Power Amp Doubling Output at 4 Ohm

A perfect transistor amp would double every time you halve the impedance. Ones with big enough power supplies more or less do this. If you have inefficient speakers that have low impedance this is an important consideration. But it is not the only one. Many class a amps will not do this and if you have efficient high impedance speakers you can look for amps that are designed to maximize other parameters of performance. All design is compromise and a powerhouse large amp MAY give up speed and transparency to amps that do not have the same power but which can react faster. There is no real rule to guide you here, every amp has to be considered individually in terms of how it meets your needs. A general principal is to have plenty of power but to go with the smaller amp if you are choosing between two that meets your needs as it will PROBABLY have a simpler circuit [need fewer power transistors] than the bigger one. All the above may not hold in individual cases and this complexity explains the theoretical advantages of active speakers in which the amp is tailored to the individual speaker. Again some designs execute this better than others.