Every market has a single order book. When you buy Yes, you may be buying from someone who is selling Yes — the shares simply change hands.

You may also be matched with someone buying No. In that case a new pair of shares is created, one Yes and one No, backed by $ 1.00 held in custody until the market resolves. Nobody had to own those shares beforehand.

You do not choose between the two, and you do not need to: your price, your shares and your payout are the same either way.