Yes, that is the common view around here. It is what people mean when they way we see light "logarithmically". Of course, no one ever explicitly specifies the log base when they make that statement. But the example for flashlights is always as given as above, which happens to be a log to base 2.iirc it takes around 4 x the lumens to appear twice as bright in general
But as I discuss in this link, logarithmic-based adjustment scales for sensory systems are typically not consistent over a wide range. Modern psychometric research suggests a series of discrete power relationships better fit various human sensory perceptions. For non-point sources of light (i.e. >5 degree beam angle), the generally reported power relationship for human perception is 0.33 (which is a cube root). That would mean that you actually need 8 times the amount of light to seem twice as bright. :shrug:
However, brief flashes of light or point sources of light (i.e., <5 degree angle) best fit a square root power relationship. And that certainly matches the common "four times the light for twice the brightness" mantra here. I haven't seen any specific psychometric tests on flashlight beams, but it seems likely that most people's relative perceptions will be in-between the square and cube root power relationships.
I'm afraid I've wandered a bit off-topic, but it would be interesting to compare peoples' relative perceptions of throwy vs floody beams, to see how they fall. I expect the floody beams should be close to that standard cube-root power relationship (as expected), but throwy beams may be closer to the square-root of point-sources perception. :wave: