Many violent relationships are characterized by a high degree of
cyclicality: women who are the victims of domestic violence often leave
and return multiple times. To explain this we develop a model of time
inconsistent preferences in the context of domestic violence. This time
inconsistency generates a demand for commitment. We present supporting
evidence that women in violent relationships display time inconsistent
preferences by examining their demand for commitment devices. We find
that "no-drop" policies — which compel the prosecutor to continue with
prosecution even if the victim expresses a desire to drop the charges
— result in an increase in reporting. No-drop policies also result in
a decrease in the number of men murdered by intimates suggesting that
some women in violent relationships move away from an extreme type of
commitment device when a less costly one is offered.
Here is the paper. Here are non-gated versions. Or put it this way: when prosecutors cannnot drop the charges against the man, the women are more likely to report the man in the first place, and also less likely to kill the man.