Why an atheist based morality is inferior
Let's set up a simple game. We'll call it Moral. It is a two person non-zero sum game.
Suppose you have the following conditions for the game:
1) A moral choice that each player agrees exists. Each player has two available strategies: one, make the moral choice (do the right thing), and two, not make the moral choice (cheat).
2) Defined individually preferred payoffs based on adherence to this moral choice, where the payoff is greater for either player if that player can silently cheat the system.
The game does not rely on what the exact details of the moral choice is only that the players agree what it is. As it exists both players when acting with rational self interest will choose to cheat.
Suppose we add a third condition:
3) A third party judge that both players believe exists and is omniscient and fair. Both players also agree that this judge can punish cheating by reducing payoffs to zero.
The game does not rely on the judge actually existing only that the players believe he exists. The judge adds the component of complete knowledge. If the omniscient judge does not exist and there is no notion of complete knowledge the players are more prone to cheat the system.