It seems women are more in the role of enforcing social norms:

While there is ample evidence of a society-wide cooperation norm, it is not as clear who upholds this norm. In the present paper, we investigate whether there are gender differences with respect to norm enforcement. We let 1403 subjects play games of punishment and reward, individually or in groups with varying gender composition. Broadly, the results indicate that there are no clear gender differences: men are about as inclined as women to punish norm-breakers. However, behavior is context-dependent: men acting among other men are less inclined to uphold a cooperation norm than are women, or men in gender-mixed groups. (more)

A self-protective goal increased conformity for both men and women. In contrast, the effects of a romantic goal depended on sex, causing women to conform more to others’ preferences while engendering nonconformity in men. Men motivated to attract a mate were particularly likely to nonconform when (a) nonconformity made them unique (but not merely a member of a small minority) and when (b) the topic was subjective versus objective, meaning that nonconformists could not be revealed to be incorrect. These findings fit with a functional evolutionary model of motivation and behavior, and they indicate that fundamental motives such as self-protection and mate attraction can stimulate specific forms of conformity or nonconformity for strategic self-presentation. (more)

It isn’t clear how innate is this female norm emphasis, but if innate then female nature probably deserves more of the credit for enabling the farming revolution, and also probably more of the blame for hindering the industrial revolution.

Added 16June: One more:

Why do men have more lenient ethical standards than women? … Whereas men’s ethicality judgments were affected by the identification manipulation, women’s judgments were not. … Fixed [achievement] beliefs predicted lower ethical standards, particularly for men. In combination, these findings suggest men are more pragmatic in setting ethical standards than women. (more)