Download e-book for iPad: Algorithmic Decision Theory: 4th International Conference, by Toby Walsh

By Toby Walsh

ISBN-10: 3319231138

ISBN-13: 9783319231136

ISBN-10: 3319231146

ISBN-13: 9783319231143

This e-book constitutes the completely refereed convention complaints of the 4th foreign convention on Algorithmic choice concept , ADT 2015, held in September 2015 in Lexington, united states. The 32 complete papers provided have been rigorously chosen from seventy six submissions. The papers are geared up in topical sections similar to personal tastes; manipulation, studying and different matters; software and choice concept; argumentation; bribery and regulate; social selection; allocation and different difficulties; doctoral consortium.

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

Example text

P-trees Extend Possibilistic Logic. A possibilistic logic theory Π over a vocabulary I is a set of preference pairs {(φ1 , a1 ), . . , (φm , am )}, where every φi is a Boolean formula over I, and every ai is a real number such that 1 ≥ a1 > . . > am ≥ 0 (if two formulas have the same importance level, they can be replaced by their conjunction). Intuitively, ai represents the importance of φi , with larger values indicating higher importance. The tolerance degree of outcome M with regard to preference pair (φ, a), TD (φ,a) (M ), is defined by TD (φ,a) (M ) = 1, 1 − a, M |= φ M |= φ Based on that, the tolerance degree of outcome M with regard to a set Π of preference pairs, TD Π (M ), is defined by TD Π (M ) = min{TD (φi ,ai ) (M ) : 1 ≤ i ≤ m}.

Let us come back to the vacation example and assume that an agent prefers vacations involving water sports in Florida or hiking in Colorado over the other options. This preference is described by the formula (x1 ∧ x2 ) ∨ (¬x1 ∧ ¬x2 ) or, more concisely, as an equivalence x1 ≡ x2 . Within each of the two groups of vacations (satisfying the formula and not satisfying the formula), driving (x4 ) is the preferred transporting mode. These preferences can be captured by the P-tree in Fig. 2a. We note that in this example, the preferences at the second level are unconditional, that is, they do not depend on preferences at the top level.

We take two different approaches to establish such an assignment: (i) by use of k-approval scores; (ii) considering stability concepts such as Nash and core stability. For each of these approaches, we analyse the computational complexity involved in finding a desired assignment. Particular focus is laid on two natural special cases of agents’ preferences which allow for positive complexity results. 1 Introduction In many situations activities need to be organized for a set of agents, with the agents having preferences over the activities.

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Algorithmic Decision Theory: 4th International Conference, ADT 2015, Lexington, KY, USA, September 27-30, 2015, Proceedings by Toby Walsh


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