I think David B. is oversimplifying when he says:
If a lot of offspring get genes for cooperation and together they are hard-wired build an equilibrium better for all (i.e. what morality does), that would in fact out compete another population without those genes.
I think it’s important to remember that two opposite strategies can both succeed in different niches. I don’t think you’re justified in thinking the in-group dynamics prompted by the morality we value would necessarily be sufficient, let alone dominant. Consider our close relatives the chimpanzees. Although chimps have a complex social dynamic, that has certainly been evolutionarily successful thus far; I think we’d hesitate to call it moral. Chimpanzee mating is founded on the routine beating and brutalization of chimpanzee females, to insure they copulate with any willing male while in heat. Nothing about this is automatically inferior to the human social system from an evolutionary perspective.
Also, relative values don’t mean nothing matters. This is the whole point of society. Many people wish to respond to relativism by slapping the relativist in the face and saying, “So, I don’t believe in not slapping people in the face. What are you going to do about it?” But that’s not how it works. We gather as intelligent beings to decide what best supports the society and enact prohibitions for violations of these rules.
What I was trying to get at with my discussion of Nash Equilibria was the idea that “what best supports the society” may not actually be desirable. Evolution and relativism as described by Hendy above are both systems that promote stable and resilient societies. Neither of them necessarily optimizes moral attitudes or outcomes, as the chimp example suggests. So what is the basis for our strong preference for our society over that of chimps?
Crowhill is correct that “The hard thing to face is the possibility that there may be no justification for our moral statements.” I’m still inclined to give weight to experiential evidence here that suggests our standards are moral and true. Given that I know that stability/social cohesion is an insufficient criterion for proper action, I couldn’t act or evaluate proposed actions unless I posit some alternate, valid metric.