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According to Straus' research, the most common pattern of dating violence among young couples involves both partners hitting each other. "In every single country, it's most common that both partners are hitting, without exception," Straus said.

In the second most common scenario, the female partner is sole perpetrator of violence. "Chivalry isn't dead," Straus said. "Up to a certain point, the male will not hit back if struck by a woman because 'you don't hit women.' But if it continues, sooner or later he's likely to follow the example and hit her and that, in my opinion, is responsible for the predominance of mutual partner violence."

The least common scenario is when the male partner is the only one who hits.
...and here is link to the whole study.