  Comparing the top $k$ elements between two or more ranked results is a common
task in many contexts and settings. A few measures have been proposed to
compare top $k$ lists with attractive mathematical properties, but they face a
number of pitfalls and shortcomings in practice. This work introduces a new
measure to compare any two top k lists based on measuring the information these
lists convey. Our method investigates the compressibility of the lists, and the
length of the message to losslessly encode them gives a natural and robust
measure of their variability. This information-theoretic measure objectively
reconciles all the main considerations that arise when measuring
(dis-)similarity between lists: the extent of their non-overlapping elements in
each of the lists; the amount of disarray among overlapping elements between
the lists; the measurement of displacement of actual ranks of their overlapping
elements.
