At least, much of what we're told about inequality is wrong if we go off and have a look at revealed preferences that is. Here's what is now, on the left side of the political aisle, what is generally accepted as a truism about inequality :
Inequality matters because people evaluate their economic well-being relative to others, not in absolute terms.
And it's true that if you go look at some of the experiments done on this point then there's evidence to support the idea. Ask college undergraduates (they are used because they are extremely cheap and in high supply in the sort of environments that economists inhabit) whether they would prefer $50k a year while everyone else gets $25k, or $100k while everyone else gets $200k, then the preponderance is for the lower absolute but higher relative amount. We can also think of reasons why this might be so: higher status for a male does get more babes.
However, this is also based on what people say. And it's one of those truisms of economics, known as "revealed preferences", that you shouldn't take at face value what people say. Instead, look at what they actually do.
And with this relative and absolute stuff about income we've got a very large data set: immigrants. And we see the big immigration flows as being people from poor countries coming to rich ones. So that's certainly people being concerned about aboslute incomes. But there's more than that. The immigrants from those poor countries tend not to be the poorest of those countries. It's not the landless Bangladeshi day labourer that turns up in Bradford. They simply haven't the basic economic resources to manage the move for a start. Rather, it's people some way up off the bottom of those poor societies that become the immigrants into the rich countries. Where they, at least to begin with, start off right at the bottom of the income and even social stratifications.
So what we do actually see, out in the real world, is tens of millions of people a year willing to reduce their relative wealth, their wealth or income with respect to the societies they live in, in return for a higher absolute standard of wealth and or income.
All of which is rather at odds with those experiments about the stated preferences of American college students. And as revealed preferences tells us, when we're considering evidence about what people say they would like and the actions we can see that they actually take, then it's the evidence about people do, not what they say, which should be given the greater weight.
All of which makes the importance given to relative wealth or income very much less important than some currently claim it is. Not that I think it has no importance: but that plain and simple fact that people do, voluntarily, move to lower relative incomes but higher absolute ones means that we cannot, just cannot, insist that only relative incomes are what we use to make decisions or measurements. The claim fails because it simply isn't true.