So, all prices are pretty much determined by the prices on the exchanges.. but why? What makes Mt Gox the determining factor for all Bitcoin dollar prices? It seems like a self fulfilling prophecy, people expect to use Mt Gox as the value, so set their prices accordingly, even if they don't have any relation to the site. Is it just because those are the biggest markets? But are they? How would we know if another market was bigger?
Yes, exactly, it's because they're the biggest markets. When a trade takes place on a market. that means a buyer and seller agreed on a price, which suggests that the price accurately reflects the value of the thing traded. (Assuming there are no confounding factors, such as difficulty withdrawing from the exchange inflating the price.)
If you want to know the price of eggs in dollars, what do you do? You go to the places that exchange the most eggs for dollars and see at what price those exchanges are happening.
In order for an exchange to happen, the buyer and seller must agree that the price is fair, and both must be able to get to the exchange. This generally means the places that can attract the most exchanges have the most accurate prices.