Is it possible that polygynous societies are more likely to be relatively egalitarian (if possibly not quite as egalitarian as, say, modern polyamorous communities are) than polyandrous societies are?

In terms of cultures where some high-status men practiced polygamy, I can definitely think of some pretty repressive patriarchies, including imperial China as well as a number of Islamic and Hindu cultures. But I can also think of some comparatively egalitarian cultures that also practiced polygyny; here I'm thinking of Scythia, a few coastal Indigenous cultures of the PNW (I wanna say the more northerly cultures in particular: Haida, Tlingit, Tsimshian), and possibly the Akan cultures of Ghana and Côte d'Ivoire.

In contrast, polyandry may initially seem like a matriarchal "male harem" fantasy, but the area where I've heard of it happening most often is the Himalayas, in which case polyandry tends to take the form of two brothers sharing a woman in a manner that is still patriarchal. (I've also heard of polyandry occurring in certain cultures of the Americas and Africa, though I'm even less informed about that than about South Asian polyandry, and I already don't know that much about South Asian polyandry.)

Does anyone know the explanation for this? For starters, if I had to guess I'd say that on some level this just makes sense in numerical terms, as men are more likely to lead dangerous lives (for example their professions are more likely involve hunting, warfare, manual labor, etc.) even in cultures that are less strictly patriarchal.