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Inequality and Welfare: Is Europe Special? 517 Dimension Individual well-being Aggregator for each dimension Collective well-being Figure 12.1 The two routes for aggregating welfares in a multidimensional setting. some are technical, others are more normative. Consequently, the robustness of the country ranking according to these indicators is all but warranted. 12.2.3 Aggregating Welfare There are basically two routes to construct such indices. The basic information structure can be illustrated by the following matrix where the profiles of individuals are represented in rows according to various dimensions that are featured in columns. The typical element of this matrix is the allocation of individual i in good j, x j i : Dimensions ⎛ ⎞ Individuals ⎝ x j ⎠ i The HDI or IHDI illustrates (see Figure 12.1) a first alternative where each dimension is first aggregated into a specific aggregator (for instance the GNI per capita for the income dimension) and then we have to solve the problem of how to add carrots and tomatoes. It is important to recognize that with this first route, collective welfare does not aggregate individual welfare, which is not defined as such. This way of proceeding bypasses computing individual welfare and hence it ignores the correlation between the different distributions. The other route is deeply imbedded in the social choice literature which deals with the principles of aggregation of preference. The main concept is
518 Alain Trannoy the Bergson-Samuelson social welfare function, which dates back to Bergson (1938). This concept has been enlarged by Sen to functional, namely, a function of functions aggregating the various individual utility functions which are numerical representations of individual preferences over the various dimensions into a function, that is, a numerical representation of collective choices. The crucial role of the informational basis of social choice introduced by Sen (1970) in his book Collective Choice and Social Welfare was perfectly understood by d’Aspremont and Gevers (1977) to offer some escape to the Arrow impossibility theorem (see Arrow, 1963). The important distinctions are between the requirements of: Level comparability where the levels of each individual well-being indicator 2 are made comparable. The worst-off in a society need to be defined, as in the maxmin solution. This kind of comparison is, for instance, necessary when one has to decide who most deserves social benefits. First-difference comparability. The differences (gains and losses) in wellbeing indicators are comparable across individuals. This sort of comparability is needed to compute the sum of utilities, or to compute the total welfare gain of a tax-transfer policy measure. Ratio-scale comparability. The ratio of individual well-being indicators is comparable. The ratio-scale comparability requires each individual wellbeing indicator to have a common and natural 0. For instance, the Nash Bargaining solution (defined as a product of utilities gains with respect to some status quo) has to be computed, or each individual has to report his happiness on a common scale between 0 and 10, as is quite common in all happiness studies. This second route allows for the correlation between attributes to matter in computing social welfare. To some extent, this second approach is preferable to the first one, but obviously the construction of an individual well-being indicator represents a major challenge. There again, two routes may be followed, a normative one trying to build an individual well-being indicator on sound properties, a route followed by Fleurbaey (2009) or a more positive route built on happiness literature (Layard, 2011). One may also want to combine both, an attempt proposed by Fleurbaey and Maniquet (2011). Of course, even if it were proved that one can strictly measure individual well-being on an objective basis, it remains a normative choice to select this objective measure of well-being as the measure of individual welfare that will be used in collective choice. 12.2.4 The Relationship between Inequality and Welfare It arises from the previous developments that inequality and welfare are closely related. And yet, it is far from obvious that the two words and concepts, inequality and welfare, are intimately related in the mind of the layman, as they are
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Economics without Borders If treate
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University Printing House, Cambridg
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vi Contents 1.4.3 Reforming the Sta
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viii Contents 5.3 Approaches in Ind
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x Contents 9.3 The Trade-Off betwee
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xii Contents 12.4.4 Inequality of O
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Figures 1.1 Entry effects near and
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Tables 2.1 Chronology of EPL reform
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xx Foreword Another important facto
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Contributors roberto barcellan Euro
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Contributors xxv vigdis kvalheim No
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Introduction Richard Blundell, Este
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Introduction 3 2. Knowledge-based g
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Introduction 5 for innovation or th
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Introduction 7 burden was the polic
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Introduction 9 however, quite clear
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Introduction 11 extremely useful fo
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Introduction 13 An overarching them
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Introduction 15 involved). Another
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Introduction 17 proportion of rail
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Introduction 19 ‘macroeconomics i
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Introduction 21 private equity mark
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Introduction 27 Chapter 14 starts b
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1 Innovation and Growth: The Schump
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Innovation and Growth: The Schumpet
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2 European Union Dual Labour Market
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European Union Dual Labour Markets
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Winners and Losers of Globalization
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10 Fiscal and Monetary Policies aft
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Fiscal and Monetary Policies after
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634 Index Diversified Cities, 385 D
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636 Index Native Population, 114, 1
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