Collective Decision-Making with Goals Arianna Novaro PhD Thesis - PowerPoint PPT Presentation

Collective Decision-Making with Goals Arianna Novaro PhD Thesis Defense 12 th of November 2019 Supervised by Umberto Grandi Dominique Longin Emiliano Lorini

Collective Decision-Making with Goals PhD Defense The Research (Fields) Behind the Title Collective Decision-Making with Goals Multi-Agent Systems Computational Social Choice Interactions of multiple Aggregation of preferences or agents acting towards a goal. opinions of a group of agents. Game Theory Logical Languages Strategic agents trying to To represent goals, agents maximize their utilities. and their interactions. Arianna Novaro 2/30

Collective Decision-Making with Goals PhD Defense Challenges in Collective Decision-Making Compact Input Please input your preferences over the 50 options as a linear order. Strategic Behavior The new vote of agent 5 changes the winner. Easy Computation Please wait 80 hours while I calculate the result. I found 9 equally good plans satisfying your query. Decisive Result Arianna Novaro 3/30

Collective Decision-Making with Goals PhD Defense A Tale of Two Research Questions 1. How can we design aggregation procedures to help a group of agents having compactly expressed goals and preferences make a collective choice? 2. How can we model agents with conflicting goals who try to get a better outcome for themselves by acting strategically? Arianna Novaro 4/30

Collective Decision-Making with Goals PhD Defense Presentation Roadmap � Aggregation 1 1. Goal-based Voting 2. Aggregation of gCP-nets � Strategic Behavior 2 3. Strategic Goal-based Voting 4. Strategic Disclosure of Opinions on a Social Network 5. Relaxing Exclusive Control in Boolean Games Arianna Novaro 5/30

Part I: Aggregation

Collective Decision-Making with Goals PhD Defense Compact Languages | Goals and Preferences gCP-nets Propositional Logic Goals ϕ := ψ : p 1 ⊲ p 2 ϕ ::= p | ¬ ϕ | ϕ 1 ∧ ϕ 2 | ϕ 1 ∨ ϕ 2 “ fish ∧ white w ” “ fish ∨ chocolate : white w ⊲ red w ” Arianna Novaro 7/30

Collective Decision-Making with Goals PhD Defense Goal-based Voting | Framework ◮ n agents in A have to decide over m binary issues in I • A = { A, B, C } and I = { morning , guest talks , lunch } ◮ agent i ’s goal is prop. formula γ i with models Mod( γ i ) • γ C = guest talks ∧ ( morning → lunch ) • Mod( γ C ) = { (111) , (011) , (010) } ◮ a goal-profile Γ = ( γ 1 , . . . , γ n ) contains all agents’ goals ◮ no integrity constraints Novaro , Grandi, Longin, Lorini. Goal-Based Collective Decisions: Axiomatics and Computational Complexity . IJCAI-18. Arianna Novaro 8/30

Collective Decision-Making with Goals PhD Defense Goal-based Voting | Rules A goal-based voting rule is a collection of functions for all n and m F : ( L I ) n → P ( { 0 , 1 } m ) \ {∅} Approval: Return all interpretations satisfying the most goals. Majority: . . . how to generalize to propositional goals? agent i Mod( γ i ) (000) A EMaj Majority with equal weights to models. (010) B TrueMaj Majority with equal weights to models (100) and fair treatment of ties. 2sMaj Majority done in two steps: on goals, (111) C and then on result of step one. (011) (010) Arianna Novaro 9/30

Collective Decision-Making with Goals PhD Defense Goal-based Voting | Rules A goal-based voting rule is a collection of functions for all n and m F : ( L I ) n → P ( { 0 , 1 } m ) \ {∅} Approval: Return all interpretations satisfying the most goals. Majority: . . . how to generalize to propositional goals? agent i Mod( γ i ) (000) A EMaj Majority with equal weights to models. (010) B TrueMaj Majority with equal weights to models (100) and fair treatment of ties. 2sMaj Majority done in two steps: on goals, (111) C and then on result of step one. (011) (010) Arianna Novaro 10/30

Collective Decision-Making with Goals PhD Defense Goal-based Voting | Axioms The axiomatic method in Social Choice Theory is an established approach studying which properties are satisfied by voting rules. ◮ Challenge: How to generalize axioms to goal-based voting? issue-wise model-wise ( 0 10) ( 010 ) A A Two interpretations for B ( 0 10) B ( 010 ) unanimity (and others) C ( 0 10) C ( 010 ) ( 0 11) (011) Arianna Novaro 11/30

Collective Decision-Making with Goals PhD Defense Goal-based Voting | Axiomatic Results ◮ Negative results: Axioms often incompatible. Theorem. No resolute F can satisfy both anonymity and duality. ◮ Positive results: Characterization of the rule TrueMaj . Theorem. A rule is egalitarian, independent, neutral, anonymous, monotonic, unanimous and dual if and only if it is TrueMaj . Arianna Novaro 12/30

Collective Decision-Making with Goals PhD Defense Goal-based Voting | Complexity Results How hard is it to compute the outcome of a rule F ? WinDet ( F ) Given profile Γ and issue j ∈ I , is it the case that F ( Γ ) j = 1 ? PP: Probabilistic Polynomial Time WinDet ( F ) membership hardness Θ 2 Approval p -complete PSPACE PP EMaj P PP 2sMaj PP TrueMaj PSPACE PP γ i ∈ L ∧ , L ∨ EMaj , 2sMaj , TrueMaj P Arianna Novaro 13/30

Collective Decision-Making with Goals PhD Defense gCP-nets | Framework ◮ A variable X has values x 1 , x 2 , . . . on which agents express ceteris paribus preferences via CP statements • price = { cheap , high } , area = { Capitole , Blagnac , . . . } • high : Capitole ⊲ Blagnac ◮ A CP-net N induces an order > N on possible outcomes ab 2 c ab 2 c ϕ 2 ϕ 2 ( ϕ 1 ) ⊤ : b 2 ⊲ b 1 ab 2 c ab 2 c ϕ 1 ϕ 1 ( ϕ 2 ) c ∨ b 2 : a ⊲ a ϕ 1 ϕ 1 ab 1 c ab 1 c ϕ 2 ab 1 c ab 1 c Haret, Novaro , Grandi. Preference Aggregation with Incomplete CP-nets . KR-18. Arianna Novaro 14/30

Collective Decision-Making with Goals PhD Defense gCP-nets | Semantics Aggregate dominance relations in the individual CP-nets by using four semantics. Pareto Dominance stays if all agents have it maj Dominance stays if a majority of agents have it max Dominance stays if a majority of non-indifferent agents have it rank Sum of length of longest path to a non-dominated dominance class ab ab ab ab ab ab ab ab ab ab ab ab ab ab ab ab > 1 > 2 > 3 > P M Arianna Novaro 15/30

Collective Decision-Making with Goals PhD Defense gCP-nets | Computational Problems Dominance Dominance : o 1 > N o 2 Consistency Consistency : there is no o such that o > N o Dominance for o o ′ > N o implies o > N o ′ for all o ′ wNon-Dom’ed : there is no o ′ so that o ′ > N o (including o ′ = o ) Non-Dom’ed : o > N o ′ for all o ′ Dom’ing : Str-Dom’ing : o is dominating and non-dominated in > N Existence ∃ Non-Dom’ed : there is a non-dominated outcome in > N ∃ Dom’ing : there is a dominating outcome in > N ∃ Str-Dom’ing : there is a strongly dominating outcome in > N Arianna Novaro 16/30

Collective Decision-Making with Goals PhD Defense gCP-nets | Complexity Results one gCP-net Pareto maj max rank Dominance PSPACE-c PSPACE-c PSPACE-c PSPACE-c PSPACE-h Consistency PSPACE-c PSPACE-c PSPACE-h PSPACE-h — PSPACE-c PSPACE-c PSPACE-c PSPACE-h PSPACE-h wNon-Dom’ed P PSPACE-c PSPACE-c in PSPACE — Non-Dom’ed Dom’ing PSPACE-c PSPACE-c PSPACE-c PSPACE-c PSPACE-h Str-Dom’ing PSPACE-c PSPACE-c PSPACE-c PSPACE-c — ∃ Non-Dom’ed NP-c PSPACE-c NP-h NP-h — ∃ Dom’ing PSPACE-c PSPACE-c PSPACE-c PSPACE-c — ∃ Str-Dom’ing PSPACE-c PSPACE-c PSPACE-c PSPACE-c — Most results do not become harder when moving from one to multiple gCP-nets. Arianna Novaro 17/30

Part II: Strategic Behavior

Collective Decision-Making with Goals PhD Defense Strategic Goal-based Voting | Example A (111) (111) B (010) (010) A: “Morning, guest talks, lunch.” B: “Afternoon, guest talks, no lunch.” (011) (001) C: “Either afternoon, guest talks and lunch , C (100) or no guest talks and no lunch .” (000) TrueMaj (010) (011) Novaro , Grandi, Longin, Lorini. Strategic Majoritarian Voting with Propositional Goals (EA) . AAMAS-19. Arianna Novaro 19/30

Collective Decision-Making with Goals PhD Defense Strategic Goal-based Voting | Framework F is resolute if it always returns a singleton output. ◮ An agent i is satisfied with F ( Γ ) iff F ( Γ ) ⊂ Mod( γ i ). F is weakly resolute F ( Γ ) = Mod( ϕ ) for ϕ a conjunction on all Γ . ◮ An agent i is satisfied with F ( Γ ) . . . depends on if she is an optimist, a pessimist or an expected utility maximizer. F is strategy-proof if for all Γ there is no agent i who would get a preferred outcome by submitting goal γ ′ i . Arianna Novaro 20/30

Collective Decision-Making with Goals PhD Defense Strategic Goal-based Voting | Results Agents may know each other and have some ideas about their goals . . . Unrestricted: i can send any γ ′ i instead of her truthful γ i Erosion: i can only send a γ ′ i s.t. Mod( γ ′ i ) ⊆ Mod( γ i ) Dilatation: i can send only a γ ′ i s.t. Mod( γ i ) ⊆ Mod( γ ′ i ) L ∧ L ∨ L ⊕ L E D E D E D E D EMaj M M SP SP M SP M M M M SP SP M SP M M TrueMaj 2sMaj M M SP SP SP SP M M Theorem. Manip ( 2sMaj ) and Manip ( EMaj ) are PP-hard. Arianna Novaro 21/30