Correct, it's not "Normalize". That algorithm seeks the highest peak in the audio, then raises or lowers the TOTAL GAIN to bring THAT PEAK to the preset level. Here is the caveat. You can have an audio file that is -50 db (barely audible) with a single "clunk" (like the mic got bumped) at 0 db. If your "normalizing" to -6db, then it's going to reduce the gain of the ENTIRE FILE by 6db, leaving your desired audio at -56, with the single peak at -6.
What you want to do, is technically known as DYNAMICS COMPRESSION. This is a variable gain adjustment, on-the-fly. Radio stations use "audio processors" to do this in realtime. With digital audio, the process can be MUCH more precisely controlled, since it is NOT in realtime. With proper dynamics processing, you'd have that -50db audio raised to at least -20, and that 0db peak dropped to -6. Yes, you can "crank it to 11" by having it raise the -50 db audio to -6, and bring the 0db down to -6 also... but with too much gain increase, noise is raised, as well.
Dynamics compression is what those LOUD commercials are using. If you open the audio in an editor program like Audacity, it looks almost flat, with minimal hills and valleys. You will also see this on MOST modern music. The compress the daylights out of it, to make it all sound LOUDER. It works, too... having 0 db of dynamic range in audio sounds quite loud, and becomes fatiguing to listen to for any length of time.
What would REALLY be needed, is a "smart" detector that not only examines peak amplitude, but also the AVERAGE. If the average is always high, then the gain will be dropped proportionally. It would take some doing to make a system that could do this reliably. I have a TV with what they call "Equisound", and it is absolutely DREADFUL! I have thought of using an outboard audio processor, like my Alesis "Nanocompressor".