In Anarchy, State, and Utopia, noted anarchist/libertarian philosopher Robert Nozick argues that patterned distributions of income necessarily violate the principle of free exchange. Nozick supposes that there is some "patterned" distribution of income, i.e. some distribution that is objectively determinable. For example the notion of strict equality of income I've been writing about is certainly objectively determinable: I do not need to examine people's subjective preferences to determine what their incomes are, just the number of hours they actually work. He then supposes that a large number of people subjectively choose to freely pay Wilt Chamberlain (a famous basketball player of the 1960s) some money. Assuming enough people freely choose to do so, then Chamberlain will have much more money than the patterned distribution mandates. Thus, the patterned distribution forbids people from making choices that seem unproblematic.
There are a number of possible responses to Nozick's problem. The most obvious (but perhaps least intellectually satisfying) is to declare it a pseudo-problem, akin to the Omelas problem: the problem contradicts our moral intuition only because it makes deeply counterfactual assumptions about the world, but our moral intuitions are shaped by how the world actually is. Why would anyone want to just give Wilt Chamberlain money? Remember, almost all people who have very high incomes due to fame (athletes, musicians, actors, etc.) are embedded in industries that are paradigmatic of market failure. Even if there might be some good reasons for market failures, sports, popular music, movies, television, etc. are oligopolies and monopsonies, very far away from the perfect competition that is the core of the moral justification for capitalism. In our current system, the basis of our moral intuitions about economics, people don't freely choose to just give people like Chamberlain money, they "freely" choose to exchange their money for a good in a monopoly-controlled market; we cannot easily conclude that, absent these monopolies, they would choose to just part with their money (their share of the social product) out of benevolence or admiration.
Although the choice seems implausible, it is not impossible that people really would choose to voluntarily give their money away to admirable strangers. Thus, another resolution to Nozick's problem is to simply relax the pattern. The patterned distribution sets boundaries on the distribution of income, but permits deviations within those boundaries. Hence, my construction of nearly strict equality, which permits deviations from equality that satisfy certain criteria: deviations (1) are completely voluntary, (2) cannot accumulate, and (3) self-correct in the long run.
With certain boundaries, Nozick's problem fits neatly into these criteria. First, if people freely choose to give someone money (not as a condition of exchange), then doing so clearly fulfills condition (1). Second, a prohibition against absentee ownership means that even if Chamberlain did receive a lot more money than most people, he would have to spend it, which would eventually return the distribution to equality; Chamberlain could not use the extra money to secure lasting economic privilege.
The third criterion is more difficult to satisfy. On the one hand, if people really were willing to give someone like Chamberlain money, then people are going to want to do the same thing; removing the barriers to competition that are manifestly present in modern society will tend to reduce "Chamberlain inequality" over time. However, top quality "superstar" athletes (and popular musicians and actors) seem extremely rare: I don't think the NBA is limiting the number of superstar athletes, and people seem to derive a lot of pleasure in watching the very best ply certain trades. No matter how much money we give to "superstars," by definition there can be only a few.
But notice here that "superstars" violate the fundamental capitalist paradigm that high prices serve as a signal to incentivize entry and return a market to perfect competition: we cannot have a perfectly competitive market in "superstars," however much money we give them.
I suspect that in practice, Chamberlain inequality will persist the longest, and perhaps forever. Still, if we at least enforce absolute freedom (i.e. people do not exchange but give superstars money), and prevent accumulation and absentee ownership, we could tolerate Chamberlain inequality for a long time without terrible consequences.