After some prodding by TGGP, I tried to dig into data studies on the relation between violence and sex ratios. Alas this seems to be one of those areas where results are all across the map: More men make
"This was my though too. Less women = higher “market price” of women, but the problem is who owns this higher price."
It depends on what you are looking at. If you are looking at evolution, then the woman's gene's own the higher market price. Either she or her male relatives are going to pick out richest man for her which will mean her children will have the best chance of doing well for themselves and passing on their genes (looks and strength of the man might also play a part in the choice which will help the children be more desirable to future mates).
If we are looking at this from a purely social stand point, then it depends on the social structure. If the father chooses his daughter's husbands, then he is the one who benefits because he can make them pay for his daughter either with money or with political alliances. If the daughter gets to choose her own husband, then she is the winner because she has more choices to choose from than the men do.
With a lower female:male ratio you would have two extreme outcomes:1) larger number of sex partners per womanOR2) Fewer men with sex partners
I would imagine 1) would not have an impact on violence because the men are still getting some, but jealousy violence might increase countering that trend.
I would think 2) would lead to more violence as involuntarily celibate men engaged in riskier and riskier behavior to get into the priveleged few.
But I really have no idea in actuality, and would expect perhaps very different results from the same ratio in different cultures.
This was my though too. Less women = higher "market price" of women, but the problem is who owns this higher price.
Also it means more competition between men, but depending on society, "more competition" can mean more physical violence or higher work ethics or whatever.
This reminds me of a discussion I had with my friend years ago about wizards in fantasy literature. He said that if there were real wizards (people having exceptional uncopyable abilities) in real medieval society, they would be probably all slaves, because their skills would make it useful to enslave them. Fire wizards would spend their days in chains, powering some steam machines, or would be enlisted in army. The lesson is the same: just because you have the power, it does not mean you can get the price of the power; it can actually put you in danger. (In some books of Dave Duncan wizards are busy hiding from each other, because obviously the most efficient use of magic is to cast obedience spells on other wizards.)
By the way, this may relate to previous OB articles about programmers and doctors having to do more overtimes. Highly qualified people have some "powers", but it does not mean they get all the benefits. By working overtime and by progressive taxation their "powers" are harvested by powerful people around them.
What might be a good way to measure the degree to which women might receive the "market return" of women being more valuable on a marriage market (rather than, say, their fathers or brothers commanding the premium)? i.e., if we are going to consider women as commodities on a marriage market, who is the agency selling the commodity? Not necessarily the woman, surely? The implied dynamics and effect on violence would of course differ with this variable.
The linked papers seem unanimous on the idea that marriage reduces violence but argue over whether there are some additional effects from changing gender ratios that may overwhelm this reduction.