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An Axiomatic Approach to Formalized Responsibility Ascription

A formalized and quantifiable responsibility score is a crucial component in many aspects of the development and application of multi-agent systems and autonomous agents. We can employ it to inform decision making processes based on ethical considerations, as a measure to ensure redundancy that helps us in avoiding system failure, as well as for verifying that autonomous systems remain trustworthy by testing for unwanted responsibility voids in advance. We follow recent proposals to use probabilities as the basis for responsibility ascription in uncertain environments rather than the deterministic causal views employed in much of the previous formal philosophical literature. Using an axiomatic approach we formally evaluate the qualities of (classes of) proposed responsibility functions. To this end, we decompose the computation of the responsibility a group carries for an outcome into the computation of values that we assign to its members for individual decisions leading to that outcome, paired with an appropriate aggregation function. Next, we discuss a number of intuitively desirable properties for each of these contributing functions. We find an incompatibility between axioms determining upper and lower bounds for the values assigned at the member level. Regarding the aggregation from member-level values to group-level responsibility we are able to axiomatically characterize one promising aggregation function. Finally, we present two maximally axiom compliant group-level responsibility measures -- one respecting the lower bound axioms at the member level and one respecting the corresponding upper bound axioms.