Which is culturally solvable, but would require require people to give up their children to be raised by the state and never be allowed to know who they are. That sounds horrible, but I submit that said horror is largely driven largely by a culture of possession and selfishness, i.e. people want to raise their own children because they want to shape who they are and ensure their genes have good survival odds. Assuredly there is a biological component that drives us to take an interest in our lineage, but we know that this can be directed towards similar goals via adoption and pets, so it is conceivable that a society could direct it not towards one's individual children but children in general. Of course, the whole 'raised by the state' thing is also a pretty uncomfortable thought to any society that has enshrined "freedom" and most people who lived through the soviet union, however I think it is possible that without the concept of genetically-bound inheritance of property and status that the corruption of such structures might be less likely.

Not that I suggest any of this in serious mind you, it's just the kind of thought experiment day-dream that gets me through my workday. What this one has taught me is this: nobody actually wants a meritocracy.