You've misunderstood my point.
I'll be more specific. Let's say that an amplifier is rated 100/200/400 watts per channel into 8/4/2 ohms. What you sometimes find is that their actual, measured, continuous output into 8 ohm loads is more like 150-200 watts, ~250 watts into 4 ohm loads, and then they squeak by the 2 ohm spec right at 400 watts. Krell and Levinson used to do this with their lesser amps years ago. Does the amp output really double as impedance halves? IMO, no, but by the specs, yes it does.
I totally get your point, Irv. I'm just adding that once you know how things should work, then it's easy to see through a trick like the one you first described... as long as there are three data points.
Electrically speaking, output should double when impedance halves. That's what we call an "expected result" under Ohm's Law.
Provided the power and output stages of an amp are of good design, then there's no reason why Ohm's Law shouldn't apply. But most often they are not. That doesn't stop the application of Ohm's Law and the interpretation of manufacturer specs.
Honestly rated gear may not double with halving of impedance but it will still increase power inversely
proportional to impedance eg. 120W @ 8 ohms, 240 @ 4 ohms, 480W @ 2 Ohms.
What it can't do under Ohms Law is deviate from proportionality (eg. 120W @ 8 ohms, 240W 4 ohms, 400W @ 2 ohms) without some reasonable explanation that tells us where the watts went between 4 and 2 ohms. Manufacturers who don't make it clear where the power went can be legitimately accused of having a design with some shortcomings. Typically, this occurs from limitations connected to the power supply, output stage, or heat sinks (electrical resistance in metals increases with heat).
The real crime, however, is when there is an unproportional increase of power when impedance decreases (120 --> 240 --> 500). This is a clear violation of the laws of physics and, in almost all circumstances (except the one I outline below) evidence of a serious mistake or purposeful misdirection. Why? Because it makes no sense whatsoever that output should increase disproptional to impedance.
This only holds true when comparing like things (ie. 2 channels driven OR 1 channel driven). It doesn't necessarily apply when comparing two different things, like 4 ohm --> 2 ohm output @ 2 channels driven versus 1 channel driven @ 2 ohms in a bridged amp. Why? Because comparing two unlike things equally ignores the possibilities of efficiency gained through bridging.
So whenever I see stats that deviate from Ohms Law in any logical or meaningful way, I question whether the data is valid or invalid.
I hope this clarifies my previous post... it wasn't as much about what you wrote as the principles under Ohm's Law can be
easily used to spot industry flummery.