Download Algorithmic Decision Theory: Third International Conference, by Alessandro Agnetis, Gaia Nicosia, Andrea Pacifici (auth.), PDF

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

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

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

Example text

20 J. Ah-Pine, B. Mayag, and A. t. t. a BC) [9]). Let ν be a BC on 3N and x = (x1 , . . , xn ) ∈ Rn . t. ν is given by n |xσ(i) | ν(Nσ(i) ∩N + , Nσ(i) ∩N − )− ν(Nσ(i+1) ∩N + , Nσ(i+1) ∩N − ) Cν (x) := i=1 (14) where N + = {i ∈ N |xi ≥ 0}, N − = N \ N + , Nσ(i) := {σ(i), . . , σ(n)} and σ is a permutation on N such that |xσ(i) | ≤ |xσ(i+1) | ≤ . . ≤ |xσ(n) |. t. b, given by [11] : Cb (x) = (A1 ,A2 )∈3N x− j x+ i ∧ b(A1 , A2 ) i∈A1 (15) j∈A2 x+ x− if xi > 0 if xi < 0 i = xi i = −xi and . + xi = 0 if xi ≤ 0 x− = 0 if x i ≥ 0 i Note that Cν (x) = Cb (x) and the subscript is meant to clarify whether it is ν or b which is used in the calculation.

More surprisingly, this remains so even when the input ballots are almost trivial, that is, bgap = 1. Namely, if |Bi | ≥ (m + 1)/2 for all voters i, then all voters accept the ballot P. But if every voter i only satisfies the slightly weaker condition |Bi | ≥ m/2 , then both problems already become NP-complete. Next, formulating the problems as integer linear programs (ILPs) where the number of variables only depends (exponentially) on n implies fixed-parameter tractability with respect to the parameter n.

T. a BC) [9]). Let ν be a BC on 3N and x = (x1 , . . , xn ) ∈ Rn . t. ν is given by n |xσ(i) | ν(Nσ(i) ∩N + , Nσ(i) ∩N − )− ν(Nσ(i+1) ∩N + , Nσ(i+1) ∩N − ) Cν (x) := i=1 (14) where N + = {i ∈ N |xi ≥ 0}, N − = N \ N + , Nσ(i) := {σ(i), . . , σ(n)} and σ is a permutation on N such that |xσ(i) | ≤ |xσ(i+1) | ≤ . . ≤ |xσ(n) |. t. b, given by [11] : Cb (x) = (A1 ,A2 )∈3N x− j x+ i ∧ b(A1 , A2 ) i∈A1 (15) j∈A2 x+ x− if xi > 0 if xi < 0 i = xi i = −xi and . + xi = 0 if xi ≤ 0 x− = 0 if x i ≥ 0 i Note that Cν (x) = Cb (x) and the subscript is meant to clarify whether it is ν or b which is used in the calculation.

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