This paper analyzes the computational complexity involved in solving fairness issues on graphs, e.g., in the installation of networks such as water networks or oil pipelines. Based on individual rankings of the edges of a graph, we will show under which conditions solutions, i.e., spanning...

The purpose of this paper is to provide a binary comparison of two distance-based preference aggregation rules, Slater's rule and Kemeny''s rule. It will be shown that for certain lists of individual preferences the outcomes will be antagonistic in the sense that what is considered best...

This paper compares binary versions of two well-known preference aggregation methods designed to overcome problems occurring from voting cycles, Copeland's (1951) and Dodgson''s (1876) method. In particular it will first be shown that the Copeland winner can occur at any position in the Dodgson...

Assignments of weak orders to complete binary relations are considered. Firstly, it is shown that assigning the transitive closure of a complete binary relation does not always assign the closest weak order according to any reasonable metric on complete binary relations. It is then shown that...

In this paper we provide a binary extension of Dodgson’s non-binary preference aggregation rule. This new aggregation rule is then compared to two other rules which, as Dodgson’s rule, are also explicitly based on distance functions, namely Kemeny’s and Slater’s rule. It is shown that...

We propose a procedure for dividing indivisible items between two players in which each player ranks the items from best to worst and has no information about the other player’s ranking. It ensures that each player receives a subset of items that it values more than the other player’s...

In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selecting committees from a set of candidates. Using a general geometric framework as developed by Don Saari for preference aggregation, we show that antipodality of a unique maximin and a unique minisum...

This paper compares binary versions of two well-known preference aggregation methods designed to overcome problems occurring from voting cycles, Copeland's (1951) and Dodgson''s (1876) method. In particular it will first be shown that the Copeland winner can occur at any position in the Dodgson...