Perception and Watts: Doubling of power

There's a curious rule of thumb, which to my ears seems mostly true:

• To double the perceived volume, you must output 10x more power.

10x power = 10 dB by the way.  We've read this as we were buying amps and trying to decide between 100w/channel and 150w/channel.  We are told, repeatedly that 50 W difference isn't really that much.

On more than one occasion I've tested this and found it's pretty much spot on.  Here's my question:

How can any of us really tell what half as loud, or twice as loud is?

I mean, think about this for a bit.  I cannot tell half as bright, or twice as bright, but it seems I actually CAN tell what half as loud is.  How does this even begin to work in the ear/brain mechanism?? 😁