A Modeling Problem
First, assume a system in which a person creates a minimum of three and not more than five goals and assigns each goal a percentage weight from 1–100%. The sum of all values cannot equal more than 100%. If a person created five goals, for example, she could assign each goal a value of 20%, or she could assign 80% to one goal and 5% each to the remaining four, but she could not make all five goals worth 50%.
Now, let each goal be rated on the following scale:
- Needs Development
- Meets Expectations
- Exceeds Expectations
- Substantially Exceeds Expectations
Let each rating then be multiplied by the goal’s respective weight and the weighted results be summed. This sum is defined as a performance rating.
Assume also an evaluating authority. This authority has the power to remove each rater from his or her ratings job. That said, the authority also has an interest in promoting rater autonomy within the system. It has a vested interest in keeping any given performance rating near the median of 3. Therefore, the authority can neither dictate “only give 3s” nor can it outright deny ratings of 2 or below or (especially) 4 and above. It can, however, discourage low and high ratings; it can also encourage median ratings by emphasizing the median’s everydayness: “A 3 isn’t a bad score,” the authority might say. “It means you’re meeting your goal.” Finally, the authority can obfuscate by encouraging high ratings on low-weight goals such that it maintains the illusion of autonomy but still keeps performance ratings down.
Given all this, what are the optimal weights and ratings to assign to systems of three, four, and five goals to obtain both the highest performance rating possible and avoid attracting the authority’s attention?