Inequality of Unfairness?

http://www.nature.com/articles/s41562-017-0082

People are more concerned with economic unfairness than economic inequality. 

"we argue that humans naturally favour fair distributions, not equal ones, and that when fairness and equality clash, people prefer fair inequality over unfair equality." When the data are examined more closely, the study argues, "it turns out that there is no evidence that people are actually concerned with economic inequality at all."… when people are asked to distribute resources among a small number of people in a lab study, they insist on an exactly equal distribution. But when people are asked to distribute resources among a large group of people in the actual world, they reject an equal distribution.

The findings support our proposals that socialism is not about dividing into equal shares but dividing according to needs (fairness) but the pro-capitalists are using the results to justify the current inequality of society.

So should we now focus on what we mean by an egalitarian system?