Adding feasibility constraints to a ranking rule under a monotonicity constraint
(2015)
Advances in Intelligent Systems Research.
In Advances in Intelligent Systems Research
89.
p.1302-1309
- Author
- Raul Perez Fernandez (UGent) , Michaël Rademaker (UGent) , Pedro Alonso, Irene Díaz and Bernard De Baets (UGent)
- Organization
- Abstract
- 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.
- Keywords
- Linear Order, Group Decision Making, Weak Order, Monotonicity, Stochastic Dominance, Integer Linear Programming
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7258308
- MLA
- Perez Fernandez, Raul, et al. “Adding Feasibility Constraints to a Ranking Rule under a Monotonicity Constraint.” Advances in Intelligent Systems Research, edited by JM Alonso et al., vol. 89, Atlantis Press, 2015, pp. 1302–09.
- APA
- Perez Fernandez, R., Rademaker, M., Alonso, P., Díaz, I., & De Baets, B. (2015). Adding feasibility constraints to a ranking rule under a monotonicity constraint. In J. Alonso, H. Bustince, & M. Reformat (Eds.), Advances in Intelligent Systems Research (Vol. 89, pp. 1302–1309). Paris, France: Atlantis Press.
- Chicago author-date
- Perez Fernandez, Raul, Michaël Rademaker, Pedro Alonso, Irene Díaz, and Bernard De Baets. 2015. “Adding Feasibility Constraints to a Ranking Rule under a Monotonicity Constraint.” In Advances in Intelligent Systems Research, edited by JM Alonso, H Bustince, and M Reformat, 89:1302–9. Paris, France: Atlantis Press.
- Chicago author-date (all authors)
- Perez Fernandez, Raul, Michaël Rademaker, Pedro Alonso, Irene Díaz, and Bernard De Baets. 2015. “Adding Feasibility Constraints to a Ranking Rule under a Monotonicity Constraint.” In Advances in Intelligent Systems Research, ed by. JM Alonso, H Bustince, and M Reformat, 89:1302–1309. Paris, France: Atlantis Press.
- Vancouver
- 1.Perez Fernandez R, Rademaker M, Alonso P, Díaz I, De Baets B. Adding feasibility constraints to a ranking rule under a monotonicity constraint. In: Alonso J, Bustince H, Reformat M, editors. Advances in Intelligent Systems Research. Paris, France: Atlantis Press; 2015. p. 1302–9.
- IEEE
- [1]R. Perez Fernandez, M. Rademaker, P. Alonso, I. Díaz, and B. De Baets, “Adding feasibility constraints to a ranking rule under a monotonicity constraint,” in Advances in Intelligent Systems Research, Gijon, Spain, 2015, vol. 89, pp. 1302–1309.
@inproceedings{7258308,
abstract = {{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.}},
author = {{Perez Fernandez, Raul and Rademaker, Michaël and Alonso, Pedro and Díaz, Irene and De Baets, Bernard}},
booktitle = {{Advances in Intelligent Systems Research}},
editor = {{Alonso, JM and Bustince, H and Reformat, M}},
isbn = {{9789462520776}},
issn = {{1951-6851}},
keywords = {{Linear Order,Group Decision Making,Weak Order,Monotonicity,Stochastic Dominance,Integer Linear Programming}},
language = {{eng}},
location = {{Gijon, Spain}},
pages = {{1302--1309}},
publisher = {{Atlantis Press}},
title = {{Adding feasibility constraints to a ranking rule under a monotonicity constraint}},
volume = {{89}},
year = {{2015}},
}