Score ordinal ranking configuration according to an optimal ranking

Question

I have a list of items, each associated with their optimal ranking in the list. How can I give a score to a given order of the list.

For instance, if I know that the optimal ranking is: 4 3 5 1 2 And the current ranking of my items is 1 2 3 4 5,

Which metric can I use as a fitness metric (or score) in order to give my algorithm an information as to whether the current ranking configuration is close to the optimal ranking or not?

I don't think I can use Discounted Cumulative Gain (DCG) as all of my items are equally important (it's not more important to rank one of the items well rather than another)

Answer 1

You can find several options here

Common choices include:

• MAP
• DCG
• Spearman Rho & Kendall Tau

which can have varying utility in different settings.