According to "regular" stock market philosophy, the "correct" price for a company is the sum of all of its future cash flows. However it is not really feasible to predict what the future profits of a company in a free-ish market are going to be, since at any point a new competitor might pop up and take some market share. In addition, you can't predict if a growing company will not start stabilizing at some point in the future, which would affect its future earnings and thus its price.

So the answer to your question must be no, there are no stock markets where shares are traded on a purely quantitative base. This is because the only way for price discovery on such a market is by perfectly predicting the future, which is not (as far as we know) possible.

I meant based on reported actual figures, rather than predicted ones. It was just a random thought though - the way our financial markets work is so entrenched that I'd be very surprised if anything like it did actually exist anywhere.

It doesn't matter whether the rest of the world will do anything with it if we enjoy theorizing about it on the internet in our free time :)

I don't think reported actual figures are enough to form a good enough image of the worth of a company. The proverbial example would be of buggy whip companies (selling whips for horse drawn carts) reporting record profits the year that Ford opened his first automobile factory. Clearly the buggy whip companies did not have a bright future ahead of them, but you wouldn't be able to tell from reported figures.

Reported figures happened in the past though, it's the future cash flows which affect the price of a company and no one knows what those cash flows will be exactly, not even the company itself.