When Nicola Sturgeon delivered her inaugural speech as leader of the Scottish National Party a year ago, she made a promise. She said: “Tackling poverty and inequality – and improving opportunity for all – will be my personal mission as your First Minister.”

In Brighton in September, meanwhile, Jeremy Corbyn delivered his first address as leader to Labour’s conference. He talked of values and said: “It is because I am driven by these British majority values — because I love this country — that I want to rid it of injustice, to make it fairer, more decent, more equal.”

Battle was joined. Both politicians would insist they were restating principles to which they have held all their lives, but when Mr Corbyn spoke to Labour in Scotland yesterday one theme was already familiar: the SNP is not “a left-wing alternative”. For anyone troubled by “rising inequality, rising child poverty and widening health inequalities”, there can be only one choice.

Well, he would say that. In fact, Mr Corbyn has no choice but to say that, or something like it, if his party is to survive as an electoral force in Scotland. Set aside the issue of independence and the contest between Labour and the SNP is a battle for ownership of what sounds like common ground. One word sums it up: inequality.

Labour’s leader will tell you that the Nationalists have failed and are failing. The SNP will retort that Mr Corbyn and his riven, chaotic party cannot succeed. The prize is voters’ trust. The shared belief is that inequality – addressed through socialism, through social democracy, through a genuine left-wing alternative – is the key to that trust.

It is, in any case, one of the issues of the age. You might wonder why it ever ceased to be an issue, but the fact remains that an otherwise obscure French academic named Thomas Piketty set the world of economics on its ear in 2014 – and produced a bestseller – with a 700-page study of inequality, its history and consequences.

In the United States, meanwhile, the gulf between the rich and the rest is enshrined in shorthand: “the 1 per cent”. People otherwise rendered comatose by statistics have heard of the Gini coefficient and how it measures inequality. Here, George Osborne, the Chancellor, runs into deep trouble because his attempted reform of tax credits would deepen inequalities profoundly, brutally, and at a stroke.

Mr Osborne would deny any such intention, of course. Like the Prime Minister, he would say that he is all for equality, but only if the words “of opportunity” are attached. David Cameron made the distinction in an article for the Guardian on Monday while asserting that he had committed the Conservatives to “finishing the fight for real equality”. He was talking about discrimination rather than disparities in wealth and income, but the desire to appropriate a word was plain.

Why, though, does it matter? For those on the right, like Mr Cameron, what they term equality of outcome causes philosophical problems. They doubt that poverty and inequality explain much, or much that is important, about human nature. They reckon that because talent is not distributed equally some will always do better economically than others.

Interference by governments is therefore an assault on individual freedom and bad for a society’s economic health. An acceptance of inequality allows winners and losers. Functioning markets, like prosperity for all (as and when it trickles down), depend on those winners. Besides, who can – or should – argue with human nature?

Equality of opportunity is probably easier to glimpse at Eton College than in most other places, but Old Etonian right-wingers like Mr Cameron do not depend entirely on hoary notions of individualism. Now and then they make practical points about economic inequality.

One favourite line is to say, simply, that it doesn’t matter. Or rather, that inequality doesn’t measure anything important. The fact that one person’s income is 300 times the average is only relevant if the average counts as hideous poverty. By this school of thought, the idea of inequality, of relative difference, can actually hinder attempts to help the poor.

The arithmetic is simple, if too rarely mentioned. It produced an apparent paradox in the aftermath of the bankers’ Crash when poverty and inequality levels actually fell. Thus: if your poverty threshold is 60 per cent of median household income, as it is in the UK, a big fall in average incomes will obviously push your “poverty line” downwards. That’s what happened after 2008.

Clearly, it can work in reverse. If wages are up and the median household income is rising, the number defined as poor can increase and yet be better off than before. So why fixate on inequality as such? If poverty can only be relative – or rather, can only be measured with any accuracy in relative terms – why make a fetish of equality?

One answer: it matters to people. What Mr Corbyn calls fairness and Ms Sturgeon understands as opportunity for all are glimpses behind the myth of equality of opportunity. If you observe that the top 10 per cent of UK households have 44 per cent of the wealth while the poorest 50 per cent have 9.5 per cent, many guess – an educated guess – that there is more going on than sturdy individualism and talent paying off.

In any case, inequality measures more than relative wealth and relative poverty. Money or its absence means power or powerlessness, control over a life, a sense of well-being, even happiness. Despite ups and downs, the UK’s GDP has more or less doubled since 1970, but the “satisfaction with life” reported by British people has stayed pretty much the same. In fact, if you believe a New Economics Foundation (NEF) study from 2004, we were all a lot happier in 1976.

To those who can remember, it sounds perverse. There might have been a heatwave and some decent music that summer, but there was also a famous drought, a chaotic government, endless industrial unrest, and a 35 per cent basic rate of tax. But the NEF was trying to make a point, since reiterated by others, about things overlooked when politicians talk only of GDP and “national prosperity”.

In 1976, crime was lower, traffic was less, public investment was higher, and income inequality was as narrow as it would get. In 1938, the top 10 per cent had 34.6 per cent of available income. That would fall to 21 per cent in 1979. In the 1980s, by no accident in those Big Bang Tory years, there was a sharp reversal. The figure reached 27 per cent by the decade’s end. There have been slight advances and reversals in inequality since, but the top 10 per cent’s income share is back at 31 per cent.

This is understood by working people. With money comes power for the few and helplessness for the many. Technical criticisms of the Gini coefficient mean little beside the reality of food banks. Absolute equality of outcomes might hold no appeal, but fairness matters more than ever. Ms Sturgeon and Mr Corbyn – and the Chancellor – are judged accordingly.