Using Feasible Action-Space Reduction by Groups to fill Causal Responsibility Gaps in Spatial Interactions

TL;DR

A metric for the causal responsibility of groups is formulated and a tiering algorithm for systematically identifying assertive agents is proposed to identify assertive agents that are causally responsible for the trajectory of an affected agent.

Abstract

Heralding the advent of autonomous vehicles and mobile robots that interact with humans, responsibility in spatial interaction is burgeoning as a research topic. Even though metrics of responsibility tailored to spatial interactions have been proposed, they are mostly focused on the responsibility of individual agents. Metrics of causal responsibility focusing on individuals fail in cases of causal overdeterminism -- when many actors simultaneously cause an outcome. To fill the gaps in causal responsibility left by individual-focused metrics, we formulate a metric for the causal responsibility of groups. To identify assertive agents that are causally responsible for the trajectory of an affected agent, we further formalise the types of assertive influences and propose a tiering algorithm for systematically identifying assertive agents. Finally, we use scenario-based simulations to illustrate the benefits of considering groups and how the emergence of group effects vary with interaction dynamics and the proximity of agents.

Figures (5)

• Figure 1: Feasible action space reduction georgeFeasibleActionSpaceReduction2023a: For the robot crossing (a) represented in the grid world (b), the feasible action space reduction (FeAR) imposed by actors on affected agents are computed based on the feasible actions of the affected when actors follow their Move de Riguer (MdR) (represented by ) and how many of these are rendered infeasible by the actual actions of actors (represented by ). For affected agent 2, (c) shows how agent 1 reduces the feasible action space by two, (d) shows how 5 on its own has no influence, and (e) shows how the group $\left\{5,7\right\}$ reduces the feasible action space by two.
• Figure 2: Types of assertive influence based on group FeAR: For the illustrative scenario (a) where three agents are moving towards each other, we show how counterfactuals based on the MdR of actors (b) are used to compute iFeAR values (c) for individual actors and gFeAR values for group actors (d). While iFeAR can only identify solo influences ($1\nolinebreak\leftharpoonup\nolinebreak2$ and $2\nolinebreak\leftharpoonup\nolinebreak1$) (e), analysing gFeAR can reveal additional mediated ($2\nolinebreak\leftharpoonup_{1}\nolinebreak3$) (f) and coupled ($3\nolinebreak\Leftarrow\nolinebreak\left\{1,2\right\}$) (g) influences. Even though $\mathrm{FeAR}_{3,3}<1$ reflects the reduction in feasible action space of 3, iFeAR cannot identify the assertive actors; which are revealed by gFeAR ($3\nolinebreak\Leftarrow\nolinebreak\left\{1,2\right\}$). Also note that agent 3 has no influence on agent 1 as $\mathrm{FeAR}_{2,1}=\mathrm{FeAR}_{\left\{2,3\right\},1}$.
• Figure 3: Ranking the assertiveness of agents into tiers $\mathbb{T}_{j,n}$: In this illustrative scenario (a), when considering agent 1 as the affected, iFeAR only show agent 6 as being the assertive (b). However, counterfactuals with groups (c) reveal more assertive influences on agent 1 which are systematically ranked into tiers $\mathbb{T}_{1,n}$ (d).
• Figure 4: S1: Uncovering group effects with group FeAR: For the robot crossing scenario from \ref{['fig:CrossyRoadIntro']}, represented in the grid world as in (a), compared to just using iFeAR (b), we are able to uncover more assertive influences using gFeAR, either through the Shapley values (c) or tiers (d). For example, while iFeAR only shows the assertive influence of the robot 5 on pedestrians 3, 4 and 6, both Shapley values and tiers show that 5 is assertive towards all the pedestrians.
• Figure 5: Emergence of group effects in randomised simulations: Different simulation scenarios are shown in (a). Difference in the number of assertive agents $\Delta_j^{\mathrm{Assertive}}$ identified using individual FeAR (iFeAR) and (tiers of) group FeAR (gFeAR) for different proximity to the affected agent are shown in (b). Rankings made using FeAR, tiers from gFeAR or Shapley values of gFeAR we compared using Kendall's $\tau$. Variation of Kendall's $\tau$ with respect to the scenarios and median Manhattan distance between agents is shown in (c).

Theorems & Definitions (6)

• definition thmcounterdefinition: FeAR georgeFeasibleActionSpaceReduction2023a
• definition thmcounterdefinition: Group FeAR
• definition thmcounterdefinition: Solo influence $j\nolinebreak\leftharpoonup\nolinebreak i$
• definition thmcounterdefinition: Mediated influence $j\nolinebreak\leftharpoonup_{G}\nolinebreak i$
• definition thmcounterdefinition: Coupled influence $j\nolinebreak\Leftarrow\nolinebreak G$
• definition thmcounterdefinition: Mediated coupled influence $j\nolinebreak\Leftarrow_{G'}\nolinebreak G$