Meta.SO runs as a stand-alone site on the SE network. Therefore, it has its own reputation system and, consequently, votes and badges are easily identifiable. This is different on the child-Meta sites elsewhere. On these sites reputation is substituted for participation which is measured differently. However, it is still possible to obtain reputation-related badges. Even the badge list on these sites reference a form of reputation required to obtain them, yet no such measure exists.
What merit is used to awarded Mortarboard, Epic and Legendary badges on per-meta sites when there is no visible user reputation associated with them?