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Hall of Shoulders

Decision Science & OR

Thomas Saaty

a citation-grounded application of Saaty's decision-theoretic apparatus to contemporary space challenges, for use as a review lens in the COLLEGIUM doctoral board.

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Review Lens

Adversarial questions for candidates

The falsifiable questions this brain puts to a dissertation candidate. They seed the pre-Conclave initial review whenever a candidate's topic matches the Decision Science & OR lens.

  1. 1

    Consistency. "You weighted your criteria by pairwise comparison. Report the consistency ratio (CR) of every comparison matrix. Is any CR > 0.10, and if so, why should I trust a ranking built on incoherent judgments rather than your revisiting those comparisons?" (Falsifiable: CR values are computable and checkable.)

  2. 2

    Rank reversal / synthesis mode. "Add one realistic alternative to your set and re-run the synthesis. Does your top-ranked option change? State whether you used distributive or ideal-mode synthesis and justify why your ranking is robust to the introduction or removal of an alternative." (Falsifiable: rank reversal is directly testable by adding/removing an alternative.)

  3. 3

    Criteria independence (AHP vs. ANP). "You modeled this as a strict hierarchy. Name two criteria in your model that are actually interdependent (e.g., illumination and thermal budget; cost and reliability). If dependence exists, your hierarchy is misspecified and you should be using an ANP supermatrix. Defend the independence assumption or show the network." (Falsifiable: the independence claim can be checked against domain physics/economics.)

  4. 4

    Weight provenance and sensitivity. "Whose judgments produced these weights, and how was the group aggregated (AIJ vs. AIP)? Run a sensitivity analysis: which single pairwise judgment, if changed within its plausible range, flips your recommendation? If your conclusion hinges on one contested expert opinion, it is not yet a finding." (Falsifiable: sensitivity to each judgment is computable, per NTRS 20190025735.)

  5. 5

    Scale validity. "You used the 1-9 fundamental scale to compare a collision probability against a sovereignty concern against a dollar cost. Justify that these intangibles were compared on a genuine ratio scale and not an ordinal one dressed up as ratio. If the comparisons are not ratio-scale, your eigenvector priorities are not meaningfully combinable." (Falsifiable: the elicitation protocol and respondent understanding can be audited.)

Core Concepts & Space Translation

Analytic Hierarchy Process (AHP)

Structure a decision as a hierarchy: goal at the top, then criteria and subcriteria, then alternatives at the bottom. Decompose an intractable judgment into many small, tractable ones. Key work: Saaty, *How to Make a Decision: The Analytic Hierarchy Process*, Interfaces 24(6), 1994 (DOI 10.1287/inte.24.6.19).

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.

Pairwise comparison on the fundamental 1-9 scale

Rather than scoring elements directly, the decision maker compares them two at a time ("how much more important is A than B?") on a verbal/numeric ratio scale (1 = equal, 9 = extreme). Comparisons form a reciprocal matrix (a_ij = 1/a_ji). This converts intangible, subjective preference into ratio-scale data. Key work: Saaty 1994 (above); foundational text *The Analytic Hierarchy Process*, 1980.

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.

Priority derivation via the principal eigenvector

The local priority weights of a cluster are the normalized principal right eigenvector of its pairwise-comparison matrix; lambda_max (the principal eigenvalue) drives the consistency measure. Priorities are ratio-scale, which is what makes them combinable across levels. Key work: Ishizaka & Labib, *Review of the main developments in the analytic hierarchy process*, Expert Systems with Applications, 2011 (DOI 10.1016/j.eswa.2011.04.143).

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.

Consistency ratio (CR)

Human judgments are never perfectly transitive. Saaty quantifies inconsistency: CI = (lambda_max - n)/(n-1), CR = CI/RI (RI = random-index for matrix size n). CR <= 0.10 is the acceptability threshold; above it, the comparisons should be revisited. This is Saaty's signature epistemic guardrail: it makes incoherence *measurable* rather than hidden. Key work: Saaty 1994.

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.

Hierarchic synthesis (weighting and summing)

Global priorities are obtained by weighting each alternative's local priority under a criterion by that criterion's weight and summing down the hierarchy. Two synthesis modes (distributive and ideal) handle the rank-reversal problem when alternatives are added or removed. Key work: Ishizaka & Labib 2011.

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.

Analytic Network Process (ANP) and the supermatrix

When criteria and alternatives are interdependent (feedback, not a clean top-down tree), AHP generalizes to ANP: clusters connected in a network, priorities derived from a column-stochastic *supermatrix* raised to limiting powers. Key work: Saaty & Vargas, *Decision Making with the Analytic Network Process*, 2013 (DOI 10.1007/978-1-4614-7279-7).

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.

Benefits-Opportunities-Costs-Risks (BOCR)

Evaluate a complex decision on four separate merit networks (benefits, opportunities, costs, risks) and combine them, rather than forcing everything onto one scale. This is Saaty's structured answer to multi-objective, multi-stakeholder strategic decisions. Key work: Saaty & Vargas 2013; Ho, *Integrated AHP and its applications*, EJOR, 2008 (DOI 10.1016/j.ejor.2007.01.004).

Space translation

See Space Applications below for how this framework translates to contemporary space governance, drawn directly from the dossier's applied-literature review.