Ordinal aggregation and quantiles

Consider the problem of aggregating a profile of interpersonally comparable utilities into a social utility. We require that the units of measurement of utility used for agents is the same as the units of measurement for society (ordinal covariance) and a mild Pareto condition (monotonicity). We provide several representations of such social aggregation operators: a canonical representation, a Choquet expectation representation, a minimax representation, and a quantile representation (with respect to a possibly non-additive set function on the agents). We also isolate an additional condition that gives us a quantile representation with respect to a probability measure, in both the finite and infinite agents case.     

A nice estimation of Gini index and power Pen's parade

Under the assumption that an economic variable y such as income, is a power function of its rank among n individuals, we provide the coefficient of variation and the Gini index as functions of the power degree of the Pen's parade. In fact, knowing the power degree of the Pen's parade function, we obtain the coefficient of variation and a sharp analytical simple way to compute Gini index in terms of the power degree. Reciprocally, knowing, the coefficient of variation of a said variable, we can also provide the power degree of the corresponding Pen's parade, hence deducting its shape. Several examples are given to illustrate our methods. Special attention is given to countries' Gini indices of the World development indicators report 2009 (WDI 2009).     

An axiomatic theory of political representation

We discuss the theory of gerrymandering-proof voting rules. Our approach is axiomatic. We show that, for votes over a binary set of alternatives, any rule that is unanimous, anonymous, and gerrymandering-proof must decide a social outcome as a function of the proportions of agents voting for each alternative, and must either be independent of this proportion, or be in one-to-one correspondence with the proportions. In an extended model in which the outcome of a vote at the district level can be a composition of a governing body (with two possible parties), we discuss the quasi-proportional rules (characterized by unanimity, anonymity, gerrymandering-proofness, strict monotonicity, and continuity). We show that we can always (pointwise) approximate a single-member district quota rule with a quasi-proportional rule. We also discuss a more general environment, where there may be more than two parties.     

The measurement of income mobility: A partial ordering approach

Summary. Given a set of longitudinal data pertaining to two populations, a question of interest is the following: Which population has experienced a greater extent of income mobility? The aim of the present paper is to develop a systematic way of answering this question. We first put forth four axioms for income movement-mobility indices, and show that a familiar class of measures is characterized by these axioms. An unambiguous (partial) ordering is then defined as the intersection of the (complete) orderings induced by the mobility measures which belong to the characterized class; a transformation of income distributions is “more mobile” than another if, and only if, the former is ranked higher than the latter for all mobility measures which satisfy our axioms. Unfortunately, our mobility ordering depends on a parameter, and therefore, it is not readily apparent how one can apply it to panel data directly. In the second part of the paper, therefore, we derive several sets of parameter-free necessary and sufficient conditions which allow one to use the proposed mobility ordering in making unambiguous income mobility comparisons in practice. Received: July 12, 1995; revised version: May 13, 1997     

Filtral preorders and opportunity inequality

We compare profiles of opportunity sets by means of set-inclusion filtral preorders (SIFPs). Some significant results of the classic theory of income inequality are reproduced in the SIFP-framework.     

Auctions with uncertain numbers of bidders

We investigate bidders’ and seller's responses to ambiguity about the number of bidders in the first price auction (FPA) and the second price auction (SPA) with independent private valuations. We model ambiguity aversion using the maxmin expected utility model. We find that bidders prefer the number of bidders to be revealed in the FPA, are indifferent between revealing and concealing in the SPA, and prefer the SPA to the FPA. If bidders are more pessimistic than the seller then the seller prefers to conceal the number of bidders in the FPA, and prefers the FPA to the SPA.     

DEPRIVATION,INEQUALITY AND WELFARE*

Welfare ranking of income distributions involves a trade‐off between equity and efficiency. A person's feeling of deprivation about higher incomes may be of a relative or absolute type. We consider an intermediate notion of deprivation, a convex mix of relative and absolute deprivations. We then look at the problem of welfare ranking of income distributions when welfare increases under a globally equitable redistribution and under an income increase that keeps intermediate deprivation fixed. All deprivation indices can be regarded as inequality indices but the converse is not true. We also provide a numerical illustration of our results.     

The measurement of rank mobility

In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly represent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard (“global”) matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known “concordance” ordering. We then provide a characterization of an index of rank mobility based on partial matrices and show that, in the standard case of comparing global matrices, it is equivalent to Spearman's ρ index.     

Innis Lecture: Equity and equality

Abstract Is horizontal equity (HE) the ‘most widely accepted principle of equity’? Or does it stand in ‘opposition to the advancement of human welfare’? This paper argues that the case for the HE principle is not as straightforward as is usually thought and that it requires advanced notions of justice and well‐being. The most likely ethical basis for HE appears to combine a Rawlsian maximin principle and a view of well‐being that allows for relative local comparison effects. The paper also explores some of the dimensions of equality and well‐being along which the HE principle can be applied and presents a number of examples showing how HE considerations can provide an important input into policy analysis.     

Poverty growth in Scandinavian countries: A Sen multi-decomposition

We show in this paper that the growth rate of the Sen index is multi-decomposable, that is, decomposable simultaneously by subgroups and income sources. The multi-decomposition of the poverty growth yields respectively: the growth rate of the poverty incidence (poverty rate) decomposed by subgroups, the growth rate of the poverty depth (poverty gap ratios) decomposed by sources and subgroups, and the growth rate of inequality decomposed by sources and subgroups. We demonstrate that the multi-decomposition is not unique. It is mainly dependent on poverty lines defined on the space of income sources. An application to Scandinavian countries shows that poverty lines based on non-correlation between the income sources imply serious risks of underestimation of the contribution levels of the different components of the global poverty growth. The main contribution of our paper is to pay particular attention to the poverty growth and its source components in order to avoid underestimation of poverty growth.     

The effects of irreversibility on the timing and intensity of lumpy investment

This paper examines how changes in irreversibility of investment affect the timing and intensity of lumpy investment. We develop a continuous-time model wherein a firm is endowed with a perpetual option to invest in a project at any time by incurring a partially reversible investment cost at that instant. The amount of the investment cost is directly related to the intensity of investment that is endogenously chosen by the firm at the instant when the investment option is exercised. We show that higher irreversibility of investment induces the firm to raise its optimal investment trigger, thereby deferring the undertaking of the project. Furthermore, we show that changes in irreversibility of investment have no impact on the firm's optimal investment intensity due to two opposing effects that exactly offset each other. Finally, we show that higher irreversibility of investment reduces the value of the investment option and, therefore, makes the firm less valuable.     

An experimental study on individual choice, social welfare, and social preferences

We experimentally study subjects’ compliance with dominance relationships of income distributions in a ranking task. The experiment consisted of four different treatments: Lottery, individual choice, social preferences, and social planner. Our results suggest that people's risk attitudes do not adequately reflect their inequality attitudes. Uninvolved social planners exhibit randomization preferences, while self-interested social planners are generally more inequality averse and try to avoid extreme outcomes.     

Chronic and transient poverty: Measurement and estimation, with evidence from China

The paper contributes to the measurement of poverty and vulnerability in three ways. First, it proposes a new approach to separating poverty into chronic and transient components. Second, it provides corrections for the statistical biases introduced when using a small number of periods to estimate the importance of vulnerability and transient poverty. Third, it applies these tools to the measurement of chronic and transient poverty in China using a rich panel data set that extends over 17 years. Alternative measurement techniques are found to yield significantly different estimates of the relative importance of chronic and transient poverty. The precision of the estimates is also considerably enhanced by simple statistical corrections.     

Directional measurement of technical efficiency of production: An axiomatic approach

This contribution revisits the debate on the axiomatic properties satisfied by various radial versus non-radial measures of technical efficiency in production. This issue arises whenever isoquant and efficient subset of technology diverge and hence traditional radial measurement does not comply with Koopmans' definition of technical efficiency. This axiomatic approach to technical efficiency measurement is revisited within the framework of the more recently introduced directional distance function. This analysis provides the opportunity to define some new directional efficiency measures.     

A little fairness may induce a lot of redistribution in democracy

We use a model of self-centered inequality aversion suggested by Fehr and Schmidt (Quart. J. Econom. 114 (3) (1999) 817) to study voting on redistribution. We theoretically identify two classes of conditions when an empirically plausible amount of fairness preferences induces redistribution through referenda. We test the predictions of the adapted inequality aversion model in a simple redistribution experiment and find that it predicts voting outcomes far better than the standard model of voting assuming rationality and strict self-interest.     

Does less inequality among households mean less inequality among individuals?

Consider an income distribution among households of the same size in which individuals, equally needy from the point of view of an ethical observer, are treated unfairly. Individuals are split into two types, those who receive more than one half of the family budget and those who receive less than one half. We look for conditions under which welfare and inequality quasi-orders established at the household level still hold at the individual one. A necessary and sufficient condition for the Generalized Lorenz test is that the income of dominated individuals is a concave function of the household income: individuals of poor households have to stand more together than individuals of rich households. This property also proves to be crucial for the preservation of the Relative and Absolute Lorenz criteria, when the more egalitarian distribution is the poorest. Extensions to individuals heterogeneous in needs and more than two types are also provided.