According to a study done by the London School of Economics, referenced by the Economist in a widely shared article, there is a connection between polygamy and civil war as well as more violence in general.
Of the 20 most fragile states in the world, all are very or somewhat polygamous and polygamous states are more prone to invade their neighbors as well.
Polygamy almost always means rich men having several wives. One example The Economist use is that if the top 10% marry four wives each, the bottom 30% can’t marry at all. This creates a situation where many young men are not only sexually frustrated, but also socially marginalized, since marrying and having children is often a prerequisite for being seen as an adult for men in traditional societies (where polygamy is most frequent).
Since polygamy create a shortage of brides, the “bride-price” required can swiftly increase making it impossible for many to ever be able to marry, not by any legal means anyway. With this follows violence whereby young men take to illegal measures to secure enough to marry. In a country like South Sudan, for example, cattle-rustling, with all the violence that goes with it, is a severe problem, creating feuds that can fester a long time.
This pool of frustrated young men is also easy recruits for organized crime and of course jihadist-groups (like Daesh, al-Shabab and Boko Haram). Joining these groups means fighting, and with the fighting comes looting, and perhaps enough wealth to marry.
This is borne out in another study from Texas A&M University, also referenced by the Economist. In it researchers Valerie Hudson of Texas A&M and Hilary Matfess of Yale University said that a high bride-price is a “critical” factor “predisposing young men to become involved in organized group violence for political purposes”.
So in conclusion, even if polygamy is in retreat globally, in certain areas it’s alive and well, creating more violence and social upheaval along with keeping women in social and human bondage.