If you control two Goldnight Castigators and a source would deal damage to you, it deals four times that much damage instead. If you control a third Goldnight Castigator, the source deals eight times that much damage to you, and so on. Damage dealt to a Goldnight Castigator is only doubled, regardless of how many are on the battlefield.

If multiple replacement effects could apply to damage being dealt to you or Goldnight Castigator, you choose the order to apply those effects.