How can any of us really tell what half as loud, or twice as loud is?
Using music as a test signal for determining half or twice loudness is indeed difficult. Music varies in pitch and loudness and so is a moving target. The bel scale was developed by Bell Labs using steady tones on multiple test subjects and determining an average estimation of half or twice as loud. The difference in acoustic pressure called a bel. Decibel, of course being 1/10 of a bel. So a bel is what the average human perceives as twice of half as loud.
The actual acoustic pressure between the threshold of hearing and the threshold of pain is more than a million to one. The human ear/brain compresses this range in a logarithmic manor so as to be manageable. This is why the objective acoustic power must be increased by 10x to be perceived as twice as loud.
To answer the original question: there is generally no reason for us to worry about what is half of twice as loud. But, it is good to understand that a 200 W amp will only play 3db (21.9%) louder before clipping than a 100 W amp.