  Comparing the ranking of candidates by different voters is an important topic
in social and information science with a high relevance from the point of view
of practical applications. In general, ties and pairs of incomparable
candidates may occur, thus, the alternative rankings are described by partial
orders. Various distance measures between partial orders have already been
introduced, where zero distance is corresponding to a perfect match between a
pair of partial orders, and larger values signal greater differences. Here we
take a different approach and propose a similarity measure based on adjusted
mutual information. In general, the similarity value of unity is corresponding
to exactly matching partial orders, while a low similarity is associated to a
pair of independent partial orders. The time complexity of the computation of
this similarity measure is $\mathcal{O}(\left|{\mathcal C}\right|^3)$ in the
worst case, and $\mathcal{O}(\left|{\mathcal C}\right|^2\ln \left|{\mathcal
C}\right|)$ in the typical case of partial orders corresponding to trees with
constant branching number, where $\left|{\mathcal C}\right|$ denotes the number
of candidates. An interesting feature of our approach is that the similarity
measure is sensitive to the position of the disagreements in the ranking:
Differences at the highly ranked candidates induce larger similarity drop
compared to disagreements at the bottom candidates.
