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...by encouraging open marriage?

The expectation of marital fidelity is a mechanism for encouraging men to stick around and raise their children.

What do you expect to replace that system of incentives if you don't want to see families disintegrate? In the segments of society where expectations of fidelity are very low men tend not to be deeply involved in raising children. Why would they be?

The breeding strategies natural to men and women are very different. Women can only have a very limited number of children so their natural strategy is to strongly protect those offspring. Men on the other hand can sire any number children - they can advance their genes by simply playing the field. Men don't need to raise raise children to attain biological success, as women do.