Graphical Languages for Preference ... - Sylvain Bouveret

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Logical and bidding languages – Propositional logicA language based on weighted goalsPreference representation:A propositional language L O . . .a set of propositional symbols O,the usual connectives ¬, ∧, ∨. . . and some weights w ∈ V.ExampleO = { , , , , , , }.Agent 1’s requests:〈 (∧ ( ∧ ) ∨〈〉, −10 ,〈〉∧ , 50 .) 〉, 110 ,Graphical Languages for Preference Representation and Applications28 / 112
Logical and bidding languages – Propositional logicIndividual aggregationThe utility is obtained by aggregating the weights of the satisfied formulas,using ⊕.Individual utilityGiven an agent i, her requests ∆ i , a set π, her individual utility is:⊕u i (π) = {w | 〈ϕ,w〉 ∈ ∆ i and π ϕ}.Two reasonable choices for ⊕ : + or max.Graphical Languages for Preference Representation and Applications29 / 112
Page 1 and 2: Graphical Languages for Preference
Page 3 and 4: Introduction to compact preference
Page 23 and 24: Languages for compact preference re
Page 39 and 40: Logical and bidding languages - Pro
Page 47: Logical and bidding languages - Pro
Page 61: Logical and bidding languages - Bid
Page 64 and 65: Logical and bidding languages - Bid
Page 76 and 77: Graphical languages for ordinal pre
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Graphical languages for ordinal pre
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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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