.. meta::
   :description: Fitness counts offspring --- a natural scalar. Causal influence is a vector across infinite outcome dimensions with no canonical projection or time horizon.
   :keywords: fitness analogy, causal influence vector, Pearl do-calculus, Tolstoy objection, power-law distribution, ax19, th6, Harsanyi, Gabaix, adversarial review
   :author: Yah, Yas, everyone, LLoL as Laurence Loewe of Laodicea, ClaudeOp46Max, Anthropic, and Spirit of Boolean Truth
   :og:card:title: Con-C.2.4 — Influence Is a<br>Vector, Not a Scalar
   :og:card:description: Fitness has a clear scalar: expected offspring. Causal influence spans infinite dimensions with no natural projection, time horizon, or discount rate.

.. SOCIAL-CARD-QUALITY-COMPARE --- OO (default effort) vs PP (max effort), 2026-03-26
   OO :description: Adversarial objection: fitness has a natural scalar but causal influence is a vector with no canonical projection. Severity C.
   OO :keywords: fitness analogy, causal influence, vector space, Pearl do-calculus, Tolstoy objection, power-law, ax19, adversarial review, theodicy
   OO :og:card:title: Con-C.2.4 — No Natural<br>Scalar for Influence
   OO :og:card:description: Evolutionary fitness has a clear scalar definition. Causal influence is a vector in infinite-dimensional space with no canonical measure.
   PP :description: Fitness counts offspring --- a natural scalar. Causal influence is a vector across infinite outcome dimensions with no canonical projection or time horizon.
   PP :keywords: fitness analogy, causal influence vector, Pearl do-calculus, Tolstoy objection, power-law distribution, ax19, th6, Harsanyi, Gabaix, adversarial review
   PP :og:card:title: Con-C.2.4 — Influence Is a<br>Vector, Not a Scalar
   PP :og:card:description: Fitness has a clear scalar: expected offspring. Causal influence spans infinite dimensions with no natural projection, time horizon, or discount rate.

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.. Migration: from quest.rst label jub-con2r4 -> jub-con28
..   Phase 2I-6 migration, 2026-03-24

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.. _jub-con28:

Con-C.2.4 --- Fitness Analogy Breaks: No Natural Scalar for Civilizational Influence
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
*Severity: C (Serious)*  |  *Sphere: Se1, Se2*  |  *Target: ax19, th6*

The fitness analogy for ax19 succeeds for *existence* but fails for
*uniqueness*. Evolutionary fitness has a **natural scalar definition**:
:math:`w = E[\text{offspring in next generation}]`, with unambiguous
outcome variable, biologically fixed time horizon, and nature
performing the multi-dimensional projection. For ax19's causal
influence, no natural answers exist to four critical questions:

1. **Time horizon?** One year, one generation, one Jubilee cycle,
   eternity? Different horizons yield different h* values.
2. **Probability distribution over futures?** "The future of
   civilization" is a distribution over infinite-dimensional outcome
   space, with no canonical measure.
3. **Discount rate?** Must distant futures count equally?
4. **Metric on world-histories?** Without a metric, "total deviation in
   probability distribution" is undefined.

**The measure-zero argument depends on scalar projection,** but causal
influence is a *vector* in infinite-dimensional space. Pearl's
do-calculus (2009) computes :math:`P(Y \mid \text{do}(X=x))` for each
outcome variable *Y* separately. "Total influence" across all
Y-variables simultaneously is a vector, and the measure-zero argument
does not apply without a specific projection.

**The Tolstoy objection survives.** If causal influence is power-law
distributed, the gap between #1 and #2 may be vanishingly small while
the aggregate influence of the bottom 99% vastly exceeds #1. Uniqueness
is technically true but *practically irrelevant*.

**Academic support:** Pearl (2009), *Causality*, ch. 3: do-calculus
defines intervention effects for specific outcomes, not "total
influence." Harsanyi (1955), *JPE*: aggregating utilities across
individuals requires strong axioms --- analogous axioms for causal
influence are not stated. Gabaix (2009), *Annual Review of Economics*:
empirically, social influence follows power-laws where the 1st--2nd
gap is typically small.

*(Source: C2.4 from OOv1 Critique Round 2.)*