This study presents an empirical analysis of domestic violence case resolution in North Carolina from 2004 to 2010. The study finds that penalities, at least as set at the current levels, do not deter future arrests and convictions.

Citations: 

Sloan FA, Platt AC, Chepke LM, and Blevins CE. “Deterring domestic violence: Do criminal sanctions reduce repeat offenses?” Journal of Risk and Uncertainty 46 (2012) 51-80. doi: 10.1007/s11166-012-9159-z