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Algorithmic Decision Theory: Third International Conference, by Alessandro Agnetis, Gaia Nicosia, Andrea Pacifici (auth.),

By Alessandro Agnetis, Gaia Nicosia, Andrea Pacifici (auth.), Patrice Perny, Marc Pirlot, Alexis Tsoukià s (eds.)

This ebook constitutes the completely refereed convention court cases of the 3rd overseas convention on Algorithmic determination idea, ADT 2013, held in November 2013 in Bruxelles, Belgium. The 33 revised complete papers provided have been rigorously chosen from greater than 70 submissions, overlaying personal tastes in reasoning and choice making, uncertainty and robustness in choice making, multi-criteria choice research and optimization, collective determination making, studying and data extraction for selection aid.

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Additional resources for Algorithmic Decision Theory: Third International Conference, ADT 2013, Bruxelles, Belgium, November 12-14, 2013, Proceedings

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Springer, Heidelberg (2012) 16. : Kernel-based learning methods for preference aggregation. 4OR 7(2), 169–189 (2009) 17. : k-additivity and c-decomposability of bi-capacities and its integral. Fuzzy Sets Syst. 158(15), 1698–1712 (2007) Identification of a 2-Additive BC by Using Mathematical Programming 29 18. : Evaluation and Decision models with multiple criteria: stepping stones for the analyst. Int. Series in Op. Res. & Manag. , vol. 86. Springer (2006) 19. : Determination of weights of interacting criteria from a reference set.

Each voter may support any number of proposals in P and rejects all the others. Subsets of P are called ballots. The favorite ballot Bi ⊆ P of a voter i (1 ≤ i ≤ n) consists of all proposals he supports. The voters evaluate a ballot Q ⊆ P according to the size of the intersection of Q and their favorite ballots. More precisely, voter i accepts Q if and only if a strict majority of proposals from Q is also contained in his favorite ballot, that is, |Bi ∩ Q| > |Q|/2. We say that in this case voter i is happy with Q.

Parameterized by the size h of the solution ballot, Unanimously Accepted Ballot is W[2]-complete and Majoritywise Accepted Ballot is W[2]-hard. Both results hold even if Q+ = ∅. Proof (Sketch). Reduction 1 is a parameterized reduction from the W[2]-hard Hitting Set parameterized by the size k of the hitting set to UnaAB parameterized by the size h of the solution ballot with Q+ = ∅ (see Lemma 1). Because of Observation 2, this implies W[2]-hardness for MajAB parameterized by h even if Q+ = ∅. To show that UnaAB is in W[2], we reduce from UnaAB parameterized by h to the W[2]-complete Independent Dominating Set parameterized by the solution size k [12].

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