A Borda Rule Induced by the Deck of Cards Method

In this contribution, the Borda rule has been extended to the case of reciprocal preferences through the deck of cards method. Initially, each voter arranges the alternatives in a weak order and, subsequently, introduces a number of cards between consecutive equivalence classes representing the corresponding preference intensities. A consistency condition generates the number of cards between non-consecutive equivalence classes. Taking this information into account, a reciprocal preference on the set of alternatives satisfying a strong transitivity condition is associated with each voter. Then, a score is given to each alternative for each voter: the sum of intensities of preference between that alternative and the others. Finally, the alternatives are ranked by means of the sum of the individual scores.