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Notes -
Imagine two equal sized groups of men and women. They have identical income distributions. Then, randomly match each of them to one of the other group. Couples where the male makes more are accepted; ones where he doesn't are rejected. Then repeat the process repeatedly.
You end up with most people being matched, but there being an income gap between the members of every couple, along with a group of low income single men and a group of high income single women. You could calculate the expected distribution of the income gaps (bounded by 0 at the bottom) and the expected size of the single groups by statistical characteristics of the original income distribution.
In fact, even if women earned more on average than men, if you repeated that same process, paired men would always have higher incomes than their female partner, by construction. You'd just end up with larger groups of singles.
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