I have to disagree here. A matrilineal society, as I stated in my previous comment, does in fact often give women more access to familial resources, as these are often given to women to be managed or inherited from women, by women. This is a common theme in matrilineal societies--women have significant power over family life. The matrilineal doesn't just refer to family names--but also the line through which resources are obtained. However, you will tend to find that men dominate the political sphere in these societies(where applicable), so they are not matriarchal.
Please make the linguistic distinction when discussing these terms. Power over family life is referred to by '-lineal' suffixes and power over politics in the public sphere is referred to by '-archy' suffixes. A person who supports a matriarchal society (real or imagined) may not support a matrilineal one (real or imagined) or vice versa. These would not be logically inconsistent positions. It is confusing when people disagree on the meanings of the terms themselves.
Please make the linguistic distinction when discussing these terms. Power over family life is referred to by '-lineal' suffixes and power over politics in the public sphere is referred to by '-archy' suffixes.
The distinction between private and public life is important in large communities. It seems probable to me that the distinction would be weaker in small communities, where family obligations and family-based authority are likely to be the root of all obligations and claims to authority.
ETA: I didn't mean for that to sound like a confident declara...
"In this study, we use a large-scale incentivized experiment with nearly 1,300 participants to show that the gender gap in spatial abilities, measured by time to solve a puzzle, disappears when we move from a patrilineal society to an adjoining matrilineal society."
It is presently a commonplace of Western culture that women are worse at spatial reasoning than men, and this is commonly attributed to intrinsic biological differences.
It turns out this may be highly questionable. A study in PNAS studied two nearby tribes in northeast India, one with a strongly patriarchal organisation, one with a strongly matriarchal organisation. Both share the same agrarian diet and lifestyle and DNA tests indicate they are closely related.
In the patriarchal society, women did noticeably worse on spatial reasoning. In the matriarchal society, women and men did about the same.
The authors carefully do not overstate their results, claiming only that they demonstrated that culture influences spatial performance "in the task that we study." However, this promisingly suggests quite a bit of room for improvement of measurable aspects of intelligence may be feasible with proper attention to culture and nurture.
What measurable aspects of intelligence do you attribute to genetic causes? Can you test it this well? How would you fix it and help people be all they can be?
News coverage: ArsTechnica.