Responsibility is an AI-exclusive trait that determines that character's willingness to abide by and help enforce the law.
The Responsibility rating of a character in Oblivion is a measure of their moral character in relation to societal measures. The higher a character's responsibility rating, the higher a character's morality will be.
For example, if a character has a responsibility rating below 30, they have no problem stealing items that they need to complete an act, i.e., if it's time for them to eat, they will steal food in order to do so. Characters with high responsibility ratings will generally act as law abiding citizens. A character with a responsibility rating of 100 will immediately report crimes committed in their presence, causing a bounty on the offender's head regardless of whether a guard is present.