How does batman deal with psychopaths?

The same way he deals with all of the villains in the Batman universe: Fights them and takes them to Arkham Asylum. Also, considering the term 'psychopaths' comes from the word 'psychosis', an actual mental disorder characterized by a disconnection from reality, he'd most definitely take them there. Heck, according to the Wikipedia, it states "Many criminals who experience psychosis from the DC Universe have been patients within the Asylum and also escaped from it." In other words, most of the villains he's fought are psychotic.
Does this make sense?