Suppose I have 2 rankings:
$1$, $2$, $3$ and $2, 1, 3$ then the Kendall's distance between the two is 1 since there is only one pairwise adjacent switch.
My question is, suppose my 2 rankings each consist of 3 items, then what's the average Kendall's distance between them? What's the average distance between 2 rankings with 8 items? Or X items?
I tried permuting all possible cases of rankings with 3 items (i.e. {1, 2, 3}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}, {2, 3, 1}, {2, 1, 3} and then calculating the Kendall's distance from each ranking to all the other ones. Then I took the average and got 1.5. Not sure if that's correct, and rankings with lots of items become computationally difficult for me, so I was wondering if there's a more straightforward solution.
note: couldn't find a suitable tag so I just used permutation