There are several things to keep in mind when you judge a public forum debate round. First and foremost, the team that wins should be the team that persuaded you more that their side of the resolution is correct. This can happen in many ways -- you might like their case better, you might think they gave an excellent final focus, or you might be overall more persuaded by their speaking style.
Secondly, a judge should do their best to keep an accurate “flow” of the round. Debaters and judges have a particular way of flowing, so if you’re new to the practice, the best option is to take notes on each speech in different columns on your flow. Ideally, the column of a speech will be adjacent to the column for the following speech so that you can directly compare what was said and unsaid from speech to speech.
Thirdly, judges must limit their intervention in the round. One should make the decision based on who brought up the best material in the context of the round. Any and all biases you have towards the resolution should be left at the door when judging a PF round.
Fourth and finally, the judge should write their reason for decision on the ballot. Ideally, the judge will also give a verbal explanation of their decision as well as areas of improvement to the students in the debate round.
Overall, judging is difficult! You may be unsure which side won the round. The old saying applies: “practice makes perfect.” The more rounds you judge, the more you will understand the ins-and-outs of this activity. Pay attention and do your best -- the rest will sort itself out.