Ideally, a power amp should be able to deliver twice as much power at half the impedance. The way it can achieve this is if:This statement is false, on account of the fact that list following it is not what is needed. What is important here is that the amp is able to act as a voltage source and to that end, it does not have to double power as the load impedance is halved- at full power. Any amp that has an output impedance low enough will effectively double power as impedance is halved, with the exception of when the amp nears clipping. That is the only time that doubling power might be an issue, and only important if you have a low impedance load and you really for some reason need that last 3dB, which is not a very audible increase to the human ear.
This 'doubling down' thing is mostly marketing and **waaaaay** overplayed.