Haven't tried it here, but on MR when viewing a thread, if at the top of the thread one clicks on "Sort by Reaction Score," the 25 posts with the most "likes" or "reactions" are arranged in order by the greatest number descending downward. So for the monthly POTD thread there anyone can quickly view the top 25 images and determine who the "winner" is. That isn't actually a contest, though, it's just members offering an image each day for others' enjoyment. The one key "rule" is that just one image per day can be submitted in that thread, and another is that the shot must have been taken by the member posting it. (We do have one exception there, for a disabled member who cannot physically push the shutter button herself.) Images are posted by whoever comes along, sees the thread and has a photo they'd like to share. Critiques are not offered unless specifically requested, and I have the feeling that many viewers just hit the "like" button no matter what, regardless of actual quality of the image displayed.
Separately within the Digital Photography subforum there is also a weekly competition over there, where the winner gets to choose the topic for the next round and also gets to (groan) judge the competition. Why the groan? Many of us are fond of being in second or third place on the "podium" and receiving acknowledgement from our peers but most of us don't like actually winning the thing, as it can be rather time-consuming being responsible for it during the week that one is the judge. There are various rules around those competitions, such as viewers are NOT to hit the "like" button on any submitted image until after the competition has been completed and judged. Topics vary and it's interesting to see how some seem to have a lot of participation while others wither on the vine. Images can be submitted from one's archives or fresh out of the camera, but just one entry per member, and the shot MUST have been taken by the person submitting it. There are no constraints on the gear used, so everything from a smartphone to a top-of-the-line ILC and everything in between can be represented. Critiques may be offered during the judging process but many people go lightly on that, since the overall idea is to have fun, not to hurt someone's feelings. I find critique to be useful and helpful, but not everyone does, and some members may be hypersensitive to the slightest suggestion that their image is anything less than absolutely stellar.
Right now, as Eric points out, we have only a small group of people who seem to be posting in our monthly Photo of the Day thread here, and I don't know how many other members actually look in on that thread either regularly or sporadically. There seem to be a small number of "likes" on the various images, so we do have an audience, but a rather sparse one. I am not sure that we would have a significant increase in members looking at a competition thread, so it is likely that the contest participants would consist of the same few members who now post daily images in the regular POTD thread and viewed by those who are already in the habit of looking at the images. ??