Distance and Checksum Algorithms on Lists

Related to the programming competition, I've started thinking about algorithms for:

• measuring the distance between two orderings of the same list (I guess number of swaps required to go from one to the other; even better if the algorithm gave you the swaps required)
• order-sensitive checksums on lists of integers (as above, the lists always contain the same elements but the goal is to have a checksum that distinguishes different orderings with minimal clashes)

Any suggestions for approaches to these? Working Python code would be even better :-)