Decision-Making Breaks Under Explanation—— The Responsibility to Stop: Defined by OR-RDC

0. Introduction: Decision-Making Had No Defined End

A strange phenomenon is occurring in modern high-level systems (AI, logistics networks, financial algorithms). When accidents or delays occur, the more companies and developers increase their "explanations," the more ambiguous the question of "who should take responsibility" becomes, causing consensus-building to evaporate.

We call this "The Evaporation of Responsibility."

This is not merely a problem of individual moral failure or corporate concealment. It stems from a structural void within "Operations Research (OR)," the very optimization theory we have relied upon.

This article is not about what the OR-RDC (OR-Responsibility Design Committee) does, but a treatise to unravel why the OR community, AI governance bodies, and regulatory authorities have hitherto failed to solve this problem.

1. The "Reversal" Phenomenon in the Field

Conventionally, accountability was believed to be something where "disclosing information restores trust." However, in the modern era where complexity has crossed a critical threshold, this common sense has reversed.

In the field, the following loop occurs frequently:

1. An unforeseen event occurs (delivery delay, AI error).

2. The cause is explained post-hoc ("It was an outlier in weather variables," "It was out-of-distribution data").

3. The model is extended to incorporate the exception ("We will handle it next time").

4. Variables become complex, and the locus of responsibility disperses ("The interaction of these variables was unpredictable to anyone").

5. Decision-making halts.

What must be noted here is the fact that operations collapsed not because the system's "accuracy" dropped, but because the "Explanation Cost" increased uncontrollably.

(Definition: Explanation Cost) Let $A(t)$ be the set of explanation elements (variables, exception rules, dependencies, audit procedures) added post-hoc at time $t$. We define the Explanation Cost at time $t$ as:$$E(t) := |A(t)| + \kappa \cdot C(A(t))$$where $C(A(t))$ represents the complexity of dependencies between explanation elements (e.g., number of graph edges, inference steps, lower bound of audit man-hours). An "Evaporation Loop" is a state where $E(t)$ continues to increase in the time series following an accident, and the consensus-building cost required to resume decision-making exceeds the practical upper limit $B$ ($E(t) > B$).

2. "Good Intentions" Create Structural Irresponsibility

The trouble is that everyone involved in this process is acting with "good intentions." Engineers try to improve accuracy, legal teams try to explain risks, and PR tries to ensure transparency.

However, adding models or variables after an accident often mutates into "Post-hoc Rationalization." This is because one can retroactively create a model that explains the result as having been rational at the time.

The more we increase explanations, the more we retroactively rewrite the boundary of "what was foreseeable." As a result, the "Unknowable Boundary"—where we originally should have stopped—disappears, completing a state where no single subject bears responsibility.

3. Why Existing OR Could Not Handle This

Why have experts in mathematical optimization (OR) remained silent on this issue? The answer is simple: OR is a "theory for producing solutions."

Traditional OR (Stochastic Programming, Robust Optimization, etc.) stands on one powerful implicit assumption:

"Objective functions, constraints, and sets of uncertainty are formally definable in advance."

Within this framework, "conditions to stop calculation" appear only as computational conveniences, such as "limits on computational resources" or "convergence criteria." The vocabulary to describe Stop Conditions for Social Implementation (Must)—stopping because responsibility cannot be taken—did not exist in OR.

• Robust Optimization / DRO: Pre-defines uncertainty sets (or distribution sets) and provides performance guarantees for those sets. While this strengthens the "handling of uncertainty," it does not possess, as a standard form, a mechanism (temporal irreversibility) to systematically prohibit the "addition of explanation elements" or "redefinition of objectives/evaluation axes" that occur after an accident.

• Deep Uncertainty (DMDU/RDM): Prioritizes adaptation, branching, and robust policy design over predicting the future. While close in that it premises unknowability, it does not aim for the vocabulary (Responsibility Fixation / Prohibition of Post-hoc Changes) to "prohibit and fix" as an OR constraint the phenomenon where post-accident explanation proliferation erases responsibility boundaries.

• XAI / Model Governance: Establishes explanation generation, visualization, and auditing. However, in situations where increasing explanation itself stops consensus-building, it often lacks a framework to fix the "boundary to stop explanation proliferation" and "who takes over" as mathematical specifications first.

Existing theories all discuss "how to move forward (optimize)," leaving the seat for discussing "how to hold ground (stop)" empty.

4. The Empty Seat = "Pre-Decision Constraint"

What OR-RDC seeks to fill is precisely this void. We define this as the "Pre-Decision Constraint."

This is a condition that must be satisfied for the calculation itself to be socially established before performing the optimization calculation $minimize \ f(x)$.

• Where do we give up calculation and stop?

• Who takes over at that time?

• Where is the boundary beyond which explanatory variables must not be increased post-hoc?

This domain has previously been delegated to "ethics" or "intuition on the ground." However, now that AI and algorithms have accelerated, human "intuition" and "conscience" can no longer keep up. A theory describing this as a mathematical constraint was necessary.

5. Three New Axes Introduced by GhostDrift

GhostDrift theory introduces the following three axes into this "empty seat." These are not axes of optimization, but conditions for the existence of decision-making.

1. Unknowable Boundary: The limit point where further exploration only produces "post-hoc excuses." We define this as the "Finite Closure of the Feasible Region" and prohibit calculation or extension beyond it.

2. Post-hoc Impossibility: A constraint that temporally and structurally prohibits changing objective functions or parameters after seeing the results.

3. Responsibility Fixation: Inseparably binding a "Subject ID" to decision variables, burning "whose judgment processed this" into the data structure level.

6. OR-RDC Creates "Specs," Not "Ethics"

Why is it necessary to standardize this as a "Committee"? Because in the absence of standards, players who externalize responsibility always win.

As long as "stopping when dangerous" or "admitting ignorance" is left to individual ethics, short-term optimization players who ignore risks and push forward will win in the market, passing the bill (environmental load, accident processing, loss of trust) onto society.

What OR-RDC formulates is not norms. It is Technical Specifications (Specs) to judge "irresponsible optimization" as "Invalid" in an auditable manner.

• Stop Conditions (Boundary)

  • Input: Operational state $s_t$ (e.g., prediction error, OOD metrics, exception addition count, Explanation Cost $E(t)$)

  • Output: {CONTINUE, ESCALATE, STOP} and Evidence Log (Minimum Set)

• Handover Procedure (Protocol)

  • Input: Stop/Intervention event $e_t$ and Authority Level $r$ (Human/Org/Machine)

  • Output: Signed Handoff Record (Who/When/What was accepted)

• Responsibility Log (Evaluation)

  • Input: Decision $x$, Subject ID $a$, Objective Function $f$, Constraint Set $\Omega$, Time $t$

  • Output: Auditable Immutable Log $L_t$ (Post-hoc changes detectable)

Only when these are standardized can a structure be created where "sincere operation" does not lose to "reckless optimization."

7. Conclusion: OR-RDC is "Filling the Void"

OR-RDC is not a movement to shout some new ideology. It is a project to formally implement the function of "Responsibility Design," which has been left empty between OR (mathematical optimization) and social implementation for a long time.

AI runaways, logistics collapses, financial flash crashes. These seem like separate problems, but at their root lies a common structural defect: "The ability to fix responsibility has not kept up with the ability to optimize."

OR-RDC was established to repair this defect and upgrade OR to a "truly completed theory capable of enduring social implementation." This is not an invention, but a "filling of the void" due to historical necessity.