Stereotypically, women are attracted to rich men. Women also have less earning power than men (modulo the difficulties of exactly comparing earning power).
The traditional narrative has the causality in the following direction: because women face institutional barriers in earning lots of money, they must seek out men with money.
However, we could hypothesize a different mechanism: in a hypothetical society in which women do not face barriers in earning lots of money, they have less incentive to seek out men. This will result in less couples, less children, population decline, and the society will implode on itself, resulting in either extinction or change in society. Therefore, only societies that place barriers on women from making money (or more broadly, create incentives for coupling) will survive: kind of a social Darwinist argument applied to societies competing against each other instead of individuals competing against each other. This hypothesis does seem to be supported by data that increasing education for women (and thus increasing their earning power) correlates with a declining birth rate, and more egalitarian societies having lower birth rates.
There are some leaps of logic in the argument:
The biological imperative to procreate is pretty powerful. We have not described any force powerful enough to override the imperative to explain declining birth rates.
Regardless of their own earning power, women could still continue to be attracted to rich men, because, all other things being equal, more money is more better. Therefore, whatever psychological mechanisms that program a woman's ideas of what she finds attractive could still continue to operate in more egalitarian societies, and still drive women to couple. We have not described what those mechanisms are and why they should stop operating.
We revisit another aspect of this model. If men's attractiveness in the eyes of women is determined by their wealth, then the biological imperative to procreate will incentivize men to earn more money, so to be more economically productive. A more productive society will again win Darwinistically over one which is less productive. Do more egalitarian societies see less productivity in men? Is the loss of their productivity offset by the increased productivity in women?
I strongly suspect there is still much more going on, including game theory.
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