Causal Sufficiency and Structural Vulnerability: Rethinking Responsibility in Generative Relational Systems — A Preliminary Position Paper on the Foundations of Structural Attribution

Abstract

Two companion papers establish that in one class of injury the classical apparatus of causal attribution fails, and that the failure is of two kinds, one of resources and one of what a determinate contribution would require of any tribunal. Where causal sufficiency is unattainable, responsibility theory may turn to the structure of the relational system and ask which transformations of that structure a party brought about. This paper recapitulates those problems, separates the operation of law from the justice of its results, and examines whether the turn can be made. It offers no rule for deriving a share of responsibility from a structural change, and it holds that none is presently available. Its claims are four. The object of an attributive enquiry may be relocated from the production of an outcome to the production of a vulnerability, and the relocation is intelligible independently of any measure of contribution. A description of structural change is by itself normatively inert, since organisational reform alters connectivity, feedback and reachability in the same registers as degradation does, and no quantity computed on the structure distinguishes the two. A criterion is therefore required, and the paper proposes a candidate: a structural change carries normative weight where it removes the paths by which that very change could be contested and reversed. The candidate is self-referential where the alternatives are not, since a change leaving the channel of its own correction intact remains corrigible whatever else it does, and two changes to one structure are exhibited that agree on size, density and connectedness and differ only in whether the path of contestation survives. The invariants employed are then defined in the standard way, as quantities equal on topologically equivalent flows, and a pair of dynamics is exhibited whose basins differ in the number of holes they contain, so that the register of loops is shown to carry structural and not quantitative information. A constructed case is then carried through both enquiries: over the weightings the record admits, the share attributed to each of two withdrawals occupies most of the available range, while membership of a minimal cut is settled for all three. Finally the paper states what a finding on an invariant contributes and what it withholds. It contributes a finite evidentiary task, robustness to the strengths, rates and couplings a record leaves open, order-independent composition, and an identification of the parties concerned through the minimal sets of relations whose removal destroys the path. It withholds a share, it moves the requirement of closure from variables to positions rather than escaping it, it purchases invariance by discarding the difference between a channel that functions and one that is nominal, it leaves the minimal set undetermined where the record is incomplete, and it is silent on time. The proposal is offered as a constraint on attribution rather than as a procedure for it.