Popular ranking

In this paper we take a new approach to the very old problem of aggregating preferences of multiple agents. We define the notion of popular ranking: a ranking of a set of elements is popular if there exists no other permutation of the elements that a majority of the voters prefer. We show that such a permutation is unlikely to exist: we show that a necessary but not sufficient condition for the existence of a popular ranking is Condorcet’s paradox not occurring. In addition, we show that if Condorcet’s paradox does not occur, then we can efficiently compute a permutation, which may or may not be popular, but for which the voters will have to solve an NP-hard problem to compute a permutation that a majority of them prefer.