In his conference speech, David Cameron promised to make Britain a “land of opportunity”.

If opportunity means social mobility then he has his work cut out, because Britain is one of the most socially immobile countries in the western world. But can you guess which country is at the other end of the scale?

You might think it’s America – the original land of opportunity. In fact, it’s Denmark, closely followed by Norway, Finland and Canada. America, meanwhile, is down at the bottom of the mobility league with Britain.

These rankings are for what is called relative social mobility. If you divide the range of household incomes into equal fifths (known as quintiles), relative mobility measures the likelihood of a child born to a household in a particular quintile moving up or down to a different quintile in adult life.

In an article for Prospect, Phillip Collins argues that politicians have got relative social mobility confused with absolute social mobility:

“A paper in 2005 by Jo Blanden, Paul Gregg and Stephen Machin of the London School of Economics has enshrined 1958 as the golden year for social mobility. The cohort born in that year, whose lives have been followed by the British Household Panel, appear to be the last generation in Britain for whom movement up the social and income scale was a genuine possibility. A comparison with the 1970 cohort suggests that something happened in the 1970s to suddenly close off… opportunities…”

Politicians of all stripes have latched on to this apparent slowdown in social mobility. There are rightwingers who blame it on the demise of grammar schools, leftwingers who blame Margaret Thatcher (of course they do) and Nick Clegg has stuck his oar in too.

But, here’s the thing – the reason why absolute social mobility grew rapidly and then came to a plateau was because of a one-off, unlikely-to-be-repeated economic transformation:

“The structure of the labour market changed markedly during the 20th century. This is the explanation for the apparent stalling of social mobility. It is telling us nothing more profound than that the rapid growth of professional employment, which began after the Second World War, has slowed down. In 1900, 18 per 9cent of jobs were classified in the top two social tiers. By the time John Braine wrote Room at the Top [in 1957], that had risen to 42 per cent. But the demand for lawyers and accountants is not inexhaustible.”

In other words, the reason why so many people were able to ‘better themselves’ was because better jobs were available in greater numbers. This was a rising tide that really did float all boats, enhancing opportunities for all classes, but not necessarily enhancing opportunities to move between classes (in the sense of income quintiles):

“The odds on a working class boy making it have hardly changed at all throughout the 20th century. A boy born into the working class is no more likely to make it into the middle class now than he was in 1900. A child who is born middle class is 15 times more likely to end up middle class than a child who is born into the working class. These odds are exactly the same as they were a century ago.”

Therefore, any politician who wants to increase social mobility has to answer one or other of the following questions: If it is absolute social mobility you want to increase, how do you propose to bring about a massive new expansion in well-paid jobs? If, however, it is relative social mobility you’re concerned with, do you realise that it is, by definition, a zero sum game?

No one can go up a relative income scale unless someone else goes down. The reason why this happens more often in Denmark than in America is because the absolute distance between the top and bottom of the scale is shorter, therefore requiring a smaller change in people’s living standards to move between quintiles.

So, if you want to see more relative social mobility, you either need a plan for massively reducing income inequality – or a plan for ensuring that more children from middle and upper class households suffer a massive reduction in their living standards. Try selling that one on the doorstep.