Algorithmic Decision Theory: 4th International Conference, by Toby Walsh

By Toby Walsh

This publication constitutes the completely refereed convention court cases of the 4th foreign convention on Algorithmic choice thought , ADT 2015, held in September 2015 in Lexington, united states. The 32 complete papers offered have been rigorously chosen from seventy six submissions. The papers are equipped in topical sections reminiscent of personal tastes; manipulation, studying and different concerns; application and selection conception; argumentation; bribery and keep watch over; social selection; allocation and different difficulties; doctoral consortium.

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In: CP, pp. 973–987 (2012) 11. : Aggregating Conditionally lexicographic preferences using answer set programming solvers. , Tsouki`as, A. ) ADT 2013. LNCS, vol. 8176, pp. 244–258. at Abstract. We consider the situation in which group activities need to be organized for a set of agents when each agent can take part in at most one activity. The agents’ preferences depend both on the activity and the number of participants in that activity. In particular, the preferences are given by means of strict orders over such pairs “(activity, group size)”, including the possibility “do nothing”.

Given an instance (N, A, P ) of o-GASP, an individually rational assignment π : N → A is contractually individually stable, if there is no agent i ∈ N and no a ∈ A∗ \ π(i) such that (i) (a, |π a | + 1) i (π(i), |πi |), (ii) for all i ∈ π a it holds that (a, |π a | + 1) i (a, |π a |), and (iii) there is no h ∈ πi with (π(i), |πi | − 1) ≺h (π(i), |πi |). In a weak core stable assignment π, there is no subset E of agents such that, by deviating from π, all members of E can strictly improve their situation.

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].

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