# **1 Introduction**

Two foundational contributions to the modern literature on poverty measurement, Sen (1976) and Foster et al. (1984), were motivated at least in part by a concern to introduce poverty indices that were sensitive to inequality. Sen’s paper begins by noting that the headcount measure is ”...completely insensitive to the distribution of income among the poor” (p.219). Foster et al. introduce a parametric class of measures which, crucially, ”satisfy the transfer sensitivity axiom” (p.763).

But whereas sensitivity to inequality of _outcomes_ (e.g. income or consumption expenditures) has been widely incorporated as a desirable property for poverty indices, we are aware of no poverty measures that are sensitive to inequality of _opportunity_ . This stands in contrast to the influence that the theory of inequality of opportunity, and in particular its formalization by John Roemer (1998), has had on the measurement of inequality more generally.

Since Rawls’s (1971) _A Theory of Justice_ , a number of moral philosophers and social choice theorists have argued that not all income differences are identical from a normative or ethical perspective. In particular, income differences due to personal choices, or otherwise attributable to personal responsibility, may be judged to be less morally objectionable than differences due to pre-determined attributes - such as gender, race or family background - over which individuals have no control. Based on increasingly sophisticated variants of this basic distinction, a number of authors have argued that egalitarian justice ought to focus less on the space of outcomes, and more on the space of opportunities. See, for instance, Dworkin (1981a, b), Arneson (1989), Cohen (1989), Roemer (1998), Fleurbaey (2008), and Fleurbaey and Maniquet (2011).

Building on that theoretical literature, other authors have suggested ways in which inequality due to pre-determined circumstances can be appropriately quantified, for the purpose of measuring inequality of opportunity in real labor-force or household survey data. See, for example, Bourguignon et al. (2007), Lefranc et al. (2009), Checchi and Peragine (2010) and Ferreira and Gignoux (2011).

Given the close proximity between the literatures on inequality and poverty measurement, it is surprising that the influence of opportunity egalitarianism on inequality measurement has not, to our knowledge, extended to the measurement of poverty. After all, if our assessment of poverty is informed by the extent of inequality in society, and if our judgment of inequality is in turn affected by whether income differences arise from personal responsibility or pre-determined circumstances, then why should our judgment of poverty not be similarly affected by that distinction?

This paper asks whether poverty measures that are sensitive to inequality of opportunity are conceptually meaningful, and empirically relevant.<sup>1</sup> Conceptually, sensitivity (or aversion) to inequality of opportunity implies two fundamental changes to the standard axiomatic approach. First, partitioning the population into types (circumstance-homogeneous groups) can lead to violations of the general anonymity axiom. Second, aversion to inequality between types, but not within them, raises problems for the transfer axiom: transfers within and across types can be valued differently, and a potential conflict arises between outcome-inequality aversion and inequality-of-opportunity aversion.

We propose logically consistent solutions to these challenges by introducing relatively modest modifications to the standard set of axioms in poverty measurement.

> 1The paper is concerned exclusively with uni-dimensional poverty. An analysis of opportunitysensitive measures of multidimensional poverty is left for future work.

2