An Ordinal Banzhaf Index for Social Ranking

We introduce a new method to rank single elements given an order over their sets. For this purpose, we extend the game theoretic notion of marginal contribution and of Banzhaf index to our ordinal framework. Furthermore, we characterize the resulting ordinal Banzhaf solution by means of a set of properties inspired from those used to axiomatically characterize another solution from the literature: the ceteris paribus majority. Finally, we show that the computational procedure for these two social ranking solutions boils down to a weighted combination of comparisons over the same subsets of elements.