[10000truths]

You could just convert the 5-star scale to weighted upvotes/downvotes, like so:

  1 stars = 0.00 upvote, 1.00 downvote
  2 stars = 0.25 upvote, 0.75 downvote
  3 stars = 0.50 upvote, 0.50 downvote
  4 stars = 0.75 upvote, 0.25 downvote
  5 stars = 1.00 upvote, 0.00 downvote

And then calculate as usual, and then re-map the result of the formula from the [0, 1] interval to the [1, 5] interval.