discrete mathematics – Relative Ranking – inflating values part of the same result set while maintaining some semblance of original distance

Data Definition:

A set of scores with size N of range(0 to 10) of decimal values:

(0.5, 0.8, 3.5, 8.5, 9.5, 9.9)


(7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.8)

Problem Definition:

A company has access to a simulation that audits products and spits out a score for each product ranging from 0 to 10. E.g the score of 5 for product ‘X’ will provide the following rating to a customer.

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The company wants to ammend the score to do two things:

  1. Inflate results via relative ranking. Each score should fit closer to 10 even though its real score is not necessarily 10.
  2. Capture distance between low and high scores while maintaining point #1. E.g. fitting the top result as 10, second result as 9, third result as 8 etc.. would not be acceptable as the distance is lost here.

Hence I am trying to come up with a function s = f(o) where s is the relative score and o is the original or absolute score for this set.

What would be a good approach or function to accomplish this?

I can provide more details or answer any questions if needed