Further to this - bandits are openly flaunting the law (Count Roderick) and the count's personal representative (you). As a knight you are expected to be judge, jury and (if need be) executioner in the Count's name. As a landowner, you are personally doubly responsible top the Count for enforcing law and order.
The conventional wisdom is that if you show bandits mercy, that will just get you more bandits. You are free to behave as you wish. However, there may be consequences.
Offering them military service in exchange for mercy would make troops that were even less reliable than peasants, or so common wisdom would say.