I haven't run back through the math, but every source I've seen that relates perceived loudness (not actual power level) to decibel increases equates 10dB to a doubling or halving of loudness. Here's one summary that I've seen on more than one occasion:

• 1dB: Imperceptible Change
• 3dB: Barely Perceptible Change
• 5dB: Clearly Noticeable Change
• 10dB: About Twice as Loud
• 20dB: About Four Times as Loud

I'm not saying that these values equate to actual sound power (or intensity), but they are pretty widely-used guidelines for how people perceive changes.