I want to calculate the Top-Down Concordance coefficient that quantifies the agreement between two rankings by emphasizing more on the lowest rankings. The original paper is:
R.L. Iman and W.J. Conover, A measure of top-down correlation, Technometrics 29(3) (1987), pp. 351–357.
but it is also described in a more recent one.
My problem is how to calculate the Savage Scores from tied ranks. E.g.
Ranking A:
[ 1., 2., 3., 4., 5., 7., 7., 7., 9., 10., 11., 12.]
Ranking B:
[ 1. , 2. , 3.5, 3.5, 5. , 6. , 7. , 8. , 9. , 10. , 11. , 12. ]
In this case I have taken the average of the scores of the tied observations. As you can see there is a group of 3 tied ranks (7) in Ranking A and a group of two tied ranks (3.5) in Ranking B. How should I calculate the Savage Score for these ranks? For instance, there are several ways I can think to get the Savage Score for Rank 7 in A:
1/7 + 1/9 + 1/10 + 1/11 + 1/12 or 1/7 + 1/7 + 1/9 + 1/10 + 1/11 + 1/12 or 1/7 + 1/7 + 1/7 + 1/9 + 1/10 + 1/11 + 1/12 etc.
Or doesn't Top-Down Concordance support tied ranks at all? In that case is there any other concordance coefficient emphasizing on the lower ranks that you would suggest?