BLA for collaborative decision Bipolar Leveled sets of Arguments a new framework for collaborative decision Florence Bannay, Romain Guillaume IRIT, Toulouse University, France February 2015 Workshop BRA - Madeira F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 1 / 24
BLA for collaborative decision Addressed problem Provide a tool for helping people to make a collaborative decision. Classical decision analysis : ◮ first formulate the decision goals ◮ identify the attributes of potential alternatives ◮ choose Our particular deliberation problem : ◮ involve several agents ◮ distributed and incomplete knowledge about the alternatives ◮ objective is to check the acceptability of an alternative F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 2 / 24
BLA for collaborative decision Recruitment Example Recruitment done according to the decision goals : goal meaning polarity level ap don’t want an a nti-social p erson ⊖ 0.5 ej hire an e fficient person for the j ob ⊕ 1 ph find a person able to p resent h erself ⊕ 0.5 ⊕ et find a person e asy to t rain 1 ⊕ st hire a st able person 0.5 Features of a candidate ( attributes ) : feature meaning feature meaning cbs C V b ad s pelling i i ntroverted candidate cgr C V g ood r eadability jhop j ob hop per cps C V p oorly s tructured lpe l ong p rof. e xperience eb e duc. b ackground spe exp. spe cific for the job gp g ood p ersonality u u nmotivated candidate F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 3 / 24
BLA for collaborative decision How to make a collaborative decision ? Aim = to choose an alternative that agrees everyone reach an agreement about the importance of the goals 1 reach an agreement about the attributes that are useful 2 reach an agreement about the decision process 3 share the knowledge about a new alternative 4 decide according to the agreements done 5 go to ❹ 6 F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 4 / 24
BLA for collaborative decision Contents Introduction 1 Addressed problem Example Fixing collectively the goals and attributes 2 Bipolar Leveled Argument set Arguments Attacks Validation of arguments for a precise candidate 3 Knowledge of voters Decide about Admissibility of a candidate 4 Realized goal Admissibility Statuses Admissibility thresholds 5 Several agents : Vote Strategies F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 5 / 24
BLA for collaborative decision Bipolar Leveled Argument set ⊕ ⊖ a 1 b 1 a 2 b 2 1 arguments in arguments a 3 favor of the against the candidate candidate a 4 b 3 0 . 6 a 5 b 4 a 6 0 . 3 F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 6 / 24
BLA for collaborative decision Arguments Definition A basic argument a is a pair ( ϕ, g ) where reas ( a ) = ϕ ∈ L F (propostional language about features) and concl ( a ) = g ∈ LIT G (literals of a propositional language about goals). Level and polarity of an argument = level and polarity of its conclusion. Example a = ( eb, ej ) : hiring a candidate with a good e ducational b ackground will achieve the goal to have an e fficient person for the j ob. polarity= ⊕ , level=1 b = ( u, ¬ ej ) : hiring an u nmotivated candidate will make fail the goal to have an e fficient person for the j ob. polarity= ⊖ , level=1 F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 7 / 24
BLA for collaborative decision Attacks Definition (attacks) Arguments a and b are conflicting iff concl ( a ) ∧ concl ( b ) ⊢ ⊥ and reas ( a ) ∧ reas ( b ) � ⊥ . if a and b are conflicting then : either only one attack between e.g. a attacks b meaning that when K ⊢ reas ( a ) ∧ reas ( b ) the goal concl ( a ) is achieved or two symmetric attacks : a attacks b and b attacks a meaning that when K ⊢ reas ( a ) ∧ reas ( b ) we don’t know whether concl ( a ) or concl ( b ) is achieved. F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 8 / 24
BLA for collaborative decision Recruitment BLA Bipolar set of arguments associated to the vacant position : ⊕ ⊖ ( jhop ∧ ¬ spe ∧ lpe, et ) ( jhop ∧ lpe, ¬ et ) ( eb, ej ) ( u, ¬ ej ) 1 ( spe, ej ) ( lpe, ¬ ap ) ( jhop ∧ lpe, ap ) ( gp, ¬ ap ) ( i, ap ) 0.5 ( cgr, ph ) ( cps, ¬ ph ) ( cbs, ¬ ph ) ( jhop ∧ ¬ spe ∧ lpe, ¬ st ) F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 9 / 24
BLA for collaborative decision Contents Introduction 1 Addressed problem Example Fixing collectively the goals and attributes 2 Bipolar Leveled Argument set Arguments Attacks Validation of arguments for a precise candidate 3 Knowledge of voters Decide about Admissibility of a candidate 4 Realized goal Admissibility Statuses Admissibility thresholds 5 Several agents : Vote Strategies F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 10 / 24
BLA for collaborative decision Knowledge of voters Given a bla A , given a candidate c , given a knowledge base K : the feature ϕ holds for candidate c : K ⊢ ϕ , the feature ϕ does not hold for c : K ⊢ ( ¬ ϕ ) , the feature ϕ is unknown for c : K � ϕ and K � ¬ ϕ . Definition (Valid argument according to K ) an argument a = ( ϕ, g ) is valid iff K ⊢ ϕ Definition (Valid BLA according to K ) set of valid arguments according to K F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 11 / 24
BLA for collaborative decision Example of valid BLA Valid BLA if K = { eb, lpe, jhop } ⊕ ⊖ ( jhop ∧ ¬ spe ∧ lpe, et ) ( jhop ∧ lpe, ¬ et ) ( eb, ej ) ( u, ¬ ej ) 1 ( spe, ej ) ( lpe, ¬ ap ) ( jhop ∧ lpe, ap ) ( gp, ¬ ap ) ( i, ap ) 0.5 ( cgr, ph ) ( cps, ¬ ph ) ( cbs, ¬ ph ) ( jhop ∧ ¬ spe ∧ lpe, ¬ st ) F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 12 / 24
BLA for collaborative decision Contents Introduction 1 Addressed problem Example Fixing collectively the goals and attributes 2 Bipolar Leveled Argument set Arguments Attacks Validation of arguments for a precise candidate 3 Knowledge of voters Decide about Admissibility of a candidate 4 Realized goal Admissibility Statuses Admissibility thresholds 5 Several agents : Vote Strategies F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 13 / 24
BLA for collaborative decision Realized goal and Admissibility status Definition (realized goal) The goal g is realized iff ∃ a an unattacked argument s.t. concl ( a ) ≡ g . � R ⊕ = positive realized goals of level e e R = set of realized goals R ⊖ = negative realized goals of level e e Definition (admissibility status) Let e = max g ∈ R l ( g ) . The status of c is : - Necessary admissible ( N ad ) if R ⊕ e � = ∅ and R ⊖ e = ∅ - Possibly admissible ( Π ad ) if R ⊕ e � = ∅ - Indifferent ( Id ) if R = ∅ - Possibly inadmissible ( Π ¬ ad ) if R ⊖ e � = ∅ - Necessary inadmissible ( N ¬ ad ) if R ⊖ e � = ∅ and R ⊕ e = ∅ - Controversial ( Ct ) if R ⊕ e � = ∅ and R ⊖ e � = ∅ F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 14 / 24
BLA for collaborative decision Necessary admissible/inadmissible Necessary admissible Necessary inadmissible ⊕ ⊖ ⊕ ⊖ a 1 a 1 b 1 b 1 a 2 a 2 b 2 b 2 1 1 a 3 a 3 a 4 a 4 b 3 0 . 6 b 3 0 . 6 a 5 a 5 b 4 b 4 a 6 a 6 0 . 3 0 . 3 F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 15 / 24
BLA for collaborative decision Indifferent/Controversial Indifferent Controversial ⊕ ⊖ ⊕ ⊖ a 1 a 1 b 1 b 1 a 2 a 2 b 2 1 b 2 1 a 3 a 3 a 4 a 4 b 3 0 . 6 b 3 0 . 6 a 5 a 5 b 4 b 4 a 6 a 6 0 . 3 0 . 3 F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 16 / 24
BLA for collaborative decision Admissibility thresholds threshold 1 : c ∈ N ad threshold 2a : c ∈ N ad ∪ Id ad threshold 2b : c ∈ N ad ∪ Ct ad threshold 3 : c ∈ N ad ∪ Ct ad ∪ Id ad 1 2a N ad 2b 3 Id ad Ct ad N ¬ ad F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 17 / 24
BLA for collaborative decision Contents Introduction 1 Addressed problem Example Fixing collectively the goals and attributes 2 Bipolar Leveled Argument set Arguments Attacks Validation of arguments for a precise candidate 3 Knowledge of voters Decide about Admissibility of a candidate 4 Realized goal Admissibility Statuses Admissibility thresholds 5 Several agents : Vote Strategies F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 18 / 24
BLA for collaborative decision Voter strategy Common knowledge = features of a candidate, supposed consistent and complementary Vote= give information about a candidate Strategy= choice of the information to hide/give wrt private preferences about candidates ◮ Naive Optimistic strategy = give all the literals that are known to hold and appear in a positive argument for my preferred candidate. ◮ Naive Pessimistic strategy = give information only if it cannot be used against my preferred candidate F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 19 / 24
BLA for collaborative decision Example of optimistic/pessimistic strategy Naive Optimistic agent v 1 , Naive Pessimistic agent v 2 , K v 2 = { lpe, jhop, spe, u } K v 1 = { lpe, jhop, spe, u } ⊕ ⊖ ⊕ ⊖ ( jhop ∧ lpe, ¬ et ) ( jhop ∧ lpe, ¬ et ) ( spe, ej ) ( u, ¬ ej ) ( spe, ej ) ( u, ¬ ej ) ( lpe, ¬ ap ) ( jhop ∧ lpe, ap ) ( lpe, ¬ ap ) ( jhop ∧ lpe, ap ) F. Bannay, R. Guillaume Workshop BRA - Madeira February 2015 20 / 24
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