I've never seen one for short story writing.
Most of the ones I've seen on FB were for 'cutest kid' or something. I was going to do one for a friend last week because her child was in the running for a $25,000 college scholarship, but then I had to register with all my information in order to vote. That was a no-go.
Honestly, I wonder if any of these are legit or are they hooking you in to send you spam? They hook you because they know you want to show everyone your kid is cute. But does it lead to bad behavior? No, I don't think so. Everyone wants to promote something (cute kid, story, etc.) and I think this appears an easy way to do it.