In the aftermath of The Cataclysm it was quickly obvious to the observant that the baser elements of human society were taking advantage of The Chaos to better themselves at the expense of others. Unfortunately, organizing to do something about it was not nearly s easy, especially given the fragmented nature of human society. Finally, a number of religious leaders got together and started an initiative to form a single organization dedicated to preventing the exploitation of the common man. Something like this had only ever happened once before and it was no easy undertaking; human religions have a long history of disagreement.
After over a decade of discussion, argument, and fighting, the organization that would come to be known as the Bleeding Hearts was formed and began to uphold its charter by pursing those that were selfishly taking advantage of others or behaving without concern for the wellbeing of others. Unfortunately, in the time it took the religious leaders to reach a consensus a number of atrocities had occurred that they felt they should have been able to prevent or at least alleviate. Their guilt brought them to set the idea of atonement as one of the central tenets of the Hearts.
This became one of the driving motivations for the original leaders of the Hearts; to try and atone for their indecision in the past by striving ever harder in the present. This concept also extends to those that the Hearts find lacking. Frequently, those approached by the Hearts are offered 'suggestions' for what they could do to atone for whatever the Hearts have taken exception to. However, if the Hearts can't find an atonement that would sufficiently counterweight the scales of a target, then the only prudent course is to prevent future infractions, by force if necessary.