In an ideal world I think that this is a great idea. But as many have pointed out in trying to fix one problem without looking at all the angles is more likely to just create new one.
In addition to other problems listed is how to determine if the underdog post has great content. If you don't have a way of recognizing great content users will just start upvoting posts of users with little activity in mass with no regard to quality.
You would need to have dedicated people looking for great underdog content to upvote. Let's say I'm that person. I find quality underdog content and upvote it. Anyone else who upvotes it gets a better reward. I suddenly get a ton of users and bots upvoting the content I upvote without even reading the content. Which is just another problem.