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.

Hence often piously called matriarchal, as in "The Afro American family tends to be matriarchal"

In practice, "matrilineal" societies are often societies where no one knows, or much cares, who the father is. As our society becomes increasingly like this, the proposition that women benefit from this arrangement starts to smell funny. Men in a matrilineal society contribute substantially less to the support of women and children, and often the relationship is that between a pimp and his bitches: the women (plural) support the man (singular). The male contribution is frequently large and negative.

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 declaration. I'm really open to learning something here. Are the public and private spheres so distinct in smaller communities? I wouldn't expect them to be, but I don't have a lot of anthropological knowledge. But if my expectation is correct, then the -lineal/-archal distinction wouldn't be so relevant.