Responsibility Functions for Explaining Deviations in Decision - - PowerPoint PPT Presentation

Responsibility Functions for Explaining Deviations in Decision Behaviour

• CHANGES+ Colloquium -

Sarah Hiller | Anna-Katharina Kothe April 2020

Outline

Introduction Responsibility Decision Scenario Application Discussion

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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)

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Framework

Ingredients: Agents I Directed tree V , E Possible actions Av, consequences cv : Av → Sv

i v1 w1 w2 w3 w4 a b

Figure: Graphical depiction of a morally evaluated multi-agent decision tree with uncertainty.

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Framework

Ingredients: Agents I Directed tree V , E Possible actions Av, consequences cv : Av → Sv Set of ethically undesired

• utcomes ǫ

i v1 w1 w2 w3 w4 a b

Figure: Graphical depiction of a morally evaluated multi-agent decision tree with uncertainty.

Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 4

Framework

Ingredients: Agents I Directed tree V , E Possible actions Av, consequences cv : Av → Sv Set of ethically undesired

• utcomes ǫ

Ambiguity nodes Va Probabilistic uncertainty Vp

i v1 w1 w2 w3 w4 a b 1 − p p

Figure: Graphical depiction of a morally evaluated multi-agent decision tree with uncertainty.

Sarah Hiller | Anna-Katharina Kothe GaNe Future Lab 4

Framework

Ingredients: Agents I Directed tree V , E Possible actions Av, consequences cv : Av → Sv Set of ethically undesired

• utcomes ǫ

Ambiguity nodes Va Probabilistic uncertainty Vp Information sets ∼

i j v1 j v2 w1 w2 w3 w4 load pass shoot pass pass shoot

Figure: Graphical depiction of a morally evaluated multi-agent decision tree with uncertainty.

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.

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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 | cv(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 | cv(a), σ, ζ) − min σ ℓ(ǫ | v, σ, ζ)

Responsibility

R(v, a) := max

ζ∈Z ∼(v) ∆ω(v, ζ, a)

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Criteria

Differentiated control groups Uncertainty Ethically (un)desired outcomes Non-linearity

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Game specification

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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- mon resource. Contribute 0, . . . , 4 to mitigation effort. Differentiated case: half of the agents only start in round 6. If the mitigation effort is not met, everyone loses everything with a certain probability p, which increases step-wise from

2 12 to 6 12 to 9 12 to 11 12 with rising

total appropriation. Everyone’s choices are made public after each round.

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Game specification

Two between-subject treatments

◮ Baseline development ◮ Endogeneous differentiated development

Players in the US and China

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Computing responsibility

• thers

i

20

i

• thers
• thers
• thers
• thers

1 2 3 4 3 2 1 4

Phase 1: appropriation Phase 2: mitigation

• thers
• thers

i i i i

• 20
• 20
• 4
• 4
• 4
• 4

i i i

p 1-p p 1-p p 1-p

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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

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Expected behaviour change

Always ensure R = 0

1 2 3 4 t1

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Expected behaviour change

Always ensure R = 0

1 2 3 4 t1

Instead: ai,t =      with probability p = λR(v, ndt) ndt else where ndt is the mean of what agents selected in the experi- ments in the non-differentiated case in round t.

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Expected behaviour change

United States

Expected appropriation 2,5 3 3,5 4 Period 1 2 3 4 5 6 7 8 9 10

China

Period 1 2 3 4 5 6 7 8 9 10

Figure: Expected value of the appropriation of the early developer group, E[ai,t | λ = 0.5].

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Experimental Results

Results for mean appropriation per period in both treatment groups, taken from Kline et al. (2018)

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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

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