Kendall tau distance

The Kendall tau rank distance is a metric that counts the number of pairwise disagreements between two ranking lists. The larger the distance, the more dissimilar the two lists are. Kendall tau distance is also called bubble-sort distance since it is equivalent to the number of swaps that the bubble sort algorithm would make to place one list in the same order as the other list. The Kendall tau distance was created by Maurice Kendall.

The Kendall tau ranking distance between two lists ${\displaystyle L1}$ and ${\displaystyle L2}$ is

where

${\displaystyle K(\tau _{1},\tau _{2})}$ will be equal to 0 if the two lists are identical and ${\displaystyle n(n-1)/2}$ (where ${\displaystyle n}$ is the list size) if one list is the reverse of the other. Often Kendall tau distance is normalized by dividing by ${\displaystyle n(n-1)/2}$ so a value of 1 indicates maximum disagreement. The normalized Kendall tau distance therefore lies in the interval [0,1].

...
Wikipedia