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Basic question about stereo pan laws

Because of research relating to surround audio I need to get this right...

As we all know, there are several possible formulas for panning a sound from one channel to another.  One law for maintaining constant perceived volume is "constant power pan", which assumes that the speakers sum in an incoherent manner such that the power rather than the amplitude is summed, wherein the power is the square of the amplitude.  Most texts then go on to show that because sin^2 + cos^2 = 1 for all angles 0 to 90 degrees, we should map the pan from one speaker to another to this 90 degrees.

My question is, if the speakers sum in power, can't the power ratio itself be used to determine the panning?

i.e. Look at figure 1, most texts describe the blue curve, while the red curve seems to be easier to calculate and make just as much sense (and be generalizable to any target summing simply by taking the linear x | 1-x panning and changing it to x^y | (1-x)^y where y can be anywhere from 0.5 to 1.

Which scheme is more accurate in terms of the panning direction change and why?

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