  Ranking a set of objects from the most dominant one to the least, based on
the results of paired comparisons, proves to be useful in many contexts. Using
the rankings of teams or individuals players in sports to seed tournaments is
an example. The quality of a ranking is often evaluated by the number of
violations, cases in which an object is ranked lower than another that it has
dominated in a comparison, that it contains. A minimum violations ranking (MVR)
method, as its name suggests, searches specifically for rankings that have the
minimum possible number of violations which may or may not be zero. In this
paper, we present a method based on statistical physics that overcomes
conceptual and practical difficulties faced by earlier studies of the problem.
