By Toby Walsh

This publication constitutes the completely refereed convention complaints of the 4th overseas convention on Algorithmic determination concept , ADT 2015, held in September 2015 in Lexington, united states. The 32 complete papers awarded have been rigorously chosen from seventy six submissions. The papers are geared up in topical sections resembling personal tastes; manipulation, studying and different concerns; application and choice thought; argumentation; bribery and keep watch over; social selection; allocation and different difficulties; doctoral consortium.

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Extra info for Algorithmic Decision Theory: 4th International Conference, ADT 2015, Lexington, KY, USA, September 27-30, 2015, Proceedings

Example text

1 In fact, the case of 2-approval scores can be embedded in the 3-approval setting. The 2-approval case, however, allows for a very intuitive determination of an assignment of maximum score as described in the proof of Theorem 4. 44 A. Darmann Theorem 6. Let κ ∈ N. For any fixed k ≥ 4, under k-approval scores in o-GASP it is NP-complete to decide if there is an individually rational assignment with score at least κ, even when all agents have decreasing preferences. Proof. The proof proceeds by a reduction from E3-Occ-Max-2Sat [4].

4c), another compact representation of T , should we allow empty leaves and exploit the structure of T . ϕ1 ϕ1 ϕ2 ϕ3 ϕ2 ϕ3 l1 ϕ3 l2 (a) T ϕ2 ϕ3 ϕ1 ϕ2 ϕ3 ϕ2 ϕ3 l3 (b) T : pruned T (c) T Fig. 4. P-trees with empty leaves That example generalizes and leads to the question of finding small-sized representations of P-trees (we conjecture that the problem in its decision version asking about the existence of a compact representation of size at most k is NPcomplete). From now on, we assume that P-trees are given in their compact representation.

1. ). Reasoning with Preference Trees over Combinatorial Domains 21 ϕ ψ1 ψ2 Fig. 1. A preference tree Trees such as the one in Fig. 1 are called preference trees, or P-trees. They were introduced by Fraser [5,6], who saw them as a convenient way to represent conditional preferences. Despite their intuitive nature they have not attracted much interest in the preference research in AI. In particular, they were not studied for their relationship to other preference formalisms. Further, the issue of compact representations received only an informal treatment by Fraser (P-trees in their full representation are often impractically large), and the algorithmic issues of reasoning with P-trees were also only touched upon.

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