Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach

Abstract

Preference rankings virtually appear in all field of science (political sciences, behavioral sciences, machine learning, decision making and so on). The well-know social choice problem consists in trying to find a reasonable procedure to use the aggregate preferences expressed by subjects (usually called judges) to reach a collective decision. This problem turns out to be equivalent to the problem of estimating the consensus (central) ranking from data that is known to be a NP-hard Problem. Emond and Mason in 2002 proposed a branch and bound algorithm to calculate the consensus ranking given $n$ rankings expressed on $m$ objects. Depending on the complexity of the problem, there can be multiple solutions and then the consensus ranking may be not unique. We propose a new algorithm to find the consensus ranking that is equivalent to Emond and Mason's algorithm in terms of at least one of the solutions reached, but permits a really remarkable saving in computational time.