A former ministerial colleague of Iain Duncan Smith once put it to me that he was a striking example of cognitive dissonance: that is, of holding two or more contradictory beliefs in his head at any given moment. On the one hand, he genuinely sees himself as the great liberator of the poor, the man who wept at Britain’s modern-day penury on Glasgow’s Easterhouse estate; on the other, he is the champion of policies that have driven some of the poorest people in society into despair.

Today’s newspapers obsess over the so-called “purge” of middle-aged white men (given the composition of the cabinet, how could it be anything else); today’s Daily Mail front page indulges the newspaper’s often flagrant sexism by discussing Esther McVey’s thighs. But the real reshuffle story has been the astonishing survival of work and pensions secretary Iain Duncan Smith, the most disastrous custodian of the welfare state since its postwar foundation: a man whose policies have caused suffering while failing catastrophically on their own terms.

His department has just released its “Evaluation of Removal of the Spare Room Subsidy”, or the bedroom tax as it is more commonly known. The stated objective was to encourage tenants to downsize to smaller properties to free up space. On that measure, it could hardly have failed more: just 4.5% of tenants able to do so have moved. Landlords with the smallest number of tenants hit by the bedroom tax have downsizing rates around four times higher. As the report says, “this suggests that landlords with the highest proportion of affected tenants will have more difficulties in meeting the demand for downsizing.”

In clinical researcher language, the report is an insight into the human misery of this failed policy. Fifty-seven percent of those affected report cutting back on household essentials; six out of 10 are cutting back on food or heating; around a quarter are borrowing money; and four-fifths are finding it “very” or “fairly” difficult to make up the financial loss. Only four out of 10 victims have paid the extra money in full.

We already know that around two-thirds of affected households include disabled people, and that in, say, Newcastle, there were just 50 smaller properties available for 7,000 households hit by the bedroom tax when it was introduced. The tax forces poor and disabled people to cough up money they do not have, and to downsize to smaller properties that do not exist. A humane government would have blamed the overcrowding crisis on the failure of successive administrations to build council housing, rather than on disabled people hoarding “spare” bedrooms. Not this one.

The bedroom tax is in competition with an impressive litany of Iain Duncan Smith’s failures. Take universal credit which, according to that notorious socialist hotbed the Economist, will not cover all 5.3 million working-age welfare recipients until 2614 if it keeps going at the current rate. Or the employment and support allowance reassessment of disabled people, which has stripped support from vulnerable people, many of whom have won their benefits back on appeal – but only after a traumatising experience and at huge cost to the taxpayer. Then there’s the shift from disability living allowance to the personal independence payment, which last month the public accounts committee savaged as a “fiasco”, leaving many facing six-months delays – and the dying having to wait for weeks for support.

Duncan Smith hoped to be remembered as a great reformer, the man who freed the poor from a welfare state that encouraged dependency. But he should be remembered as the man who claimed that work was the route out of poverty while representing a constituency with the second-highest number of low-paid workers in Britain; the man whose incompetence and failure was paid for by the misery of some of the most vulnerable people in society. Spare a moment for some of the sacked Tory ministers: they must be asking – like so many of the rest of us – “what on earth does this man have to do to lose his job?”