And what would that social institution be?

Over at Science Daily... there was a small article regarding the nature of mating between the two differing genders. It Was Brawn Over Beauty in Human Mating Competition, Anthropologist Says

Many researchers have considered mate choice the main operator in human sexual selection. They thought that people's mating success was mainly determined by attractiveness; but for men, it appears that physical competition among males was more important....

"On average men are not all that much bigger than women, only about 15 percent larger," said Puts. "But, the average guy is stronger than 99.9 percent of women."

Men are far more aggressive than women, and approximately 30 percent of men in small-scale foraging communities die violently

These ideas may seem to paint a rather bleak picture of human nature with men duking it out among themselves for most of human evolution. "Things are different for us now in many ways," said Puts. "It's heartening to think that human behavior is flexible enough that the right social institutions can increase equality and peace."(my emphansis)