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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 more violence: here, here,
More men make less violence: here, here, here.
I quit, and tentatively conclude the evidence is unclear.
Sex Ratio & Violence
"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.