Con-C.3 — ax19 Imposes Total Order on Incomparable Quantities#
Severity: C (Serious) | Sphere: Se1 | Target: ax19, th6, th7
ax19 claims that at every moment t, there exists a unique individual h* with strictly maximal causal influence over all future outcomes. The uniqueness argument (“exact equivalence in effect is measure-zero”) is mathematically valid only for scalar quantities on a continuum. But causal influence is not a scalar:
Person A’s choices maximally affect climate policy
Person B’s choices maximally affect AI development
Person C’s choices maximally affect nuclear proliferation
These domains are incomparable without a weighting function that converts multi-dimensional influence into a single scalar. Providing such a function would require knowing the future (which outcomes matter most), creating a circularity: h* is defined by the future outcomes that h*’s choices will determine.
Arrow’s impossibility theorem (Sen 1970) demonstrates that there is no consistent way to aggregate multi-dimensional rankings into a single total order without violating at least one reasonable axiom. An analogous result may apply to multi-dimensional causal influence: if no unique aggregation exists, the “unique h* with maximal influence” is undefined.
Pearl’s do-calculus (2009) shows that causal influence is intervention-specific — the effect of person A’s choices on outcome X can differ from their effect on outcome Y. There is no domain-independent “total causal influence” measure that would make ax19’s uniqueness claim well-defined.
Consequences if ax19 fails: th6 (Causal Concentration) and th7 (God Seeks a Volunteer) both depend on ax19’s uniqueness claim. If no total order exists among causal influences, the “unique h* with maximal responsibility” central to th6–th7 is undefined, and the entire delegation-of-responsibility chain weakens.
(Source: C3 from OOv1 Critique Round 1.)