You guys are jumping the shark here:
What is "loudness"?
If we're talking audio, then it's probably the RMS amplitude averaged over the last 50ms or so (continuous time, not sampled). That includes the lowest audible frequencies (~20Hz) in the decision, and responds about as fast as you can perceive (any slower and you'll notice that the switching is sluggish).
You may want it slower than that, still. For example, it's not much use listening to ~50ms of a signal that peaks sporadically. The shortest snippet that you'd want to hear would be perhaps 100ms or more.
You'd also want hysteresis or a minimum timeout in play. Just slowing down the amplitude signals doesn't prevent rapid transitions when the signals are very nearly the same levels. You'll want the signal to hang around a little while, even though it's no longer the loudest signal for those milliseconds.
Also consider, you may not want switching at all. Simply mixing together the signals, leaves the most dominant signal as, well, the most dominant signal! But if they're all on similar signal levels, that's going to sound pretty congested. But suppose you could fade more gradually between them, instead of switching hard. You'd still generate the RMS amplitude signals, but instead of selecting just one, you send each through a math function first, like a squared weighting function (the audible equivalent of gamma correction!), and use that to control the gain of the respective signals being mixed together. Weak signals can be faded to quiet and squelched. A relative decision can still be made (you have to add up the amplitudes and subtract the average-over-all-channels from each, to get the relative intensities). And if you simply replace "math function" with comparator, you reduce the system to the digital (strict one-of-N) case.
All of this can be implemented with analog circuitry, though you'd be looking at a good piece of anachronistic work to get there (think 70s synthesizer equipment). Doing exactly the same computations in a DSP would be about as complicated to write, but far cheaper (and more accurate, give or take math and code errors..

).
Tim