Vilfredo Pareto deserves the credit for the first thorough statistical analysis of the distribution of income (Persky 182). Based on taxation statistics from England, Italian cities, several German states, Paris and Peru he claimed to have discovered a law of the distribution of income that revealed the same, unequal distribution of income in political units of very different size, institutional set up,and history. Based on this he claimed that the distribution of income depends on human nature rather than economic organisation and political institutions, and armed with his law claimed the futility of socialist and other egalitarian attempts to change the income distribution. Pareto's claims provoked a host of empirical rebuttals, criticism of his method and conclusions, and alternative ways of assessing the distribution of income. In fact, today the measurement of income and its distribution has become an institutionalized exercise in many countries, and impressive attempts have been undertaken to track inequality trends even on a global level (Milanovic). As a result, the measurement of the distribution of income has come to influence political perception, and how we think about the distributive justice of countries or even larger phenomena such as globalization. Yet, already the work of Pareto immediately revealed that the measurement of inequality involves difficult questions regarding the unit of measurement, and the representation and interpretation of measurement. Even if today the measurement of income has the weight of the factual and the support of refined statistical methods, it does not follow that income distribution is of primary concern for understanding inequality and distributive justice. This raises questions of distributive justice, but there are remarkably few books that would deal with both the theory and measurements of (in)equality. Hilde Bojer's Distributional Justice, Theory and Measurement deserves credit for discussing these two themes together in one book.

The book is divided into two parts: first theories of justice, then questions of measurement. The first part introduces major theories of distributional justice including utilitarianism, Rawls' theory of justice, Dworkin's approach and the capability view, as well as libertarianism and Marxism (Chapters 2--7). Generally, the author introduces the main features of the respective approaches, followed by a discussion of objections. The exception to this pattern is one very short chapter on Marxism and libertarianism, about which the author openly acknowledges her lack of enthusiasm (p. 3 – as this chapter neither introduces recent developments in either of the two approaches, and as neither of the two approaches play any apparent role for the subsequent discussion of measurements, the chapter can probably be safely skipped). Bojer adds a special chapter on children and their mothers in the first part, which is especially valuable as the approaches mentioned above generally have little to say on this topic (Chapter 8). The second part of the book is devoted to the measurement of inequality, and starts off with a clarification of the notoriously difficult concepts of income and wealth, then turning to a discussion of the temporal dimension of measurement as well as the unit of measurement (both individual versus household, and questions concerning the components of income, Chapters 9--11). She then introduces general features of economic equality measures, discusses specific examples such as Atkinson's and Kolm's inequality measure, the visual representation of inequality with the Lorenz curve as well as the Gini coefficients (Chapters 12--14). The book closes with chapters devoted to the measurement of poverty, and the decomposition of inequality measures. Two appendices deal with uncertainty and expected utility, and sampling errors respectively; a brief section with suggested further readings concludes.

Bojer offers a succinct discussion of, and a rare chance to learn about, both the theory and measurement of distributive justice. Her courage in bringing together these largely independent and vast literatures is admirable, and contributes to a critical understanding of current discussions of inequalities in the world. As already indicated by the structure of the book, Bojer moves from theories of distributional justice to questions of inequality measurement in the second part. However, it is not the case that this second part directly discusses the measurement implications, and implementations, of the theories of justice discussed in the first part. It could therefore be useful to first read the second part, and then read the first part with the knowledge of empirical measurement issues in mind. Bojer states the reason for this break at the beginning of the book, where she observes “the gap between what the philosophers write, and what is studied in empirical analyses of income distribution” (p. 1, italics added). She attributes this gap to the welfarist outlook of empirical researchers and the lack of concern of philosophers “with how their concepts can be made operational for empirical analysis” (p. 2): “philosophers tend to be long on profundity and short on empirical measurement” (p. 86). Her book sets out to tackle this, i.e. “to bridge the gap between moral philosophy and empirical research” (p. 2). But her conclusion is just as honest as it is negative: “I have not succeeded; the bridge is still unbuilt” (p. 2).

As this “gap” and the need to bridge it are of major concern for Bojer, let me turn in more detail to this task, which is made difficult not least due to the complicated relation between theory and measurement in political philosophy. What sort of “thing” is this “gap”? Is the relation between distributional theory and measurement primarily one of a movement from the former to the latter? Surprisingly, Bojer offers few explicit reflections regarding her stated objective of bridging the gap, and I will therefore use the remainder of this review to work out some clarifications. To wit, there is no such thing as the “gap,” there are many gaps, and keeping this in view may help us think about the theory and empirical analysis of distributive justice.

Let me first turn to the “gap” between distributional theories and measurement, choosing as an example what Bojer has to say about Rawls' theory of justice as fairness. Rawls defines primary goods as those which every rational human being wants, and lists basic liberties, freedom of movement and choice of occupation, powers and prerogatives of offices and positions of responsibility, income and wealth, and the social bases of self-respect as primary goods. According to Bojer, “Rawls, like many other philosophers, seriously underestimates the difficulties connected not only with the practical measuring, but also of the theoretical definition of income and wealth” (Bojer, 44). How income and wealth are measured depends not least on the purpose of the measurement, which in this case must “in some sense and to some extent answer the question: is the distribution just” (p. 86)? In Rawls' case this requires knowledge as to whether the distribution of the primary goods of income and wealth is to the benefit of the least advantaged. Moreover this is not an interest in income as the result of choices, but as a constraint and requirement for everyone's equal opportunity to determine their lives. Finally, the constraint on choice at issue is that of the constraints on life-prospects, rather than on individual consumption possibilities in a shorter, e.g. typically annual, period.

Given these specifications, how then does Rawls underestimate the difficulties of theoretical definition and practical measurement? The specifications just given lead one to expect that individual life-time prospects have to be measured. But governments in practice measure household income. Not only is household income important for assessing the standard of living of children, but income as a constraint on choice depends not just on one's personal income, but also on that of the other persons in the household. A shared household reduces costs due to “public household goods,” and at least to some extent income is likely to be shared between the members of the household. “It is therefore standard procedure in analysis of personal income distribution to analyse the distribution of household income” (p. 78, italics added). However, how households pool their incomes differs from household to household, with immediate consequences for the opportunities of its members. There is therefore a tension due to the household measure, which seems at once a more accurate measure of income than individual wage income, and a measure concealing pertinent questions of equal opportunity such as independent earning power and the opportunity of leaving an abusive marriage (p. 88). Another problem regarding income as a primary good is due to the fact that in practice income is not manna from heaven, of which everyone is likely to prefer more rather then less, but rather something that requires work, and therefore implies a reduction in available leisure time. While it is possible to estimate a full income, which takes leisure into account, Bojer seems to be right when she says that full income is hardly an uncontroversial idea (it requires making leisure and work “somehow” commensurate), and is at any rate “not at the moment in practice observable” (p. 45). Considering such criticism, I would argue that the prima facie plausibility of this part of Rawls' primary goods approach depends on the amphiboly of income as a good and a measure in his theory of justice, i.e. the plausibility of income as a good owes much to income as a measure, where the latter due to the work of economists and statisticians has become something that we tend to accept as an objective measure and that is already used for the making, the communication and the monitoring of policies. A “gap” emerges because of the scrutiny of critics such as Bojer, who drive a wedge between income as a good and income as measured.

But what about the philosophers following and reacting to Rawls? Do they show insufficient concern for empirical analysis (p. 2)? Consider Amartya Sen's criticism that the primary goods approach overlooks the differences among people that result in people having very different effective choices based on the same resource bundle. Does this criticism show no concern with empirical analysis? As the criticism is pertinent to a basic concern of measurement, i.e. the unit of analysis, for it to count as not engaged in empirical analysis seems to require in the domain of distributive justice the presumption that empirical analysis means (large-scale) statistical measurements, paradigmatically of the income distribution and the various representations this gives rise to (such as the Lorenz curve, the Gini coefficient, and the other inequality measures discussed by Bojer in the second part). If this is assumed, then “mere” criticism of a unit of measurement is not sufficient for empirical analysis, alterative measurements have to be developed. But this presumption also tends to suggest that theories of distributive justice could not stand in a critical relation to measurement (as opposed to the implementation relation, which seeks to move from the theory to the design of appropriate measures). In this critical relation, the theory of distributive justice may simply question the moral accuracy of large-scale measurement in general, or even just particular measurements. In the latter sense, Sen can be read as pointing out that the focus on income offers only distorted information regarding equality, which is moreover not just a criticism of Rawls, but by implication also puts a question mark over distributive politics focusing primarily on income transfers as a distributive tool. Indeed, as income measurement is historically due to the state's need for revenue, it would almost be a miracle, if it just so happened that this revenue tool also serves best for achieving a fair distribution.

And yet, such a critical relation to measurement hardly seems sufficient. Is there not a need for alternatives modes of operationalization and empirical analysis? In the light of the critical relation between theorizing about distributive justice and empirical analysis, two points need to be taken into account. The first one is the trivial, but consequential fact that measurement in large political units, traditionally the “nation state” and now increasingly “the world,” requires institutions that gather this information, and people who accept to be “measured.” Post-revolutionary France offers ample illustrations of the difficulties of introducing liberal democratic measures, where influential parts of the population still stick to traditional, hierarchical categories and therefore refuse to be counted as equals (Bourguet). If the operationalization of a theory for measurement in the political domain depends to some extent on the social world (or needs to change the social world), then the building of “bridges” is also to some extent the building of a “social world.” There is therefore a potentially problematic limitation involved, if the problem of the “gap” is conceptualized as merely one of developing appropriate “measurements.” Second, this becomes even more apparent, once it is clearly stated that there is no one gap between theory and measurement, and that in particular not all theories of justice may require large-scale measurements. Bojer quotes Sen's statement that the capability approach requires “a generally accepted list of valuable functionings (that) must be determined by open, public debate and reflection” (Bojer 49). But the demand for open debate coupled with a sensitivity for differences between people and their circumstances puts a question mark over the need for, and possibility of, large-scale measurements that would allow one to identify the least advantaged by means of the yardstick of income. Rather, “open and public debate” seems to call for the creation of relatively local processes for an accurate understanding of equality (and as such processes hardly exist today, it so to speak requires a novel “social world”). Put differently, empirical analysis will in this case be much concerned with questions of democratic process.

As a result, it seems to me that Hilde Bojer puts the spotlight on an important question regarding the relation between theory and empirical analysis in the field of distributive justice, and that she offers valuable discussions of the works of philosophers and economists. To think further about the objective of bridging the gaps between distributive justice and empirical analysis, it may be valuable to take into account the epistemic background out of which the discussions of distributive justice in the second half of the twentieth century have emerged so as to uncover the assumptions producing the “gap,” and in particular so as to give the call for measurement one place among other questions of political scale, democratic institutions and process that would correspond to a wider notion of empirical analysis required for the task.