As I was bundling up a cosy red coat that my five-year-old has outgrown to donate to charity last week, I gently explained to her that while we could just buy ourselves new, warm clothes when winter draws in, not everyone is so lucky.

Not for the first time, I was struck by how obvious it seemed to her – not just that other children shouldn’t have to go without, but that we have more than enough, and that that makes others’ deprivation more shocking. No child should go cold and hungry at all, but in a society where plenty is the norm, it seems peculiarly senseless.

It’s a naive response, of course, but many theorists, not least the great philosopher of American liberalism, John Rawls, have believed that humans have, beneath the cynicism we accumulate with age and experience a deep, innate sense of justice, of what is “fair”. A central part of this is that no one should be allowed to fall too far behind. To a five-year-old, a society in which some kids have a wardrobe full of party dresses and others go without a coat fails the “it’s not fair!” test.

Measures of relative poverty are a statistical way of capturing that. The 2010 Child Poverty Act, which required the government to report on how many children live in households whose income is less than 60% of the median, was a way of enshrining in law the idea that society should hold out a helping hand to economic stragglers. Labour used tax credits and benefits to systematically pursue that aim, and child poverty on this measure fell from 26% in 1998 to 17% in 2013.

But with £12bn of welfare cuts in the pipeline, Tony Blair’s target of eradicating child poverty – defined as cutting the number of children in relative poverty to 10%, and in absolute poverty to 5% – by 2020 looks hopelessly unattainable.

Family income matters: kids from poorest families are more likely to struggle at school and to suffer health problems

Rather than face up to that, the Department of Work and Pensions is moving the goalposts – or, more accurately, playing a different game altogether. The welfare reform bill, now passing through the House of Lords, will see the scrapping of income-based measures, including relative child poverty, as a yardstick by which policy can be judged. Instead, the DWP will report on GCSE results and the number of children in workless families. These are important gauges of children’s life chances, and point to the importance of doing more than just shovel benefits at the needy, but given the well-documented rise of in-work poverty, they don’t tell the whole story.

Like many statistical constructs, measures of relative poverty are imperfect, but many of the arguments made against them are misguided. Iain Duncan Smith says income-based poverty measures are crude, and direct policy towards achieving “poverty plus a pound” – as if shifting a few quid a week into parents’ pockets solves society’s problems (though his fist-pump in parliament when George Osborne announced his “national living wage” showed that he knows very well the importance of raising incomes).

In Duncan Smith’s world, social mobility is more important: it doesn’t matter where you start from, as long as you can get up and out. But family income really matters: evidence shows, for example, that kids from the poorest families are more likely to struggle at school and to suffer health problems.

The other charge made against the child poverty target is that it’s a relative, not absolute measure – so, the lazy argument goes, the bar is always rising as society gets richer. Some of the assumptions underlying that idea are just wrong (not least because the act also made the government report progress against other measures, including absolute poverty).

The median income – unlike the average, or mean – is not lifted by a sharp rise in earnings at the top of the pile, for example. Think about an economy with only three families in it, earning £10k, £20k and £30k respectively. The median income is £20k, and the family at the bottom is in relative poverty because their income is less than 60% of the median. Doubling the income of the richest household makes no difference to that – the middle is still the middle. But giving the poorest family an extra £2k would shift them up to the poverty line.

If you imagine Britain’s 20 million or so households lined up poorest to richest, the median is probably as good a measure as any of what counts for the norm. Yes, the norm shifts over time, but so it should: our understanding of the necessities for a decent standard of living change with society. My grandparents grew up without a fridge; that doesn’t mean I think any family should go without one in Britain in 2015.

Dickensian squalor was so morally objectionable, as that great plucker of the heartstrings knew well, because it co-existed with the Victorian splendour that should have made decent standards of living affordable. Scrooge could so easily have made Tiny Tim’s Christmas, but chose not to – at first.

Research by Kitty Stewart at the London School of Economics shows that almost 90% of respondents to the government’s consultation thought we should retain an income-based measure of poverty. It may be crude and imperfect, but it focuses minds; and the relative poverty measure enshrines the idea that no child should be left too far behind – and everyone should be able to afford a winter coat.

Duncan Smith professes to care about the causes, not just the symptoms of poverty, but as the Child Poverty Act is systematically dismantled, it’s increasingly hard to believe this government cares at all.