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Lumifer comments on No Universally Compelling Arguments in Math or Science - Less Wrong
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In the equilibrium, the average consumer buys from the average firm. Otherwise it doesn't stay average for long.
However the core of the issue is that democracy is a mechanism, it's not guaranteed to produce optimal or even good results. Having "bad" voters will not prevent the mechanism of democracy from functioning, it just might lead to "bad" results.
"Democracy is the theory that the common people know what they want, and deserve to get it good and hard." -- H.L.Mencken.
The median consumer of a good purchases from (somewhere around) the median firm selling a good. That doesn't necessarily aggregate, and it certainly doesn't weigh all consumers or firms equally. The consumers who buy the most of a good tend to have different preferences and research opportunities than average consumers, for example.
You could get similar results in a democracy, but most democracies don't really encourage it : most places emphasize voting regardless of knowledge of a topic, and some jurisdictions mandate it.