We live surrounded by inequality. Some have wealth, health, education, satisfying occupations. Others get poverty, ill-health and drudgery. The Conservative reaction, personified by David Cameron, is to promote social mobility and meritocracy.

History shows this will fail to increase mobility rates. Given that social mobility rates are immutable, it is better to reduce the gains people make from having high status, and the penalties from low status. The Swedish model of compressed inequality is a realistic option, the American dream of rapid mobility an illusion.

How do we know we cannot change the rate of social mobility? One piece of evidence is what happened to social mobility rates as England moved from the pre-industrial world of squire and servant, to the modern noisy meritocracy of the rude boys of finance. What happened as the political franchise was extended in the early 19th century? What happened as mass public education was introduced later in the century? What happened as education, healthcare and pensions for the poor were financed by taxation of the incomes of the wealthier? The answer is that social mobility remained at its slow pre-industrial pace. Tracking the status of rare surnames across generations we can measure social mobility rates for wealth and education in England from 1670 to 2012. The descendants of earlier elites only become average after about 10 generations, or 300 years. Status persists as strongly in the Cameron meritocracy as in pre-industrial England. Lineage is destiny. At birth, most of your social outcome is predictable from your family history.

An illustration of the power of lineage even in modern England comes even from the first names children receive at birth. Naming your daughter Jade means she has one hundredth the chance of attending Oxford as a girl whose parents chose for her Eleanor. Similarly for Bradley versus Peter.

Is this just the survival of sclerotic olde England, where the dead hand of the past exercises an especially powerful grip? No. The modern US has rates of social mobility that are no higher than those of England. Elites and underclasses endure just as strongly as in the UK.

Even more surprising, in the model social democracy of Sweden, social mobility rates again are as slow as in England. Sweden has a class of people descended from its 18th century aristocracy who have distinctive, and legally protected, surnames: Leijonhufvud, Gyllenhaal, Rosencranz and von Essen, for example. Someone with such a surname is still, eight generations later, three or four times more likely to be a doctor or attorney, or to be in the royal academies, than the average Swede. The descendants of 18th century aristocrats are still wealthier than average, and live in the more expensive areas of Stockholm. Sweden is a better society to be lower class in, not because it offers rapid upwards mobility, but because the living conditions of the poor are better. Since the material gains from achieving high status are much less in Sweden, it also shows that you do not need the wide earnings inequalities seen in the US or UK to incentivise people to high professional performance.

More surprising even than the immobility of England, the US and Sweden is that of China. In 1949 the Communist revolution drove out, killed, or expropriated the old upper classes. Their descendants were subject to further persecution in the cultural revolution, where those of suspect background were even denied higher education.

Yet surname evidence again shows that the descendants of the pre-revolution elites crop up unexpectedly frequently among high government officials, university professors, and students at elite universities.

Why is social mobility so resistant to change? The reason is the strong transmission within families of the attributes that lead to social success. Given this, government policy can do no more than nibble at the fringes of status persistence.

Marriage is highly assortative in all societies. Even in 19th century England, where women had no formal educational status and little control of wealth, women married men who were very like their fathers or brothers in wealth and education.

With parents having such similar attributes, children resemble strongly their parents in social capabilities. Now in a world where women have as many status markers as men, we may even see more highly assortative mating, and even a decline in social mobility rates.

How then can we reduce the inequalities associated with status? There is the obvious mechanism of redistribution through the tax system. Provide minimum levels of consumption to all, funded by transfers from the prosperous.

But also you can create labour market institutions that compress wages and salaries, as in the Nordic societies. In Denmark, for example, workers in fast-food chains such as McDonald’s earn the equivalent of nearly £14 an hour under collective bargaining, more than double the average UK fast-food wage. Economists worry that such interventions in the free market will reduce output. Income per capita in Nordic societies, however, is just as high as in the UK.

You can also structure educational systems to narrow the social rewards to those at the top of the ability distribution, or to amplify these rewards. In the UK we choose at present to admit to Oxford and Cambridge the top 0.4% of each cohort based on academic performance. This is a highly meritocratic system. But it is also a system that ensures that Oxbridge attendance confers high status. The beneficiaries of this status are mainly the children of the English upper classes, given limited social mobility.

A perfectly feasible alternative would be to define a much larger share of students equally able to benefit from an Oxbridge education – all those with 3 A grades at A-level, for example – and then admit from this pool at random. This system, similar to the one used in Dutch medical schools, would widen the pool from which the Oxbridge elite are drawn to 3% of each cohort. Proportionately more students without elite family lineages would be admitted. Oxbridge would be less elite, and we would have a less socially divided society. Other European societies – Germany, the Netherlands, and Italy for example – have maintained much less hierarchical education systems. There are important choices we can make about how hierarchical we make our educational systems, and consequently how much status differentiation we build into society.

The message here is that while mobility seems governed by a social physics that defies easy intervention, the magnitude of social inequalities varies considerably across societies, and can be strongly influenced by social institutions. We cannot change the winners in the social lottery, but we can change the value of their prizes.