> How do we tell people to not believe upvotes?

We shouldn't. It's inherent in sites with votes/ratings that the system is designed to indicate a comment's worthiness in its context. Upvotes in /r/science generally indicate scientific accuracy, in /r/funny generally indicate good humor. The site is responsible for collecting them accurately and fairly.

Don't show it to them? Like HN does.

Replace upvote with vote for two Significant Identification Labels, which would be

  I am Left (X) or Right (X)
    Written from Left-View (X)
    Written from Right-View (X)
    
    Biased (X) or Fair (X)
    
    Pushes Left View (X)
    Pushes Right View (X)
    
    I Agree (X) or I Disagree (X)
    
    Makes Sense (X)

As You might see it's geared towards outputting two different Labels, one from I am Left View and one Right View both showing under each other.

The idea is to show both view besides each other to signify there are more side than one to a coin. Right now in Reddit they are both reduced into one counter.

The resulting Significant Identification Labels would be along the following:

  Left Wing
    Pushes Left Wing (X)
    Pushes Right Wing (X)
    Says it
      is Biased Towards
        Left(X)
        Right (X)
      is Fair (X)
      Makes Sense (X)
  
  
  Right Wing
    Pushes Left Wing (X)
    Pushes Right Wing (X)
    Says it
      is Biased Towards
        Left(X)
        Right (X)
      is Fair (X)
      Makes Sense (X)