My camera club went through a few variations of the print competition over 20+ years before the quantity of prints entered dropped so low that I quit going. The digital competition is still going strong, but I have no interest in that as I can view thousands of high-quality digital images any time, anywhere.
For a long time, our print competition was as follows:
Prints were displayed 1 at a time in a light box. Three judges sitting 6 to 8 feet in front of the light box, audience behind. Judges gave each print 3 scores, on a range of 1 to 5, for technical, composition, and interest. One judge would give comments. Scores were tallied and a tie-breaker round followed. There was always a tie-breaker because of the limited 1 to 5 scale. Most judges were incapable of making coherent comments (fear of public speaking). No discussion between judges, no change to preview all prints before judging. 90% of the scores were a 4 or 5. A print had to be complete garbage to get a 3. Never saw a 1 or 2.
This method was a mess, and I hated it. I lobbied for years to change it. It was slow, boring, and controversial. Finally, my suggestion was tried. All prints were first put on display. Audience and judges could wander the room for about 1/2 hour. Judges turned in their scores, but using a 1 to 10 scale. Scores were tabulated and winners announced. The 1 to 10 scale drastically reduced ties. And then ties were ignored. If 2 prints tied for 1st place, they both got a blue ribbon.
So, judges could see all prints before voting if they wanted. And judges were free to talk to each other if they wanted, but that rarely happened. A couple regular judges were close friends, so they walked about together, arguing. They were our best and most respected judges.
Unfortunately, this experiment started as the decline in prints and shift to digital happened. The last meeting I went to there were only 3 prints entered in the "master" category, and 2 of them were mine.
I've never seen a competition were judges did a re-vote when initial votes varied too much. Olympics, dog shows, talent shows, boxing, etc. I think that would be a bad idea. I'm familiar with dog shows and horse shows, and those judges get to wander about and see all the animals they want before the voting. As a judge, I like that freedom, and I think it gives better results. Of course, most animal contests have only 1 judge.