Rational Choice and Social Welfare

The origin of the tremendous development of studies on rights and freedom within social choice theory and normative economics can be traced back to the famous short paper of Amartya Sen published in 1970 (Sen, 1970b); see also his book published the same year (Sen, 1970). In this paper, it is shown in the framework of aggregation procedures that there is a conflict between collective rationality (in terms of properties of choice functions or in terms of a transitivity-type of the social preference property — in fact, acyclicity of the asymmetric part of the social preference), Paretianism (a unanimity property) and some slight violation of neutrality (neutrality meaning that the names of options or social states are not to be taken into account) possibly combined with some slightly unequal distribution of power among individuals interpreted as an individual liberty property. Although, since then, rights have been considered within another paradigm, viz. game forms (see for instance Gärdenfors (1981, 2005), Gaertner, Pattanaik, and Suzumura (1992), Peleg (1998a,b) and Suzumura (2008)), and freedom has been mainly analyzed in the context of opportunity sets following the pioneering paper of Pattanaik and Xu (1990) (see also the survey by Barberà, Bossert, and Pattanaik (2004)), some authors (for instance Igersheim (2006) and Saari and Pétron (2006)) have recently revisited the foundational framework of Sen and Gibbard (1974) either by studying the informational structure of the aggregation procedure or by examining the consequences of taking a Cartesian structure to define the set of social states, consequences that take the form of a restriction of individual preferences. The purpose of this paper is different. I wish to formally study a weakening of the conditions associated with the notion of individual liberty. I have always considered that this condition was rather strong in Sen’s original paper. In fact, the condition is quite strong in the mathematical framework and only the interpretation, to my view, makes it not only acceptable but obvious. In his comments to a paper by Brunel (now Pétron) and Salles (1998), Hammond (1998) writes:

In the social choice rule approach …, local dictatorship becomes a desideratum, provided that the ‘localities’ are appropriate. Our feelings of revulsion should be reserved for non-local dictatorships, or local dictatorships affecting issues that should not be treated as personal.

This paper constructs continuous Paretian social welfare functions for which one agent is a homotopic dictator but another is, in a precise sense, almost all powerful. The significance of this arises from the widely differing views¹ that have been expressed about a theorem in Chichilnisky (1982) showing that, for all continuous Paretian social welfare functions there must be a homotopic dictator. What the analysis in this paper therefore shows is that Chichilnisky’s theorem is not a genuine Arrow-type impossibility theorem in the sense that desirable properties are not shown to entail some undesirable concentration of power.

Population ethics is about principles for social evaluation of alternatives with different population sizes. Different environmental policies lead to different population sizes as well as different quality of lives involved. Therefore, as a necessary step towards laying foundations for such policy recommendations, discussing relevant issues on population principles is of critical importance.

Welfarism is defined as a methodology that evaluates social welfare according to the level of satisfaction with regard to individuals’ subjective preferences. For this methodology, the criticisms by Dworkin (1981a, 2000), Sen (1979, 1980), and others are well known. They criticized the limited scope of information used to evaluate social welfare in the aforementioned methodology. Moreover, they criticize the welfarist neutral attitude vis-à-vis the problem of what types of preferences are satisfied. There are types of preferences, such as the utility of individual offensive tastes, that of expensive tastes, that of formation of the adaptive preference, or that of cheaper tastes such as in the case of the ‘termed housewife,’ all of which should be carefully and distinctively treated in the evaluation of social welfare from an ethical point of view. The point of these critiques is that the welfarist evaluation has no concern for such preferential differences.

The envy test concept is an all-or-nothing notion, and this is problematic when there is no achievable envy-free option. The idea of ranking the ‘unfair’ social states on the basis of how much envy they contain goes back at least to Feldman and Kirman (1974) and Varian (1976), but it is in Suzumura (1981a, b, 1983) that one finds a first systematic study of this issue. More recent contributions to this line of research include Chauduri (1986), Diamantaras and Thomson (1990), Tadenuma (2002), and Tadenuma and Thomson (1995).

It is not rare that multiple criteria are applied to make individual or social decisions. In the context of resource allocation problems, most prominent criteria are efficiency and equity of allocations. Pareto efficiency is probably the most widely accepted criterion among economists, but it is silent about the distributional equity of allocations. On the other hand, several concepts of equity have been proposed and extensively studied in welfare economics. Two of them are central: no-envy (Foley, 1967 and Kolm, 1972) and egalitarian-equivalence (Pazner and Schmeidler, 1978). We say that an allocation is envy-free if no agent prefers the consumption bundle of any other agent to his own and that an allocation is egalitarian-equivalent if there is a consumption bundle, called the reference bundle, such that every agent is indifferent between the bundle and his own.

In the literature of intergenerational equity, Rawlsian maximin principle is one of the most well-known criteria for distributive justice among generations.¹ Since this principle has an intuitive appeal to egalitarian writers, several attempts to characterize the principle have been made in welfare economics. Arrow (1973), Dasgupta (1974a, b), and Riley (1976) scrutinized the performance thereof in the context of optimal growth. Arrow shows that the utility path as well as the consumption path generated by the maximin principle has a saw-tooth shape. Dasgupta shows that it gives rise to a logical deficit such as time-inconsistency. The other line of researches has been stimulated by the axiomatic approaches of Hammond (1976, 1979) and Sen (1970, 1977). In this line, researchers extended axiomatizations of the maximin principle and applied them to intergenerational equity. The maximin path is characterized by a constant path, which emphasizes its egalitarian perspective.²

Binary relations are at the heart of much of economic theory, both in the context of individual choice and in multi-agent decision problems. A fundamental coherence requirement imposed on a relation is the well-known transitivity axiom. If a relation is interpreted as a goodness relation, transitivity postulates that whenever one alternative is at least as good as a second and the second alternative is, in turn, at least as good as a third, then the first alternative is at least as good as the third. However, from an empirical as well as a conceptual perspective, transitivity is frequently considered too demanding and weaker notions of coherence have been proposed in the literature. Two alternatives that have received a considerable amount of attention are quasi-transitivity and acyclicity. Quasi-transitivity demands that the asymmetric factor of a relation (the betterness relation) is transitive, whereas acyclicity rules out the presence of betterness cycles. Quasi-transitivity is implied by transitivity and implies acyclicity. The reverse implications are not valid.

An extensive literature, both theoretical (see for instance, Bruno and Fischer (1990), Calvo and Leiderman (1992), Friedman (1971), Goldman (1974), Sargent and Wallace (1973)) and empirical, (see for instance, Aghevli and Khan (1977), Anderson, Bomberger, and Makinen (1988), Babcock and Makinen (1975), Cagan (1956), Christiano (1987), Easterly, Mauro, and Schmidt-Hebbel (1995), Engsted (1993), Metin and Maslu (1999), Michael, Nobay, and Peel (1994), Pickersgill (1968), Salemi and Sargent (1979), Taylor (1991)) has arisen around the special semi-logarithmic demand for money function introduced by Cagan (1956). Cagan’s motivation behind the demand for money function was mainly in terms of transactions costs and its relationship to the consumer’s ability to affect the real value of cash balances. Cagan argued that the real cost of holding cash balances fluctuates widely enough to account for the dramatic changes in the holding of cash balances observed during hyperinflation. He hypothesized that during periods of hyperinflation the demand for money is almost entirely explained by the variation in the expected rate of change in prices and that changes in expected inflation have the same effect on real balances in percentage terms regardless of the absolute amount of initial cash balances. In other words, during hyperinflations, the demand for money takes the special form: m = ke^{−λπ e}, where m is the real demand for money, π ^(e) is the expected rate of inflation and k, λ are positive constants.

When there is no uncertainty, it is well known that the Hicksian compensating and equivalent variations are exact measures of individual welfare change. That is, the sign of either of these measures of Hicksian consumer’s surplus correctly identifies whether a change in prices and income makes an individual consumer better or worse off.¹ It is also well known that Marshallian consumer’s surplus is not an exact measure of individual welfare change except under restrictive assumptions.²

Following Zermelo’s (1912) pioneering analysis of chess and similar games, von Neumann (1928) devised a standard paradigm, according to which multiperson decision problems in modern economic analysis and other social science are nearly always modeled as noncooperative games in strategic form. This paradigm relies on two key assumptions, of which the first can be stated as follows: Assumption 1. A multiperson decision problem is fully described by a game in extensive form, whose structure is commonly known to all players in the game.

Traditional measures of unemployment were only concerned with the total number of people unemployed. In recent years such measures have come under criticism for ignoring those who may not currently be unemployed but are vulnerable, that is, they live under the risk of becoming unemployed (see Cunningham and Maloney (2000), Glewwe and Hall (1998), Thorbecke (2003)). Alongside this criticism a small but rapidly growing literature is emerging that looks at various aspects of vulnerability and tries to measure it (Amin, Rai, and Topa (2003), Ligon and Schechter (2003), Pritchett, Suryahadi, and Sumarto (2000)).¹

The purpose of this chapter is to consider a class of rules for comparing sets of objects¹ in terms of the degrees of diversity that they offer. Such comparisons of sets are important for many purposes. For example, in discussing biodiversity of different ecosystems, one is interested in knowing whether or not one ecosystem is more diverse than another. Similarly, when discussing issues relating to cultural diversities of various communities, one may be interested in knowing how these communities compare with each other in terms of cultural diversity. In the economics literature, there have been several contributions to the measurement of diversity. Weitzman (1992, 1993, 1998) develops a measure of diversity based on cardinal distances between objects. Among other things, Nehring and Puppe (2002) provide a conceptual foundation for cardinal distances in Weitzman’s framework. Weikard (2002) discusses an alternative measure of diversity; Weikard’s measure is based on the sum of cardinal distances between all objects contained in a set.