Is a perfect investor possible?

The previous post made me think of an idea I've had for a while that isn't really fully formed, which is: is it possible for there to be a "perfect" investor, or is there some formal/logical reason why such perfection would be self-defeating?

On the face of it, it would seem that the presence of a perfect investor would break the market. For normally when we make an investment, it's based on some empirical fact about what we're investing in--that the company is profitable, or that the currency will be devalued, or a trade agreement will be signed, whatever. But suppose God were an investor, and invested in X. In this case, I would also invest in X, not because of anything having to do with X, but simply because God invested in it and I know that God can do no wrong in the market. What's more, all other investors would think the same way, and also make the same investment. At this point, market behavior would become detached from empirical reality, and a prolonged (infinite?) period of irrational exuberance for X would follow.

Of course, one way out would be to simply point out that a truly perfect investor would strive to keep the fact of his perfection a secret by deliberately losing money on investments from time to time. Specifically, the investor could only continue to win so long as his success itself did not become the basis for other players' decision making. In such a scenario, whatever empirical data being collected by the perfect investment algorithm would cease to be relevant, because a new theory--that generates some other set of empirical data--would now be regulating investor decisions. (In this case, the "new empirical data" would be what investment choices the perfect investor is making. The new theory would be, "whatever the perfect investor invests in is a good investment". In the short term, switching to this new theory would not hurt the perfect investor--everyone would continue to invest in X. But eventually the pattern would have to collapse, for the same reason that pyramid schemes always collapse: at some point, you run out of new investors in X--and besides, there would undoubtedly be bizarre and disastrous global effects of so much wealth accumulating to one arbitrary investment.)