The question arises: what if not 1 wins against 4, but 4 wins against 1? Then only 3 is eliminated, and 1, 2, and 4 each have one loss, creating a cycle: 2 > 4, 4 > 1, 1 > 2. Which of the three goes to the final?
I highly respect Wicc's opinion and agree that a double-elimination format is more appropriate, but for the first tournament for beginners, a simple single-elimination format is better.