@AlexP although correct in math, it could be different. There could be more sexually active men ready for polygyny, but having only one mate. Society isn't perfect, making the reality possibly different from the theory.

"Strange thing:" Ask yourself why wouldn't a matriarchal society practice polygyny, and you will find out your prejudices and possibly unconscous biases. Voting to close this question as hopelessly opinion based. (Thank you @Trioxidane for revealing my biases.)

@AlexP I am not sure about your math. For example consider 33 families of 2 woman and 1 men each, and one man left over. Then of the 100 people 99% are in polygynous groups.

@Daron: Trioxidane has already revealed my unconsious bias, and I have retracted that dogmatic statement.

@AlexP If also insist a 50-50 split of men-women then the upper limit is 75% in polygnous groups. Namely all the women and 50% of the men, with the other 50% of them men left over.

@Daron: Polygynous not polyandrous. That is, all the women and half the men tops.

@AlexP Yes I wrote it backwards, duh!

In my fictional Matriarchal society (based on spaceship culture), your loyalties are all to your birth family. Men never leave their mother's ship, except to go work for the family. Who your mother matters, not your father. Your uncles are the men that help raise you, not a father. The men are either pursuing sexual relationships or rented out by their grandmothers/mothers/sisters for a stud fee (which also assures paternity and secures interfamily alliances).

@AlexP I do not understand your comment about biases. Could you please elaborate, and explain to the less socially aware among us why this question should be closed?

@KeizerHarm: The question assumes naively that a matriarchal society is somehow expected to abhor polygyny. Such an assumption is rooted in the querent inherent prejudices; as we former Marxists used to say, the conscience of the querent is historically determined, being the product of the society in which they live. The point being that nobody can truely answer why a random matriarchal society practices polygyny; reasons may range from "this is how it's always been", to "we had a war and most young men died" to "the Holy Book mandates it" etc. etc. etc.

@KeizerHarm: Look at it this way. Why don't we practice polygyny, and consider it to be "a rather serious crime to have two wives at a time", in the words of G&S? In the end, isn't it simply because our civilization is descended culturally from the Hellenistic civilization, and thus this is how it always been for the last 2,500 years or so? Plus of course the position of the Church, which unthinkingly adopted the pagan cultural conventions of the detested Roman Empire, ignoring their own Holy Book? (Just like we have 5 fingers because we are descended from half-fish with 5 fingers.)

@AlexP Yes, every potential answerer writes from their own values, and in the case of cultural institutions such as marriage those will be coloured by their cultural backgrounds, (setting aside whether truly everybody on this site is descended from Hellenism). That does not mean that any questions about the reasoning behind cultural institutions are unanswerable. Intelligent people can in fact talk about reasons and try to set aside their biases - or draw examples from other cultures with different approaches, to broaden our cultural horizon. Plus "lots of possible answers" is no close reason.

@AlexP I also think it is reasonable to expect a correlation between misogyny and polygyny, given that in many sets of items, the kind that exists in plural is the expendable, less individually valuable kind. And even if there were no reason to expect this correlation and it's all cultural biases at work, the solution is not to shut down the querent for that assumption: the solution is to correct them via counter-example, and make this site a learning experience for them, which is what we are all here for.

@KeizerHarm: Lots of possible answers all equally correct is absolutely a reason to close. Or at least, this is what I believe.

@AlexP The condemnation of an entire category of questions (namely every single question about the reason behind cultural practises) is so impactful that I think it deserves a meta discussion first.

@KeizerHarm: Fully agree.

@KeizerHarm Men are expendable in all human societies regardless of marriage practices and power distribution. Human males are expendable due to their relatively minor role in reproduction. Both matriarchy and patriarchy aim to protect females and ensure that they have enough time and resources to produce offsprings. They are just different approaches to the same problem.

I concur in the VTC. Any answer would have to primarily be a plot contrivance. The reason would in every case flow back to the cultural evolution of the peoples, along with the history of the planet, and that is all part of the story line. Giving an answer is in effect writing the storyline for the OP. The Handmaid's Tale used a very low fertilely rate as the reason for polygyny - in order for a family to be guaranteed of heirs, they HAD to have several females, but this does not GUARANTEE polygyny. It was a plot device based entirely on the story line..

@JustinThymetheSecond Where is the border between "factor" and "plot contrivance"? You are making an even more sweeping suggestion than AlexP; if I interpreted it right, you think we should close questions that can be answered with historic events. Just that there are a lot of possible such events that could be responsible for polygyny, does not mean that all of those events are equally suitable.

@JustinThymetheSecond And applying your rule consistently would close a ton of good questions. This site makes rules for a setting, and events in the past are things that contribute to rules. Backstory is not part of the plot, backstory is background info on which to build a plot.

@JustinThymetheSecond And we already have one answer to this question that does not use historic events at all: males being rare. So by your criteria, given that this can be answered with things other than historic events, the question should remain open.