I have a set of 10 items each with a weight between 0-1. A person can rate each of these 10 items with a score between 0-100, but is given, say, only 500 points to allocate among these 10 items The person does not know the weight of each item and the total score will be the weighted average.
A person could rate each item as 50 and another person could rate the top 5 items with the highest weights with all 100's. The weights are such that the difference in total scores received by rating all items with 50, and only the top-5 highest weighted items with 100s and the remaining 5 items with 0, is not significant given that the spread in the weights (all between 0-1) is not high.
Given that a person can randomly rate all the items with 50's and still receive a total score very close to the highest possible score obtained by rating the top-5 weighted items with all 100's, is problematic.
Are there any existing alternative approaches/methods/algorithms to solve such a problem so that a person who rates all items 50 will get a score far away from the maximum possible score?