Graphical Languages for Preference ... - Sylvain Bouveret

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Introduction to compact preference representationCombinatorial spaces. . .The combinatorial trap. . .Four binary variables. . .x 1 x 2 ≻ x 2 x 3 x 4 ≻ x 1 ≻ ∅ ≻ x 2 ≻ x 1 x 2 x 3 x 4 ≻ x 1 x 3 ≻ x 2 x 4 ≻ x 3 x 4 ≻ x 1 x 4 ≻x 1 x 3 x 4 ≻ x 2 x 3 ≻ x 4 ≻ x 3 ≻ x 1 x 2 x 4 ≻ x 1 x 2 x 3 → 15 subsetsGraphical Languages for Preference Representation and Applications11 / 112
Introduction to compact preference representationCombinatorial spaces. . .The combinatorial trap. . .Twenty binary variables. . .x 8 x 5 ≻ x 5 x 3 x 9 ≻ x 8 ≻ ∅ ≻ x 5 ≻ x 8 x 5 x 3 x 9 ≻ x 8 x 3 ≻ x 5 x 9 ≻ x 3 x 9 ≻ x 8 x 9 ≻x 8 x 3 x 9 ≻ x 5 x 3 ≻ x 9 ≻ x 3 ≻ x 8 x 5 x 9 ≻ x 8 x 5 x 3 x 1 x 2 x 5 x 8 x 9 ≻ x 1 x 5 x 6 ≻x 7 ≻ x 2 x 3 x 4 x 5 x 6 x 7 x 8 ≻ x 1 x 2 x 3 x 4 x 5 ≻ x 1 x 3 ≻ x 2 ≻ x 1 x 3 x 7 x 9 ≻ x 1 x 5 ≻x 1 x 7 x 8 x 9 ≻ x 2 ≻ x 4 ≻ x 6 ≻ x 1 x 7 ≻ x 1 x 2 x 3 ≻ x 1 x 2 ≻ x 2 x 5 x 4 ≻ x 1 ≻x 2 ≻ x 1 x 2 x 5 x 4 ≻ x 1 x 5 ≻ x 2 x 4 ≻ x 5 x 4 ≻ x 1 x 4 ≻ x 1 x 5 x 4 ≻ x 2 x 5 ≻ x 4 ≻x 5 ≻ x 1 x 2 x 4 ≻ x 1 x 2 x 5 ≻ x 1 x 5 ≻ x 5 x 3 x 9 ≻ x 1 ≻ ∅ ≻ x 5 ≻ x 1 x 5 x 3 x 9 ≻x 1 x 3 ≻ x 5 x 9 ≻ x 3 x 9 ≻ x 1 x 9 ≻ x 1 x 3 x 9 ≻ x 5 x 3 ≻ x 9 ≻ x 3 ≻ x 1 x 5 x 9 ≻x 1 x 5 x 3 x 9 x 6 x 5 x 1 x 9 ≻ x 9 x 5 x 6 ≻ x 7 ≻ x 6 x 3 x 4 x 5 x 6 x 7 x 1 ≻ x 9 x 6 x 3 x 4 x 5 ≻x 9 x 3 ≻ x 6 ≻ x 9 x 3 x 7 x 9 ≻ x 9 x 5 ≻ x 9 x 7 x 1 x 9 ≻ x 6 ≻ x 4 ≻ x 6 ≻ x 9 x 7 ≻x 9 x 6 x 3 ≻ x 9 x 6 ≻ x 6 x 5 x 4 ≻ x 9 ≻ x 6 ≻ x 9 x 6 x 5 x 4 ≻ x 9 x 5 ≻ x 6 x 4 ≻ x 5 x 4 ≻x 9 x 4 ≻→ 1048575 subsets → the expression takes more than 12 days.Graphical Languages for Preference Representation and Applications11 / 112
Page 1 and 2: Graphical Languages for Preference
Page 3 and 4: Introduction to compact preference
Page 17: Introduction to compact preference
Page 23 and 24: Languages for compact preference re
Page 39 and 40: Logical and bidding languages - Pro
Page 61: Logical and bidding languages - Bid
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Logical and bidding languages - Bid
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Graphical languages for ordinal pre
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dsc 1 ≻ nsc 1 ; dsc 2 ≻ nsc 2 ;
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N ̸ d¯sc 1 ≻ n¯sc 2 and N ̸ n
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Graphical languages for cardinal pr
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a utility ratio function w(x M |x K
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Collective decision makingOutline1
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Collective decision making - Voting
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Collective decision making - MultiA
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monotonic: π ⊆ π ′ ⇒ π ≼
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ConclusionConclusionGraphical langu
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Bouveret, S. and Lang, J. (2008).Ef
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Gonzales, C., Perny, P., and Queiro
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Bell Journal of Economics, pages 40
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Graphical Languages for Preference ... - Sylvain Bouveret

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