A heuristic algorithm for the consensus ranking problem

Preference rankings virtually appear in all field of science (behavioural sciences, machine learning, decision making and so on). The well-known 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 NP-hard. A branch and bound algorithm has been previously proposed to calculate the consensus ranking given n rankings expressed on m objects. We propose a new algorithm to find the consensus ranking that is perfectly equivalent to the previous algorithm in terms of solutions reached but permits a remarkable saving in computational time