Justice is achieved through the optimization of individual well-being throughout the group, i.e. maintaining each individual's well being near the mean of the group.
Game theory, would suggest that in a changing dynamic world, with limited, yet growing resources; the reality of Justice as a virtue allows the group (a species) to profit from behavior such as empathy, and self-sacrifice; which would explain how said emotions have become embedded within many species throughout evolutionary time.
Karma expresses the flow of well-being towards achieving Justice as it relates our evolved emotional responses to events and our actions. It is similar to keeping count of standard deviations from the mean.
Many ways of achieving justice have bean thought out; most religions deal extensively on the subject as do all political systems. In the end; justice as something more complex than even the simplest cooperative games is NP - complete and we will continue forever changing and optimizing our laws and beliefs regarding our communal well-being to our current situations.
As sentient being, I agree the pursuit of justice is a responsibility we hold to ourselves, it is crucial to our survival.