Maybe I'm missing something, but how are randomness and the emh related?
AFAIK random walk theory assumes the market is unpredictable and is consistent with the emh while other theories like the adaptive market hypothesis assume the opposite and are still consistent with emh.
If the EMH were true, price curves would always display maximum entropy, i.e. randomness, because there would be no spare redundant information that could be used to make predictions about the future. (This is based on Shannon's Communications Theory, but the maximal entropy bound applies to any system that mixes a predictable signal with random noise.)
It doesn't matter if you use an evolutionary explanation for price curves, as in AMH, or claim they're controlled by planetary alignments - because the prediction that price curves show maximum entropy is falsifiable regardless of possible causes.
And when it's tested, it is indeed falsified. See e.g.
tl;dr There are standard tools for estimating entropy, and they all agree that markets aren't truly random. Therefore they can't be maximally efficient.
Quants make a living by mining the signal from the randomness. There's a lot of debate about the best way to do this, but there's no serious disagreement among quants that it's possible - and the people who make money by employing them tend to agree.
Interesting, I'm familiar with information theory but not in the context of financial markets. I'm a little confused though because I assume you're referring to the channel coding theorem (mixing a signal with random noise), but that seems like begging the question to me. Don't you have to make the assumption that the market is a predictable signal with noise for it to be applicable?
I'm sure people employed to predict the stock market believe they are able to predict the stock market, but as far as I'm aware it's an open question in academia.
Also, I should point out, although I do believe markets are random, the intent my original post was more to point out the parent's argument by authority.
http://www.amazon.com/Mis-behavior-Markets-Benoit-Mandelbrot...