Given that I have two lists that each contain a separate subset of a common superset, is there an algorithm to give me a similarity measurement?

Example:

A = { John, Mary, Kate, Peter } and B = { Peter, James, Mary, Kate }

How similar are these two lists? Note that I do not know all elements of the common superset.

Update: I was unclear and I have probably used the word 'set' in a sloppy fashion. My apologies. Clarification: Order is of importance. If identical elements occupy the same position in the list, we have the highest similarity for that element. The similarity decreased the farther apart the identical elements are. The similarity is even lower if the element only exists in one of the lists.

I could even add the extra dimension that lower indices are of greater value, so a a[1] == b[1] is worth more than a[9] == b[9], but that is mainly cause I am curious.