The first step in solving this problem is to think about what cognitive systems might increase the amount of altruism directed towards others, and then examine the adaptive function of each to determine whether they will solve the problem particularly efficiently.
Paul Bloom attempted a similar analysis (link is external) (about three years ago, but I’m just reading it now), arguing that empathetic cognitive systems seem like a poor fit for the global altruism problem. Specifically, Bloom makes the case that empathy seems more suited to dealing with single-target instances of altruism, rather than large-scale projects.
Empathy, he writes, requires an identifiable victim, as people are giving (at least proximately) because they identify with the particular target and feel their pain.