Only market determines prices. 

You mint yes and no tokens (only on the platform, they are not crypto tokens). Their combined value is exactly 1$ (because either yes or no happens and the payout of one will be 1, payout of the other 0).

You can then add a limit sell order to the order book for whatever price you want. And when someone wants to buy for the price, voila the market has spoken and initial price is born. The process then repeats, like on any other market. 

How much is in the bets is not interesting, because you can create arbitrary amount of bets, without price risk. Holding both tokens does not add any information to how risky it is. 

Volume is interesting. Most interesting is the full order book.