Scoring samples after clusterings

I want to assign a score to all points in a group that I cluster several time.

I want the score to indicate how much this point is grouped with the same individuals all time.

I suppose this idea allready exists, however I didn't found anything, only scoring on global clusters, as mutual information score.

I had an idea, for a point x, to count each point y that is in the same cluster of x in two clusterisations, or in different clusters in the two cases.

Do you know if this is a good idea ? If there is another scoring function that can do that ?