Here actually is the problem with using relative poverty as a measure:
Compared to the 1960s, China today has higher income inequality,
but also incomparably lower levels of material poverty. By Brady’s
definition, China was less impoverished in the near-starvation years
of the 1960s than it is as an economic superpower today. According to
the OECD, during the last three decades the share of Chinese living
in absolute poverty dramatically declined from eight in ten to one in
ten (Garroway and de Laiglesia 2011). During the same period, relative
poverty, measured exactly as Brady measures it, roughly doubled.
Although inequality and relative poverty are not irrelevant for measuring
the well-being of a society, we should be apprehensive about a measure
of poverty that is incapable of detecting the largest decline in material
poverty in human history.
As pointed out, a measure of poverrty that not just ignores, but actually gets the sign wrong on, the largest reduction in poverty in the history of our species is of limited value.
Not of no value: as Adam Smith's linen shirt example shows. If you can't afford a linen shirt, but not being able to afford a linen shirt marks you out as being poor, then in that society you are poor if you cannot afford a linen shirt. But as our Chinese example shows only worrying about relative poverty is simply nuts.
Which leads us to something of a conclusion: it's fine to consider the distribution of incomes within a society. But we do it rather too much with the constant political obsession over relative poverty. We need to be paying a lot more attention to absolute standards of living: most especially how these change over time. Most specifically I'm thinking about the effects attempts to reduce relative poverty might affect our ability to increase absolute standards of living in the future.
For as ever in economics there is actually no solution. There are only a series of trade offs. We could, obviously, confiscate all of everyone's money and share it out equally. This is not going to make our children richer than ourselves equally obviously. Similarly, no one at all is suggesting that there should be no taxation at all to aid the lame and the halt of our society even if that might increase future growth rates. It's a matter of balance and to my mind there's much too much attention being paid to the relative part and not enough on the absolute incomes of the future.