So lets take perceived out of it.
Why? It's exactly what we're talking about. When you say that a speaker is "twice as loud," I think that you're referring to an end user's perception.
Is it a measurable fact that a speaker with a 3db higher sensitivity rating would be twice as loud(with the same input power), and will require half the power to produce the same loudness?
A speaker with a 3 dB higher sensitivity will be 3 dB louder as measured on an SPL meter. I believe that the measured energy will be "double" from a mathematical point of view. But to a user, a 3 dB increase isn't that much (i.e., not double). As suggested, just sit down and do it at home. Play music, TV, pink noise, whatever and listen for a while (go for something without tons of dynamic range). Then turn it up by 3 dB per your receiver or pre/pro's volume knob. Does it sound twice as loud? No. Drop it back down to where you started, get reacclimated, and bump it up by 7 or 10 dB and see if you think it's double there. As noted above, it's very subjective, so it just depends on the user.
Yes, you doubled the required amplifier power when you did that 3 dB increase, but the loudness that you hear, that you
perceive, didn't double. Yes, the SPL measured energy doubled from a mathematical/engineering point of view, but I don't think that's what we're talking about.
If you have one speaker that's 3 dB more sensitive than another then, yes, the more sensitive speaker will require half the amplifier power to generate the same SPL output.
For the record, I think I'm the guy that's been "slamming" zumbo in PMs. In general, my tone has been the same as this post, and I've been trying to explain these differences using the same descriptions I've used here.