Contests where the public votes for their favorite poem or story post every entry they receive for viewing. So, if two hundred people enter and only three win, the remaining writers have lost "first rights" to their pieces just to be considered. Most literary magazines and contests require submissions be previously unpublished, and the saleability decreases merely because a writer wanted a shot.
The biggest problem though, is what part of the greater public actually votes. Sure, some voters will be patrons of whatever website hosts the contest, but most of the people voting will be brought in from the networks of the writers themselves. It goes from the "best" piece winning to whoever can convince the largest number of people to get involved. For fledgling writers who don't have a strong platform, it nearly guarantees defeat.
Some people will argue that not everyone who is told about the contest by one writer will definitely choose that writer's work. Maybe not. But, how likely is it a fan, friend, or family member will make a decision based soley on which pieces they believe the best? Anonymity won't solve the issue because a writer can still inform others which poem or story is theirs.
If a contest insists on using the public vote, it should be a separate category or only count as a percentage of a larger whole. Let writers create their masterpieces instead of campaign for them.