Due to the role of insurance in economy, the factors determining the demand for insurance (e.g. income) have been the subject of many studies. On the other hand, income inequalities significantly affect many purchasing decisions and the perception of income among individuals. The aim of this study is to verify the relationship between social welfare and insurance expenditure. This verification was carried out on the basis of data on various socio-economic groups in Poland by using reduced social welfare functions such as: the Sen Index, Kakwani Index, Dagum indexes and the ‘naïve’ welfare function (income). As part of the research, a linear regression was applied between the dependent variable (average monthly expenses on insurance per 1 person in households by socio-economic groups) and the explanatory variable (reduced welfare functions) for a given social group. Reduced social welfare functions was determined on the basis of the average monthly disposable income per capita in households and the Gini coefficient for this group. Social welfare in the form of reduced welfare functions turned out to be a statistically better predictor of insurance expenditure than the income itself for social groups with relatively small income disparities (low Gini coefficient). For the group of farmers in Poland, where the income disproportions were statistically the largest, income turned out to be a better predictor.

Child labor is often condemned as a form of exploitation. I explore how the notion of exploitation, as used in everyday language, can be made precise in economic models of child labor. Exploitation is defined relative to a specific social welfare function. I first show that under the standard dynastic social welfare function, which is commonly applied to intergenerational models, child labor is never exploitative. In contrast, under an inclusive welfare function, which places additional weight on the welfare of children, child labor is always exploitative. Neither welfare function captures the more gradual distinctions that common usage of the term exploitation allows. I resolve this conflict by introducing a welfare function with minimum altruism, in which child labor in a given family is judged relative to a specific social standard. Under this criterion, child labor is exploitative only in families where the parent (or guardian) displays insufficient altruism towards the child. I argue that this welfare function best captures the conventional concept of exploitation and has useful properties for informing political choices regarding child labor.