God's Purpose According to Election

We can logically conclude that the basis for God choosing Isaac over Ishmael was due to the illegitimacy of Ishmael's conception and birth with Hagar and not Sarah. But how do we explain God's choice of Jacob over Esau given they were both legitimate, both the children of the same parents (Isaac and Rebecca), both conceived at the same time, both born at the same time?

On what basis does God choose those whom he shows mercy to?