Given a set and a partition of it, I want to calculate a score (between 0 and 1) reflecting how much is the set "dominated" by the largest subset of the partition. The intuitive idea I'm trying to capture is, considering a set of answers to a question, what's the probability that the most common answer is correct. It might take into account the ratio between the size of the largest subset and the size of the entire set, the ratio between the largest subset to other subsets, etc.
Examples: (The numbers refer to the size of each subset in the partition)
- The score of
60,40should be lower than80,20because the largest subset is smaller in comparison to the entire set. - The score of
70,30should be lower than70,5,5,5,5,5,5because there's a second subset that challenges the dominance of the largest subset. - The score of
90,5,5should be lower than90,5,1,1,1,1,1because an answer given by 5 persons challenges the dominance of the most common answer more than 5 different answers given by 5 different persons.
The closest metric I've found in search is the Gini Coefficient, but it doesn't refer specifically to the (one) largest subset, but to the general inequality between the subsets.
Is there a known metric that captures the idea I've described?