Before someone closes the q, let me tell u how horrible the premise is.
- didn't deliver on this promise, skipped that, as other stuff took more time and was quite interesting on its own.
Based on what comes to your mind or what is written in answers so far, we see how far modern western society is from the past, from survivial and choices about a life people did make regularly, even in not so distant past. We live in the future, praise the Lady.
What should come to anyone's minds first? What is the most important and fundamental, and absolutely not opinion-based here, but just math? And it is quite important in all the questions to find parts, as many as possible, which do not depend on opinions.
It is that they can manage the proportions of males and females in society.
Let it sink in, we didn't have, and to some degree still do not have(it is mildly expensive, or it involves killing fetuses, soo it not so convenient) such ability until those days - to set any proportion of males or females in society. And they have had it since inception. It is such a big thing, and all you can imagine is inheritance laws? - so innocent, soo pure - love the future.
Such ability is a variable that will gain its owner.
By owner I mean any of many things - some society rules, traditions, habits, ruling classes, matriarchy or patriarchy societies(meaning a rigid system of a little bit of everything which creates such), and probably gender neutral societies could be a thing as well, as a 3rd well-known option, etc, I guess list can be expanded, but not the point.
Which one it may be? - basically any. Which one could get to the time of their own industrial revolution, meaning which way will be more efficient and survive selection process happening on a level of societies - that is opinion based part of the q and hard to tell.
It is hard to tell, but pretty certain that wars of ancient times will be bigger, conquering females will be one of the top 3 causes - as a result of management mistakes(in the line of one family one-child policies, but translated to the setting result of choices having more females or more males in society - for reasons, I will mention later, briefly).
A little stop for those who need to know how to control gender proportions in the setting
Male selects a female and conceives a child, within a month. (If fail, next month attempt with a different woman, 3rd attempt same, 4th att... no no no, do not waste women's time go to public house(or whatever alternative of it at that time there is) and there is a bunch of ugly ones, try your luck)
Women bear a child - we have male or female - this is a way to identify and separate pairs by which offspring they produce.
From here we can work it up, what do we need, if we need more males - male producing pairs get permission if females - female producing pairs have permission.
Each male has around 2 attempts (it can be more or less depends) - and here we start with a 50/50 mix, which is a result of promiscuous sex, and no one is sure who is a parent of whom(not likely, even apes pay attention to that). (As the situation develops there can be more or fewer attempts, so as it may be a result of current planning - goals)
There is a 25% chance for one male to fail to get desired outcome (no matter the goal male or female) in two consecutive attempts with 2 different women. Meaning that there is a 75% percent chance to get desired outcome - quite hefty.
Let's denote the desired outcome as X+, it can be male and female, and X- a child of a different gender than the goal, and look at what we have as a result of attempts to sort out. Np - total number of parents in the system, Nc+/Nc-/Nc - number of children(success, fail, total)
1st attempt : 50% X-, 50% X+, Nc = 0.5×Np, Nc+ = 0.25×Np, Nc- = 0.25×Np (0.25, for short)
2nd : 0.5Np participants, same 50/50 chances, Nc = 0.25×Np, Nc+ = 0.125×Np, Nc- = 0.125
So after 2 attempts we have Nc+ = 0.375×Np , Nc- = 0.375×Np
So after 2 attempts, we have 75 percent of replacement of population number.
And 50 percent of women had one child Nc+(so far in our model) and as a pair it is FM+ and 50% had 2 children (half of them FM+ pairs), out all of them for 75% of women/male the society can obtain a designated result with 100% certainty, there unlucky 25% of pairs(and females) which didn't produce Nc+.
For a replacement, we need another 25% of children to be produced, and 75% percent determined pairs can accomplish that easily. With any excess you like.
Let's say FM+ from the first attempt have a second child and then population of next-generation is proportions are X+ 62.5%, X- 37.5%, about two X+ per each X- and 100% replacement population as by number.
If FM+ combinations have 3rd child - to compensate natural losses or for growth or wars or fight other environmental factors, then next-generation proportions are about 2.6 to 1, about 130% of replacement necessities, which isn't that much, I guess, by old standards, with all the deaths they had for all the reasons.
Further improvement of proportion can be brought by traditions and selective processes in society.
In one go, with easy rules, the best outcome is 3 to 1 (75% X+, 25% X-). 30% survivial rate among males(regular child mortality, even without a fight since 5yo with bat'leth) will bring that to a 10 to 1 or close to that. Modern time can bring it to barely passable 2-3 to 1, definitely a decrease compared to good old times.
- also it is interesting that they can shift gears quite fast from one to another within a generation. Black death aftermatch and restoring population could have been faster. After war recouping can be faster etc. So it may be used as a tool and be a change in policies each 10, 20 years to resolve or address this or another problem.
Opinion part of the A addressing opinion part of the Q.
Inheritance rules, eh? Before inheritance marriage should come to a mind - it can be - no marriage before testing Nc+ or Nc-, pray to your gods (or in contrary embraces such outcome) that you won't get in that unlucky/lucky 25% pairs with (for males) double Nc- shame/proud title.
- fail can be useful, or lucky coincidence as well, depending on situation and timing - there is a shortage of Nc- for some reason, then FM- get their additional lucky quotas. So bad things are not always bad.
Obviously, if any such system of selection is in place, it requires more strict control and count of Nc+- and FM+- pairs and it can happen quite early on in times.
- in a sense how early it may be a thing, I was amused by @Ash point "Nobody realizes in hunter-gatherer stage how it works." - it was just 70-80 thousand years ago - they had tools by that time, long before that they had a fire, they had tribes, they were quite capable. They survived 2 bottlenecks by that time. They do not have to know how it works to use it, because they did it long before for a loooong time (about a million+ years) for other things. Their wits were no less strong than present-day Dota player or of a boomer(or who was before them). And why so, why will they figure it out? Because if they do not they die out. They do wrong choices - bum - death. So 50% (random number) will die out others will stick to some procedures, like long before nobles and genetics they figured out - do not have offsprings with your offsprings and close relatives.
So things may be used way before they will have means to explain or understand. And there is a simple strategy for that, a social construct, that the owner of the variable - one is a respected member of a tribe(as much as a successful hunter) if he produces Nc+, a guy who gets Nc- will dream to become a good hunter/warrior to get a second chance, our first guy gets a second wife in his tipi. Elites of elites get double Nc+ for both wives, bottom elite class 50/50.
That is enough to increase and sway population proportions in what they find to be good. It sets to some natural proportion, depending on specifics rules they use and how they manage it all, as a result of all sorts of factors. So no matter the rules it will settle to certain proportions, and as long as they stick to those traditions they will have consistent results, so as copying such traditions will work for others as well - so it is possible to adopt good ones and dump bad ones.
Now speculative part from one who answers.
I mentioned matriarchy, patriarchy, and some gender neutrality which emulates (more or less) our proportions.
For each system, and here I used (ma/pa)triarchy as substitution of predominantly female or male (so not as gender roles, so it was misuse on my part, but just here)
Each of those systems can or has to be supported by its own set of simple, swarm-like, rules. Those rules for each system can be similar or different, I mean there are many such sets of rules, simple procedures for each case, and some of those may be similar by being flexible enough to be used in any of 3 cases.
Such rules probably, may, have higher chances to survive as they allow adjust proportions according to historical needs, but they are a notch more complex than those which fit only one situation, inevitably because they have some additional variable, switch - but it still can be a simple rule, just with complex behavior of it when applied en masse. I mean simpler than one can randomly imagine, and one needs to think which one it can be.
And if there are(they are) such simple rules, with do fit all 3 cases, then we get a situation of females against males, in some sense.
You say patriarchy(in the classical sense) - you haven't even seen the patriarchy as of yet.
Males promiscuous sex, more offsprings the better, females selective breeding trough inducing more competition in males.
Those are (in my understanding) opposite forces(ed: not necessarily), in male cases it prefers more females in society, in the female case it maybe prefers more males, kinda.
So overall it looks like it has 50/50 chances to end with one dominance(as a number, count) or another, but there is a catch, 2 catches.
- females can bear children, males do not
- males are fertile for a longer period of time than females.
It is a source of asymmetry in those probabilities, the rest females and males pretty much on equal footing, we can argue about nuances, but on a grand scale of things - it does not matter that much.
The speed with which a society can grow or can replenish its losses is strictly proportional to the number of females in that society. By increasing the percentage of females in society, they can become as expendable as males. And having a higher percentage of females - has certain advantages. And real-world example of that is magnificent hyenas. And why it is that way for them? because they have to, puppies birth is a problematic process for them, and here are my guesses, which leads to more fatality cases for mother and their offsprings, which basically makes females expendable and they have to compensate and bring the selective process to the male population and spare resources in doing all that.
So a higher percentage of females in society has advantages if both genders are more or less equal in capacities doing all the other stuff(they are, as for homo sapiens), but it does not necessarily mean males have a luxurious life. This probably depends on how wheels of history will turn, and on some random factors.
It can take all kinds of different forms - like male children each year under fool moon fight to death since 5yo - those who survive and aren't crippled are elite, cripples but alive still may be breeding material.
They can have a submissive position or dominant position in society and here it may depend - what is the prize for both genders? Dominant or submissive position for females there is no fundamental difference, no big changes for them(biology wise, evolution wise, etc), they somewhat get elite males goal achieved in both cases, nothing to do, as in terms of gene propagation they are restricted by capacities of their own body. For males taking dominant role gets a reward of survivial, satisfaction of as much sex as they bear with whom they like it to have, as many children as they can make - win win win - in case of dominant position, goes along with fighting to death since 5yo spirit; submissive position - they can't select they targes, not that it matters so much but affects the mood and goes against the spirit of fighting since 5yo - possible but improbable.
This is just one of few more options, which come to mind, they're definitely more of those, but the one mentioned - it pretty much goes along with male and female goals, evolution selection process, and desires, increasing the survivability of society.
- everyone does, I will jump that bridge as well, lol
Let bring back that dead horse, inheritance - there is a good chance a male having multiple females, his goal is ruling and management and elite special ops in war, he has 10's of children, inheritance get a survived male or best one of those few. Females get nothing, they do not own anything(except smart ones whose wealth is all the gold on them), nor do they decide whom they have sex with, they work, hunt, craft - basically working-class (same as beehives).
In a premodern and modern setting, it may be even more beneficial to keep such order, because it greatly reduces risks for females in terms of childbearing, saves time for more work. As for the replacement of the population, they need slightly more than 1 child per a female or half of what they typically would need or have in our society.
As for extra males, let's say they still didn't figure it out, not sure in which way it may convert - boxing to death? Are duels still a thing? Work harder to earn more money? Whatever - there will be a solution.
I didn't spend much time on gruesome parts of the history of that patriarchy but believe me, there will be plenty, slavery will be a child's play compared to that.
there can be a different position that men do better this or that, and it may have some influence on what's may or may not happen. Again in some way, it's a matter of the selection process, if it still works in the setting - and again hyenas are a great example - be sure that females are quite capable there, lol. Maybe homo sapiens will be no more and neanderthals win, with some portion/percentage of homo sapiens genes.
there are some advantages in proportional number for each gender, cons, and pros - it is a mix bag.
at times it may be beneficial to have more males if they outperform females at something, but in a long run, it is not a great situation, placing more burden on females to produce a replacement population, which wasn't that easy anyway in history, so in a long run it less beneficial.
In essence, it will, most likely, be significantly different societies through history. And most likely more females, than males 10 to 1 something, with strong patriarchy until and including the equivalent of modern times and still strong with no reasons to be abandon, because it is capable to satisfy biological goals for both genders, and free time for more work which leads to gaining/keeping advantage edge.
Realism of the premise
Power of genetics may suffice, similar to inheriting blood type.
Sure for all mammals, it will most likely be all the same(not only humans), but it does not matter for them that much, permanent pairs are rather an exception in the animal world, and it won't matter for exceptions as well, and one would not distinguish that at first glance. It may have some influence on tricks and tips about domestic animals breeding, but not by much.
By saying "like blood type inheritance" - by it I do not mean exactly like that, it may be a bunch of genes, wide cluster in different chromosomes, which form a firm system, which is hard to influence by selective breeding. In that sense Y-chromosome solution is very robust - hard to create something out of nothing(but happens as @The Square-Cube Law mentioned in his comment) so as in nature we know more than one case of gender disproportions and gender conditional changes(some worms, insects(?), sea creatures, but do not cite me on that) and such.
So mammals are a somewhat successful exception (one of many, clearly, as that dimorphism exists for long before the class formed)
So yeah, the premise is viable/real, and if investigated without assumptions it can be quite interesting. Fruitful things totally can be a world-building process if it is a deep dive. Changes are fundamental, starting way before the stone age(changes for humans).
Influencing, using that may even be one of kickstarting things for intelligence, so the influence of the premise goes well before first fire. So fundamental it is. It really a gold mine in terms of worldbuilding. I haven't seen such monumental premises for a long time, for sure it is the first one this year.
Black Mirror series and the premise can be part of it(if they didn't already, idk), or it can be made on its own in a series, different stories, different causes of failures, and rare successes in ways the intelligent since pre pre homo sapiens creaturs approach the management of the problem.