Paula Sarabando

Multiattribute Choice With Ordinal Information: A Comparison of Different Decision Rules

In the context of additive multiattribute aggregation, we address problems with ordinal information, i.e., considering a ranking of the weights (the scaling coefficients). Several rules for ranking alternatives in these situations have been proposed and compared, such as the rank-order-centroid weight, minimum value, central value, and maximum regret rules. This paper compares these rules, together with two rules that had never been studied (quasi-dominance and quasi-optimality) that use a tolerance parameter to extend the concepts of dominance and optimality. Another contribution of this paper is the study of the behavior of these rules in the context of selecting a subset of the most promising alternatives. This study intends to provide guidelines about which rules to choose and how to use them (e.g., how many alternatives to retain and what tolerance to use), considering the contradictory goals of keeping a low number of alternatives yet not excluding the best one. The comparisons are grounded on Monte Carlo simulations.

Levels of incomplete information in group decision models - A comprehensive simulation study

We present a comprehensive computational study on the effects of providing different forms of incomplete preference information in additive group decision models. We consider different types of information on individual preferences, and on weights of the group members, and study their effects on conclusiveness, efficiency and fairness of outcomes at the group level. Furthermore, we analyze possible violations of the axiom of independence of irrelevant alternatives (IIA) as well as the impact of problem characteristics, in particular initial agreement between group members. Our results indicate that providing information in the form of a ranking of differences between consecutive alternatives comes close to providing exact cardinal preference information in several outcome dimensions. However, group decision procedures based on incomplete preference information also show a significant amount of violations of the IIA axiom.

Splitting methods for the Eigenvalue Complementarity Problem

ABSTRACT We study splitting methods for solving the Eigenvalue Complementarity Problem (EiCP). We introduce four variants, which depend on the properties (symmetry, nonsymmetry, positive definite, negative definite, indefinite) of the matrices included in the definition of EiCP. Convergence analyses for each one of these versions of the splitting method are discussed. Special choices for the splitting matrices associated with these versions are recommended and tested on the solution of small and large symmetric and nonsymmetric EiCPs. These experiments show that the four versions of the splitting method work well at least for some choices of the splitting matrices. Furthermore, these versions of the splitting methods seem to be competitive with the most efficient state-of-the-art algorithms for the solution of EiCP.

Comparison of decision rules to mediate negotiations with incomplete information

Decisions in society resulting from negotiation among two parties are often inefficient (in terms of Pareto efficiency) as the parties fail to identify an agreement that would make both better off. A third party mediating the negotiation can increase the chances of reaching a Pareto efficient alternative. However, in most practical situations the mediator does not have a precise model of the parties’ preferences, and therefore cannot identify which alternatives are efficient. This paper assesses the performance of decision rules that a mediator can apply in multi-issue bilateral negotiation analysis given ordinal information about the importance of the issues and the value of the potential alternatives in each issue. We assume the preferences of the parties can be modelled by an additive multiattribute value function, but without assuming the precise parameters of this model are known. We study three mediation criteria: maximising the sum of the values, maximising the product of the excesses, or maximising the minimal proportion of potential. Monte-Carlo simulation is used to assess how good the alternative chosen by each decision rule is, and to provide guidelines about the use of these rules in a context of selecting a subset of promising alternatives.