Commercial speech does not currently enjoy the same protection under the Bill of Rights as other forms of speech. Donald Wittman has an interesting argument in favor of the double standard:
The law of large numbers may explain the puzzle that the Bill of Rights protects free speech but not commercial advertising. False political advertising may fool a minority, yet it will have no harmful effect since votes for the minority will not be translated into political power. In contrast, a business does not have to persuade a majority of consumers, only a few, to have any sales. So the majority may want to protect a minority in the commercial area. (The Myth of Democratic Failure, pp.16-17)
For Wittman to be strictly correct, he needs the median voter to be totally unaffected by false political advertising. Brain-washing 40% of the population is fine as long as the remaining 60% hold firm. But that's a pretty unrealistic scenario. A weaker, but more plausible story that Wittman could tell is that false advertising hurts democracy less than markets because the median voter is harder to fool than the mean voter. He could even generalize, and say that democracy is better than markets because the median voter is more rational than the mean voter.
The main problem with this argument is that the empirics go the other way. Take my research on economic beliefs. There is a small minority of well-educated people with relatively sensible views on economics, and an extremely tiny minority of economists with highly sensible views. Then there's everybody else. The mean belief is more rational than the median belief, not the other way around as Wittman's argument requires.
If democracy chose economic policies based on mean preferences, the experts could at least pull up the average, much like Bill Gates pulls up the average American income. But that's not how it works. To win, a politician needs to please the median voter. It makes little difference if a few thousand economists think you a fool.