What about the second argument—that strongly relative lines allow for “costs of social inclusion”?<sup>28</sup> It can be agreed that certain private expenditures assure participation in customary social activities.<sup>29</sup> However, one can question the (implicit) assumption that the cost of inclusion is a constant proportion of mean income. The social-inclusion needs of very poor people may well be low, but it is hard to see why they would go to zero in the limit. Very poor people may be highly constrained in their spending on things that facilitate their inclusion, and so be more socially excluded; but that does not mean that their social inclusion needs are negligible. The cost of a socially-acceptable linen shirt (in Adam Smith’s famous example) will be positive for the poorest person. Ironically, allowing for non-negligible social inclusion needs for the poorest leads us away from strongly relative poverty measures.

When the poverty line is set as a constant proportion of the mean or median, an equiproportionate increase in all levels of consumption will leave the poverty rate unchanged.<sup>30</sup> This is a questionable, even perverse, feature of such poverty lines; it is hard to accept that a process of economic growth that leaves inequality unchanged does not reduce poverty (Ravallion and Chen, 2010). By the same token, it is hard to accept that the incidence of poverty rises when someone at the poverty line gains (say) 5% of her income, but the overall mean increases by more than 5%.

Seemingly perverse poverty trends have been found using strongly relative measures. For example, the UNDP (2005, Box 3) (based on Nolan et al., 2005) shows how relative poverty measures for Ireland were rising despite higher absolute living standards for the poor. Another example can be found in Easton (2002), who argued that relative poverty measures for New Zealand were deceptive in showing falling poverty despite lower absolute levels of living for the poor. The UNDP (2005, p. 334) writes: “It is clear that when economic conditions change rapidly, relative poverty measures do not always present a complete picture of the ways that economic change affects people’s lives.”

> 28 Another common defense is that such poverty lines are more “comparable”; for example, UNDP (2005, p.334) writes that “To ensure comparability across high-income countries, most comparative databases...measure poverty on a relative basis.” The sense of the term “comparable” is unclear when the poverty line’s real value (by any agreed cost-of-living index) can be orders of magnitude larger in one date or country than another.

> 29 Probably the most influential exponent of this view has been Townsend (1979).

> 30 This stems from the fact that the headcount index (in common with most other poverty measures) is homogeneous of degree zero between the mean and the poverty line for any given Lorenz curve. Note also that, for a given Lorenz curve, the median is directly proportional to the mean (the constant of proportionality is _L_  (5.0)

> where _L_ ( _p_ ) is the Lorenz curve). Thus the strong relativity property also holds when the poverty line is a fixed proportion of the median.

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