Teresa Peña

Preference aggregation and DEA : An analysis of the methods proposed to discriminate efficient candidates

There are different ways to allow the voters to express their preferences on a set of candidates. In ranked voting systems, each voter selects a subset of the candidates and ranks them in order of preference. A well-known class of these voting systems are scoring rules, where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners. One of the most important issues in this context is the choice of the scoring vector, since the winning candidate can vary according to the scores used. To avoid this problem, Cook and Kress [W.D. Cook, M. Kress, A data envelopment model for aggregating preference rankings, Management Science 36 (11) (1990) 1302-1310], using a DEA/AR model, proposed to assess each candidate with the most favorable scoring vector for him/her. However, the use of this procedure often causes several candidates to be efficient, i.e., they achieve the maximum score. For this reason, several methods to discriminate among efficient candidates have been proposed. The aim of this paper is to analyze and show some drawbacks of these methods.

Multiobjective stochastic programming for feed formulation

The minimum cost linear programming model used traditionally for feed formulation does not take account of variability of nutrients in feed ingredients. Therefore, it may be that the nutrient requirements of the animal are not adequately met. In this paper, we show how a multiobjective stochastic model that permits confronting the cost of the ration with the probabilities of meeting the nutrient requirements of the animal can enhance the process of animal diet formulation. The model presented here does not require any a priori information from the decision maker, eliciting his preferences through an interactive process. This is the main advantage in relation to other models found in the literature for treating the problem of nutrient variability, which introduce stochastic constraints in the single objective minimum cost model requiring fixing the level of probability desired for each one of the nutrients in advance.

Aggregating preferences rankings with variable weights

One of the most important issues for aggregating preferences rankings is the determination of the weights associated with the different ranking places. To avoid the subjectivity in determining the weights, Cook and Kress (1990) [5] suggested evaluating each candidate with the most favorable scoring vector for him/her. With this purpose, various models based on Data Envelopment Analysis have appeared in the literature. Although these methods do not require predetermine the weights subjectively, some of them have a serious drawback: the relative order between two candidates may be altered when the number of first, second, …, kth ranks obtained by other candidates changes, although there is not any variation in the number of first, second, …, kth ranks obtained by both candidates. In this paper we propose a model that allows each candidate to be evaluated with the most favorable weighting vector for him/her and avoids the previous drawback. Moreover, in some cases, we give a closed expression for the score assigned with our model to each candidate.

Scoring Rules and Consensus

In this paper we consider that voters rank order a set of alternatives and a scoring rule is used for obtaining a set of winning alternatives. The scoring rule we use is not previously fixed, but we analyze how to select one of them in such a way that the collective utility is maximized. In order to generate that collective utility, we ask voters for additional information: agents declare which alternatives are good and their degree of optimism.With that information and a satisfaction function, for each scoring rule we generate individual utility functions. The utility an alternative has for a voter should depend on whether this alternative is a winner for that scoring rule and on the position this alternative has in the individual ranking. Taking into account all these individual utilities, we aggregate them by means of an OWA operator and we generate a collective utility for each scoring rule. By maximizing the collective utility, we obtain the set of scoring rules that maximizes consensus among voters. Then, applying one of these scoring rules we obtain a collective weak order on the set of alternatives, thus a set of winning alternatives.

Generating OWA Weights from Individual Assessments

In this contribution we propose a method for generating OWA weighting vectors from the individual assessments on a set of alternatives in such a way that these weights minimize the disagreement among individual assessments and the outcome provided by the OWA operator. For measuring that disagreement we have aggregated distances between individual and collective assessments by using a metric and an aggregation function. We have paid attention to Manhattan and Chebyshev metrics and arithmetic mean and maximum as aggregation functions. In this setting, we have proven that medians and the mid-range are the solutions for some cases. When a general solution is not available, we have provided some mathematical programs for solving the problem.