"AMERICANS want to live in a much more equal country (they just don't realise it)". So says Dan Ariely, who, along with Mike Norton, found that Americans ridiculously underestimate the amount of inequality in their country. In reality, American society is staggeringly unequal: the top 20% hold 84% of the wealth, while the bottom 40% have just 0.3%. But according to Mr Ariely, Americans, whether liberal or conservative, rich or poor, prefer a wealth distribution that is more egalitarian than Sweden’s.

Mr Ariely’s data may seem to hold out hope for the egalitarian cause. Once you enlighten Americans with the facts about inequality in their society, the argument goes, they will be outraged and demand redistributive policies that reduce the wealth and income gaps. But Mr Ariely's approach is deeply flawed: he misinterprets his survey results and misunderstands the political philosophy of John Rawls, the theorist who inspired his inquiry.

Don't get me wrong, extreme inequality is objectionable for all sorts of reasons. But we cannot conclude from Mr Ariely’s data that Americans find these reasons persuasive or that they would support measures to reduce it. Americans still believe, despite strong evidence to the contrary, that the American dream is alive and well.

Let's look at part of Mr Ariely's study. Imagine that you, like his subjects, were asked which of the following two wealth distributions you preferred to enter, assuming you had an even chance of ending up in any of the five slices:

Who in the world would prefer to chance it with the distribution on the left? Even Paul Ryan might opt for democratic socialism under the circumstances. Mr Ariely reports, not shockingly, that 92% of his respondents preferred to join the distribution in the fictional “Equalden” (on the right) to that which obtains in America (on the left), including nine out of ten Republicans. He concludes that “the political discourse could benefit from a Rawlsian approach” whereby public policy is guided by “our common goal: a much less extreme level of inequality.”

Opposition to extreme inequality is a rallying cry on the left, but it doesn’t always mobilise the troops, as William Galston observed recently. I’m with Mr Ariely about the vices of inequality, and Rawlsian principles, properly applied, can illuminate the fiscal debate. But Mr Ariely’s particular use of Rawls misreads both the American zeitgeist and "A Theory of Justice".

Mr Ariely’s first error is to misapply Rawls’s “veil of ignorance”. Rawls imagines individuals blinding themselves to facts about their particular talents, class, race and gender when developing principles of justice for a political society, not when selecting among pie-chart distributions. Now consider Mr Ariely’s question to his subjects:

[I]magine that if you joined this nation, you would be randomly assigned to a place in the distribution, so you could end up anywhere in this distribution, from the very richest to the very poorest.

Rawls makes clear that this is exactly the wrong question to ask. Mr Ariely’s query twists a Rawlsian project to develop the outlines of a just society over time for everyone into an egoistic individual calculation of where I would be better off today.

More fundamentally, Mr Ariely conflates the Rawlsian pursuit of distributive justice—“a fair, efficient, and productive system of social cooperation [that] can be maintained over time, from one generation to the next”—with allocative justice. This may sound like a semantic distinction. It isn’t. Think of it as the difference between cutting up a pizza and giving everyone slices (allocative justice) and developing principles according to which various amounts of pizza end up on people’s plates (distributive justice). In the latter case, no allocator divides the pie for everyone else.

For Rawls, “a distribution cannot be judged in isolation from the system of which it is the outcome”. A Rawlsian would thus have no answer to Mr Ariely’s normative question. We cannot assess the relative justice of the pie charts for Equalden or America until we know the circumstances that produced each. If the lovely distribution in Equalden was achieved by curtailing religious liberty, compelling people to work in careers of the government’s choosing or defining social roles according to race or gender, it would be a Rawlsian nightmare despite the nice-looking distribution. Likewise, if the American level of inequality could be shown to maximise the position of the least advantaged—as unlikely as that may be—it would be unobjectionable under Rawls’s so-called Difference Principle.

Mr Ariely’s single-minded focus on equality as a concept that can exist in isolation from other social goals introduces more problems with his argument. If his survey had truly inquired into inequality “in terms of its effect on society as a whole”, as he claimed it did, the study would have been incredibly valuable. But it did not. Mr Ariely simply asked people how much equality they preferred, without explaining the types of social goods that some degree of inequality can buy.

It would be very hard to argue that the extent of inequality we see today in America is necessary to benefit its least well-off citizens, much less that it maximises their welfare. As Joseph Stiglitz argues in his new book, the costs of extreme inequality include “an economic system that is less stable and less efficient, with less growth, and a democracy that has been put into peril.” No society with a poverty rate approaching 16% can be said to be doing all it can to raise the level of the most disadvantaged.

Mr Ariely’s heart is in the right place, but his survey doesn’t prove what he hopes it will. Americans aren’t yet convinced that extreme inequality is dangerous to our polity. They cling to the ideal of equal opportunity and the American dream even as these concepts increasingly lose any connection to reality. Instead of tricking survey respondents into a superficial egalitarianism, we need to continue to make the argument that fairness and productivity will be the rewards of a more equal America.