Let's say almost everyone believed in the Efficient Market Hypothesis (EMH). Then, trading would decrease significantly, since most people would think that stocks are already fairly priced. That means the few people who trade would move the market significantly, based on whatever idiosyncratic value-theories they had.
But then the EMH believers would see wild moves in the market and stop believing in EMH. They would start trading more to gain profits.
And as more traders participated, the market would behave more and more like the EMH were true. Eventually, the market would stabilize. Prices wouldn't swing so much. This would increase the number of EMH believers.
It would be interesting to survey belief in EMH among traders. If my model is correct, the percentage of EMH believers should be roughly constant, or at least oscillate around some optimum value.