Ranking Candidates Through Convex Sequences of Variable Weights

Scoring rules are a well-known class of positional voting systems where fixed scores are assigned to the different ranks. Nevertheless, since the winners may change according to the scores used, the choice of the scoring vector is not obvious. For this reason several methods have been suggested so that each candidate may be evaluated with the most favorable scoring vector for him/her. In this paper we propose a new model that allows to use different scoring vector for each candidate and avoid some shortcomings of other methods suggested in the literature. Moreover we give a closed expression for the score obtained by each candidate and, in this way, it is possible to rank the candidates without solving the proposed model.