Adding feasibility constraints to a ranking rule under a monotonicity constraint
- https://doi.org/10.2991/ifsa-eusflat-15.2015.184How to use a DOI?
- Group Decision Making, Linear Order, Weak Order, Monotonicity, Stochastic Dominance, Integer Linear Programming.
We propose a new point of view in the long-standing problem where several voters have expressed a linear order relation (or ranking) over a set of candidates. For a ranking a > b > c to represent a group’s opinion, it would be logical that the strength with which a > c is supported should not be less than the strength with which either a > b or b > c is supported. This intuitive property can be considered a monotonicity constraint, and has been addressed before. We extend previous approaches in the following way: as the voters are expressing linear orders, we can take the number of candidates between two candidates to be a measure of the degree to which one candidate is preferred to the other. In this way, intensity of support is both counted as the number of voters who indicate a > c is true, as well as the distance between a and c in these voters’ rankings. The resulting distributions serve as input for a natural ranking rule that is based on stochastic monotonicity and stochastic dominance. Adapting the previous methodology turns out to be non-trivial once we add some natural feasibility constraints.
- © 2015, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Raúl Pérez-Fernández AU - Michael Rademaker AU - Pedro Alonso AU - Irene Díaz AU - Bernard De Baets PY - 2015/06 DA - 2015/06 TI - Adding feasibility constraints to a ranking rule under a monotonicity constraint BT - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology PB - Atlantis Press SP - 1302 EP - 1309 SN - 1951-6851 UR - https://doi.org/10.2991/ifsa-eusflat-15.2015.184 DO - https://doi.org/10.2991/ifsa-eusflat-15.2015.184 ID - Pérez-Fernández2015/06 ER -