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Consistent union and prioritized consistent union: new operations for preference aggregation

Michaël Rademaker (UGent) and Bernard De Baets (UGent)
(2012) ANNALS OF OPERATIONS RESEARCH. 195(1). p.237-259
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Abstract
We discuss some new approaches to preference aggregation, keeping the natural property of transitivity of strict preferences in mind. In a previous paper, we discussed various ways in which to construct and process strict partial order relations in the context of ranking objects on the basis of multiple criteria. We now broaden the scope to include more general expressions of preferences as inputs and introduce the concept of a NIP-triple, composed of a relation of necessary couples, a relation of impossible couples and a relation of possible couples. The use of NIP-triples allows for a more straightforward characterization of the consistent and prioritized consistent union as well as a smooth formulation of algorithmic implementations. We also introduce a NIP-triple closing operation, which can be combined with the consistent union operations for increased flexibility. Some properties of the proposed operations are examined. The consistent union operation is commutative, as is its composition with the closing operation. Both the consistent and prioritized consistent union are associative, but not when they are composed with the closing operation. Nevertheless, the composed operations surely have their use, which is also discussed.
Keywords
Preference relation, Strict partial order relation, Transitivity, Decision support, Preference aggregation, SOCIAL CHOICE FUNCTIONS, T-TRANSITIVE CLOSURES, RANKING, POLLUTION

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Citation

Please use this url to cite or link to this publication:

Chicago
Rademaker, Michaël, and Bernard De Baets. 2012. “Consistent Union and Prioritized Consistent Union: New Operations for Preference Aggregation.” Annals of Operations Research 195 (1): 237–259.
APA
Rademaker, M., & De Baets, B. (2012). Consistent union and prioritized consistent union: new operations for preference aggregation. ANNALS OF OPERATIONS RESEARCH, 195(1), 237–259.
Vancouver
1.
Rademaker M, De Baets B. Consistent union and prioritized consistent union: new operations for preference aggregation. ANNALS OF OPERATIONS RESEARCH. 2012;195(1):237–59.
MLA
Rademaker, Michaël, and Bernard De Baets. “Consistent Union and Prioritized Consistent Union: New Operations for Preference Aggregation.” ANNALS OF OPERATIONS RESEARCH 195.1 (2012): 237–259. Print.
@article{2136039,
  abstract     = {We discuss some new approaches to preference aggregation, keeping the natural property of transitivity of strict preferences in mind. In a previous paper, we discussed various ways in which to construct and process strict partial order relations in the context of ranking objects on the basis of multiple criteria. We now broaden the scope to include more general expressions of preferences as inputs and introduce the concept of a NIP-triple, composed of a relation of necessary couples, a relation of impossible couples and a relation of possible couples. The use of NIP-triples allows for a more straightforward characterization of the consistent and prioritized consistent union as well as a smooth formulation of algorithmic implementations. We also introduce a NIP-triple closing operation, which can be combined with the consistent union operations for increased flexibility. Some properties of the proposed operations are examined. The consistent union operation is commutative, as is its composition with the closing operation. Both the consistent and prioritized consistent union are associative, but not when they are composed with the closing operation. Nevertheless, the composed operations surely have their use, which is also discussed.},
  author       = {Rademaker, Micha{\"e}l and De Baets, Bernard},
  issn         = {0254-5330},
  journal      = {ANNALS OF OPERATIONS RESEARCH},
  language     = {eng},
  number       = {1},
  pages        = {237--259},
  title        = {Consistent union and prioritized consistent union: new operations for preference aggregation},
  url          = {http://dx.doi.org/10.1007/s10479-011-0852-0},
  volume       = {195},
  year         = {2012},
}

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