February 22, 2017

Algorithmic Decision Theory: Second International by Dorothea Baumeister, Gábor Erdélyi, Jörg Rothe (auth.),

By Dorothea Baumeister, Gábor Erdélyi, Jörg Rothe (auth.), Ronen I. Brafman, Fred S. Roberts, Alexis Tsoukià s (eds.)

This e-book constitutes the refereed court cases of the second one foreign convention on Algorithmic determination thought, ADT 2011, held in Piscataway, NJ, united states, in October 2011. The 24 revised complete papers offered have been conscientiously reviewed and chosen from 50 submissions.

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Additional info for Algorithmic Decision Theory: Second International Conference, ADT 2011, Piscataway, NJ, USA, October 26-28, 2011. Proceedings

Example text

Once column W [·, n] is computed, the preferred items can then be identified in two steps: 1. one identifies profit vectors p for which W [p, n] ≤ B; 2. one extracts the non-dominated elements among them. The corresponding preferred solutions can then be retrieved by using standard bookkeeping techniques. We adapt this method as follows to fit the committee selection problem, where n one has to take into account cardinality constraint i=1 xi = K and where (p1 , . . , pC ) ∈ 0, K C ↑ . In step 1 above, one identifies profit vectors p for which W [p, n] ≤ B and pC = K.

Once column W [·, n] is computed, the preferred items can then be identified in two steps: 1. one identifies profit vectors p for which W [p, n] ≤ B; 2. one extracts the non-dominated elements among them. The corresponding preferred solutions can then be retrieved by using standard bookkeeping techniques. We adapt this method as follows to fit the committee selection problem, where n one has to take into account cardinality constraint i=1 xi = K and where (p1 , . . , pC ) ∈ 0, K C ↑ . In step 1 above, one identifies profit vectors p for which W [p, n] ≤ B and pC = K.

Conditional effects are defined in the same manner. I is the usual initial state with the addition of the the vector v(I) marking the initial values of the numeric variables, and G is simply a conjunction of conditions. t v i (s) is the numeric value of v i in the state s. The value of an expression e in as state s is the rational number that the expression simplifies to when replacing all numeric variables with their respective value, v(s), or it is undefined if division by 0 occurs. A constraint (e, comp, e ) holds in a state s if e and e are defined in s and stand in the relation comp.

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