First, each bank looks at its limit orders and determines how many are eligible to trade at that price. They can also consider how much gold their proprietary trading desk would trade at the same price. The bank then states a single value, the net amount (in ounces) of gold they wish to buy or sell. After each bank provides this value, they determine if the overall net amount is 0. If so, all transactions succeed and the fix is complete. The chair then states, "There are no flags, and we're fixed."
Otherwise, the chair must change the proposed price. If the amount of gold the banks proposed to buy is higher than the amount proposed for sale, he must raise the price. That will decrease the number of proposed purchases, both because more buy limit orders will fail and because of proprietary traders. At the same time, it increases the number of proposed sales, both because more sell limit orders succeed and because of proprietary trading.