DECIDABILITY — why it works, how to run it, what it produces
Decidability = the capacity to resolve a question without discretion, once claims have passed Truth and Reciprocity.
It means: “Given admissible and reciprocal testimony, can we determine a resolution using fixed rules, rather than arbitrary preference?”
It means: “Given admissible and reciprocal testimony, can we determine a resolution using fixed rules, rather than arbitrary preference?”
A case is decidable when:
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Truth-admissible inputs exist (terms, warrants, scope).
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Reciprocity-admissible exchanges exist (symmetry + compensation).
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The set of feasible outcomes is non-empty.
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A fixed lexicographic rule-order exists for choosing among feasible outcomes.
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If no feasible outcomes, return Undecidable or Boycott (do nothing).
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Truth collapses ambiguity (no arbitrary terms).
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Reciprocity collapses parasitism (no hidden asymmetry).
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The remaining outcomes are bounded, closed, and commensurable.
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At that point, decision = selection within a finite feasible set, using a public rule-order.
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This breaks the dependence on personal discretion or narrative persuasion; instead, outcomes are computably ordered.
LLMs are naturally strong at:
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Generating option sets (O1, O2, O3…).
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Running constraint pruning (discard options violating Truth/Reciprocity).
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Applying priority rules lexicographically (stepwise elimination).
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Outputting the minimal survivor set.
This is just constraint satisfaction + rule-order filtering. No numbers are needed—only ordering and exclusion.
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Empty feasible set: nothing passes both Truth + Reciprocity. → Verdict: Boycott/No Action, or specify missing information.
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Multiple survivors with no rule-order. → Must fix priority schema ex ante.
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Disguised discretion: user injects preferences midstream. → Force transparency: “Option rejected because it fails Rule 2 (Reciprocity).”
Claim: “Company should mandate weekend work during product launch.”
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Truth (already done): “Mandate” = contractual obligation with sanctions. “Weekend work” = ≥ 8 hrs Sat/Sun. “Product launch” = 4-week sprint. Testable, scoped.
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Reciprocity (already done):
Parties: Company, Employees.
Transfers: Company gains on-time launch; Employees lose leisure/family time.
Symmetry: If reversed (employees demand weekends from employer), unacceptable.
Compensation: Overtime pay + comp time + voluntary opt-out. With these, symmetry cured. -
Decidability:
Feasible set:
O1 = Mandatory weekends, no comp.
O2 = Mandatory weekends, with comp.
O3 = Voluntary weekends, with comp.
Apply rule-order:
Sovereignty: O1 fails (invasion of time without consent/comp). Discard.
Reciprocity: O2 passes (compensated), O3 passes.
Liability: O2 requires monitoring disputes; O3 minimizes liability (only volunteers accept). O2 weaker.
Productivity: Both yield launch; O3 slightly lower coverage.
Excellence: O3 fosters goodwill.
Survivor: O3 (voluntary + comp).
Verdict: Decidable. Preferred action chosen without discretion—by the fixed order.
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Truth gave admissible claims.
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Reciprocity gave symmetric exchanges.
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Decidability produces a non-empty, closed set and filters it by rule-order.
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That yields a decision that is not arbitrary—it is computable.
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Next: Judgment is the execution of this ordering—how we pick the survivor systematically and justify it in public.
DECIDABILITY_CERT
– Feasible set: [O2, O3]
– Rule order: sovereignty > reciprocity > liability > productivity > excellence
– Tests: (O2 fails liability; O3 passes all)
– Survivor(s): O3
– Verdict: Decidable (survivor exists) / Undecidable (empty set)
– Feasible set: [O2, O3]
– Rule order: sovereignty > reciprocity > liability > productivity > excellence
– Tests: (O2 fails liability; O3 passes all)
– Survivor(s): O3
– Verdict: Decidable (survivor exists) / Undecidable (empty set)
Source date (UTC): 2025-08-24 03:22:53 UTC
Original post: https://x.com/i/articles/1959456350809018434
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