Its basis is a concept not entirely unlike karma: good and evil deeds affect the state of your soul, and the sum total of these deeds affects what will happen to you after death. However, an important principle in Karmway is the belief that if you lead another person to begin doing good, then you are indirectly responsible for the good deeds they then go on to perform. The more good they do, the more good karma you acquire from having converted them.
(The converse applies to converting other people to do evil, but it is generally assumed that good karma is preferable to evil karma.)
This continues on indefinitely: if a person you've converted to good then goes on to convert someone else who becomes a great exemplar of goodness, then you accrue good karma for having converted the person who converted them. And so on and so forth: the successful adherent of Karmway is like the topmost point of an ever-expanding pyramid of good deeds.
Logically, this means that it's in your best interest to not only convince other people to be good, but to convince them to actively proselytize others into the philosophy of Karmway, so that they will in turn be motivated to convert others into the business of converting others to good. A purely utilitarian moral philosophy virally driven by unenlightened self-interest.