Volley theory and sound amplitude/power
It's complicated.

The simplest explanation is that sound amplitude/level/loudness is encoded by the number of participating units, including off-best frequency cells that get recruited when amplitudes are high (the concept of 'tuning width' is helpful to understand). Loud sounds will recruit cells of a wider best-frequency range with high coincidence, for example (see Carney, 1994). 

In some experimental paradigms, this hypothesis holds; in others, it does not. It is most likely that the perception of loudness is quite context-dependent and also depends on background, the presence of energy in other frequencies, and adaptation.

Similar to how absolute brightness is not all that perceptually useful (and therefore humans display incredible invariance over very wide brightness ranges), loudness is probably perceptually most useful in terms of relative loudness: sounds that are getting louder may be approaching, for example.

References



Carney, L. H. (1994). Spatiotemporal encoding of sound level: Models for normal encoding and recruitment of loudness. Hearing research, 76(1-2), 31-44.

Heinz, M. G., Issa, J. B., &amp; Young, E. D. (2005). Auditory-nerve rate responses are inconsistent with common hypotheses for the neural correlates of loudness recruitment. Journal of the Association for Research in Otolaryngology, 6(2), 91-105.

Neuhoff, J. G., McBeath, M. K., &amp; Wanzie, W. C. (1999). Dynamic frequency change influences loudness perception: A central, analytic process. Journal of Experimental Psychology: Human Perception and Performance, 25(4), 1050.

Relkin, E. M., &amp; Doucet, J. R. (1997). Is loudness simply proportional to the auditory nerve spike count?. The Journal of the Acoustical Society of America, 101(5), 2735-2740.