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

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

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

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Unanimously Accepted Ballot (UnaAB) Input: A set P of m proposals; a society V of n voters with favorite ballots B1 , . . , Bn ⊆ P; an agenda Q+ ⊆ P. Question: Is there a ballot Q+ ⊆ Q ⊆ P which every single voter i accepts (that is, |Bi ∩ Q| > |Q|/2)? Majoritywise Accepted Ballot (MajAB) Input: A set P of m proposals; a society V of n voters with favorite ballots B1 , . . , Bn ⊆ P; an agenda Q+ ⊆ P. Question: Is there a ballot Q+ ⊆ Q ⊆ P which a strict majority of the voters accepts (that is, |Bi ∩ Q| > |Q|/2)?

6) The parameter bgap measures how far a given instance is from being trivial in terms of the number of proposals: If each voter’s favorite ballot contains at least (m + 1)/2 proposals, then choosing Q = P makes every voter happy, so the instance is a trivial yes-instance. While the parameters n and m are naturally related to the “dimensions” of the input, the parameters h, bmax , and bgap measure certain degrees of contradiction or inhomogeneity in an instance. Section 2 is devoted to computational complexity results.

We will use the NP-complete Hitting Set (HS) problem [20] to show many of our intractability results. Given a finite set U , subsets S1 , . . , Sr of U , and a nonnegative integer k, HS asks whether there is a hitting set of size k, that is, whether there is a size-k set U ⊆ U such that Si ∩ U = ∅, i ∈ {1, . . , r}. The following reduction from HS to UnaAB is used several times in our intractability proofs. Note that, due to Observation 2, it implies a reduction to MajAB. Reduction 1. Let (U , S1 , .

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