Responsibility Functions for Explaining Deviations in Decision Behaviour - CHANGES+ Colloquium - Sarah Hiller | Anna-Katharina Kothe April 2020
Outline Introduction Responsibility Decision Scenario Application Discussion Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 2
Introduction Motivation: ◮ Responsibility decision-making nexus ◮ Assign responsibility: Assign call for actions Approach: ◮ Formalized Responsibility Function ◮ Game and according experiment Responsibility Functions based on Heiztig & Hiller (submitted) Decision dilemma in game and according experiment based on Kline et al. (2018) Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 3
Framework w 1 Ingredients: Agents I a w 2 Directed tree � V , E � i Possible actions A v , w 3 v 1 b consequences c v : A v → S v w 4 Figure: Graphical depiction of a morally evaluated multi-agent decision tree with uncertainty. Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 4
Framework Ingredients: w 1 Agents I a Directed tree � V , E � w 2 Possible actions A v , i w 3 v 1 consequences c v : A v → S v b Set of ethically undesired w 4 outcomes ǫ Figure: Graphical depiction of a morally evaluated multi-agent decision tree with uncertainty. Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 4
Framework Ingredients: w 1 1 − p Agents I a Directed tree � V , E � p w 2 Possible actions A v , i w 3 v 1 consequences c v : A v → S v b Set of ethically undesired w 4 outcomes ǫ Ambiguity nodes V a Figure: Graphical depiction of a morally evaluated multi-agent Probabilistic uncertainty V p decision tree with uncertainty. Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 4
Framework Ingredients: w 1 shoot v 1 Agents I j load Directed tree � V , E � pass w 2 Possible actions A v , i w 3 shoot consequences c v : A v → S v pass j Set of ethically undesired v 2 pass w 4 outcomes ǫ Ambiguity nodes V a Figure: Graphical depiction of a morally evaluated multi-agent Probabilistic uncertainty V p decision tree with uncertainty. Information sets ∼ Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 4
Responsibility Function Scenario, strategy A scenario ζ ∈ Z ∼ resolves all ambiguity and information uncertainty A strategy σ ∈ Σ of a group G ⊆ I selects actions for all future decision nodes. Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 5
Responsibility Function Scenario, strategy A scenario ζ ∈ Z ∼ resolves all ambiguity and information uncertainty A strategy σ ∈ Σ of a group G ⊆ I selects actions for all future decision nodes. Hypothetical shortfall Given a scenario ζ , the shortfall of playing a in node v is ∆ ω ( v , a ) := min σ ℓ ( ǫ | c v ( a ) , σ, ζ ) − min σ ℓ ( ǫ | v , σ, ζ ) Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 5
Responsibility Function Scenario, strategy A scenario ζ ∈ Z ∼ resolves all ambiguity and information uncertainty A strategy σ ∈ Σ of a group G ⊆ I selects actions for all future decision nodes. Hypothetical shortfall Given a scenario ζ , the shortfall of playing a in node v is ∆ ω ( v , a ) := min σ ℓ ( ǫ | c v ( a ) , σ, ζ ) − min σ ℓ ( ǫ | v , σ, ζ ) Responsibility R ( v , a ) := ζ ∈ Z ∼ ( v ) ∆ ω ( v , ζ, a ) max Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 5
Criteria Differentiated control groups Uncertainty Ethically (un)desired outcomes Non-linearity Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 6
Game specification Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 7
Game specification Phase 1 : 10 rounds appropriation Phase 2 : 10 rounds mitigation Mitigation goal: 0.53 of total ap- propriation (phase 1). Appropriate 0 , . . . , 4 of the com- Contribute 0 , . . . , 4 to mitigation mon resource. effort. Differentiated case: half of the If the mitigation effort is not agents only start in round 6. met, everyone loses everything with a certain probability p , which increases step-wise from 2 6 12 to 11 9 12 to 12 to 12 with rising total appropriation. Everyone’s choices are made public after each round. Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 8
Game specification Two between-subject treatments ◮ Baseline development ◮ Endogeneous differentiated development Players in the US and China Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 9
Computing responsibility Phase 1: appropriation Phase 2: mitigation -4 i i -20 others 0 0 others 1 2 i -4 3 0 i 4 0 0 i 1-p others others p others -4 0 i 20 1-p 1 -20 2 i 0 3 p 4 others i others -4 1-p 0 i 0 p Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 10
Computing responsibility Except for limit cases (that do not occur in the observed situations), responsibility in phase one is as follows: If we are not in reach of any of the thresholds: 0 When the first appropriation threshold might be crossed: 1 3 When the second appropriation threshold might be crossed: 1 4 When the last appropriation threshold might be crossed: 1 6 Unless agents choose 0 appropriation, in which case the responsibility is also 0 Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 11
Expected behaviour change Always ensure R = 0 4 3 2 1 t1 Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 12
Expected behaviour change Instead: Always ensure R = 0 0 with probability a i , t = p = λ R ( v , nd t ) 4 3 else nd t 2 where nd t is the mean of what 1 agents selected in the experi- t1 ments in the non-differentiated case in round t . Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 12
Expected behaviour change United States China 4 Expected appropriation 3,5 3 2,5 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Period Period Figure: Expected value of the appropriation of the early developer group, E [ a i , t | λ = 0 . 5]. Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 13
Experimental Results Results for mean appropriation per period in both treatment groups, taken from Kline et al. (2018) Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 14
Discussion and Future Work Discussion Curves are shifted between experimental results and computed expectation - possibly due to agents acting according to expectations ⇒ We will not consider this, for normative reasons No account of partial contribution in our framework ⇒ Could include in future variant of a responsibility function Future work Application with other games Extend responsibility function accordingly Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 15
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