The Bleeding Hearts' central philosophy is that everyone does both good and ill throughout their life and as long as they roughly balance out then conventional methods (UNIPOL, etc) should be sufficient to deal with any situation that might arise. It's when, by their deeds, a person starts to harm others more than they benefit them that the Hearts see the need to intervene. The Hearts don't follow the typical legal limits of causation adopted by many world governments, instead they consider all things that you potentially have influence on. It isn't uncommon for CEOs of companies that have had minor employees commit major offenses in the course of doing their job get a visit from the Hearts, even if they'd previously been exonerated of involvement by the courts. A prime example of this is the level of conflict between the Hearts and the Crossbones Exchange due to the Hearts holding them responsible for anything that their illegal distribution networks enable, not just the act of distribution itself.
Many people outside the organization don't understand the way that the Hearts see justice and frequently see their actions as capricious and illogical. On the other hand, there are people who understand how this effects them very well and there even exist 'insurance' companies whose sole purpose is to monitor a clients life and, through donations in their name or recommendations for services they can perform, ensure that they never come to the attention of the Blood Judges. Fortunately (unless you're a Bleeding Heart) the amount of computing resources required to track peoples lives at this level is tremendous and therefore it typically requires that you come to the attention of the Judges through more mundane channels before coming under serious scrutiny. Because of this, the Hearts are great proponents of the Corpers recent drive to increase the usability of the Universal Identification Card.
Heart involvement in a situation that they find imbalanced can range anywhere from a simple visit to let you know that you need to take responsibility for your actions to much more extreme sanctions. The Hearts aren't averse to labeling someone (or even a group) as irredeemable and acting to insure that they cause no more harm.