Where the conviction distribution should ride through and where the deploy gate should collapse it

The question

Where in the /decisions/ pipeline should a multi-agent conviction score's probability distribution be preserved versus collapsed to a single recommendation (the right binary-collapse point)? Context: RDCO's multi-agent /decisions/ pipeline (investing/paper-trade pages and other strategic outputs) aggregates several agent/lens conviction signals; the design question is which stage keeps the full ensemble distribution and which stage is correct to collapse it to a point estimate or binary deploy/no-deploy call.

What we already know (from the vault)

• [[binary-decision-around-continuous-probability]] gives the operational rule directly: the anti-pattern is "binarizing upstream of the decision point that actually needs the binary." Its mandate — "Push the collapse as late as the pipeline allows. Log the distribution even when the emit is binary. Give the consumer the option to read the gradient" — is the governing principle for this whole question.
• [[2026-06-16-multi-agent-ensembles-conviction-calibration]] (the seeding brief that explicitly listed this as open follow-up #4) concluded the conviction asset is the panel's disagreement spread, not the point estimate; a calibrated ensemble lands near crowd Brier (~0.20), not superforecaster (~0.023), and does not cure overconfidence — so the spread is for the founder, the point estimate is not a size-on-it number.
• [[2026-06-18-probability-aggregation-scoring-rules-panel]] established that IF the panel is collapsed to one number it should collapse via geometric mean of odds (deterministic, ~5-line, weakly dominant over median), but warned the summary stat is a rounding-error optimization next to preserving the spread.
• [[2026-05-20-verify-stack-two-gate-pass-fail-architecture]] shows the actual collapse machinery the /decisions/ pipeline already routes through: [[verify-strategic-output]] is the LLM-as-judge gate emitting a two-gate PASS | FAIL→ITERATE | FAIL→SCRAP verdict — currently a binary-shaped surface, the exact place a distribution would get destroyed if collapsed too early.
• [[verifier-as-epistemology]] supplies the precondition under everything: aggregation/spread only carries information when the agents' errors are independent; a homogeneous same-model panel's tight agreement is fake conviction, not earned conviction.

What the web says

• Bayesian decision theory: the posterior is untouched during inference; collapse happens only at action-selection, by minimizing posterior expected loss. "A Bayes estimator... minimizes the posterior expected value of a loss function"; "the posterior distribution itself remains unchanged during inference. The collapse occurs only at the decision step." (Bayes estimator, Wikipedia)
• The loss/utility function — not the probability — decides where the collapse lands. Identical posterior, different loss → different point: squared-error → mean, absolute-error → median, 0-1 loss → mode/MAP. "The choice of loss function... fundamentally determines where the posterior collapses... [it] should reflect the actual costs of estimation errors in the application domain." (Bayes estimator; Bath MA40189 ch.4)
• The "AI/ML gap": collapse requires BOTH the probability AND the utility terms; a prediction collapsed without its cost context is not actionable. The field over-invests in state-probability accuracy and under-invests in utility; "an inaccurate utility assessment may be as (and sometimes more) harmful than a poor probability estimation." The role "is not (simply) to return an accurate prediction but... to select the most rational decision" — collapse happens only at the final step via a* = argmin E[C(a,θ)] (e.g., deploy if c_miss·(1−p) < c_falsedeploy·p). (arxiv 2310.02029)
• Forecasting practice: communicate the full predictive distribution to the consumer, because the consumer sets the threshold. Gneiting et al's "maximize sharpness subject to calibration"; "communicating the full distribution enables strategic decision-making... we can set the [decision] threshold appropriately and estimate false positives/negatives upfront" — impossible with a point estimate. (calibration & sharpness, Tichy)
• The collapse boundary itself can legitimately move with cost over time (collapsing decision boundaries in optimal evidence-accumulation), reinforcing that the boundary is a function of the cost/utility structure, not a fixed property of the probability. (Evidence accumulation, PMC8857294)

Convergences and contradictions

• Hard convergence, four independent literatures → one rule. The vault's [[binary-decision-around-continuous-probability]] ("collapse as late as the pipeline allows"), Bayesian decision theory ("collapse only at action-selection"), the AI/ML-gap paper ("the distribution is never reduced to a decision on its own, only jointly with utilities at the final step"), and forecasting practice ("ship the distribution to the consumer") all land on the same boundary: distribution rides through synthesis, calibration, and display; the single irreversible action is the only legitimate collapse point.
• The load-bearing addition over the prior briefs: the collapse is owned by the loss/utility function, not the probability. RDCO's two briefs settled "what to aggregate" (geo-mean-of-odds) and "what to surface" (spread). This one settles "what triggers the binary": the asymmetric cost of a wrong deploy vs a missed deploy. That asymmetry is what should set the deploy threshold — and it is currently implicit/unwritten.
• No contradiction, one inherited caveat: all of this is conditional on [[verifier-as-epistemology]] independence. A homogeneous panel produces a fake-tight distribution — collapsing it late doesn't help if the spread it preserves was never real.

Synthesis for RDCO

Map the principle onto the four /decisions/ stages. Stage 1 — per-seat conviction (preserve): each agent/lens emits a probability, not a vote; never let a seat hard-binarize its own call. Stage 2 — synthesis/aggregation (preserve the distribution, compute but don't commit to the summary): combine via geometric-mean-of-odds per [[2026-06-18-probability-aggregation-scoring-rules-panel]], but carry the full set of per-seat probabilities and their spread forward — the aggregate is a label on a distribution, not a replacement for it. Stage 3 — calibration + display to the founder (preserve, hardest rule): the founder must see the spread, not a lone number. This is the [[binary-decision-around-continuous-probability]] "give the consumer the gradient" mandate and the Gneiting "ship the distribution so the consumer sets the threshold" finding fused — and it is exactly where [[verify-strategic-output]]'s two-gate PASS/FAIL surface is at risk of collapsing too early. The /decisions/ page should render the conviction band (e.g., seat probabilities + geo-mean + min/max or IQR), with wide spread reading as low conviction and tight independent agreement as earned conviction, never a bare "82% confidence." Stage 4 — the deploy/no-deploy gate (collapse here, and only here): this is the single irreversible action (per [[feedback_paper_trade_deploy_authorization]] the paper-trade deploy is human-gated and classifier-gated), so it is the textbook Bayes action point — argmin E[loss]. Collapse the distribution against the cost asymmetry of this specific decision, not against a generic 0.5 cutoff.

The concrete recommendation: preserve the distribution through stages 1–3; collapse at stage 4 (the deploy gate) and nowhere earlier. The verify-* two-gate verdict ([[2026-05-20-verify-stack-two-gate-pass-fail-architecture]]) is correctly binary for the gate, but the conviction distribution must reach the founder's eyes before that gate fires — the gate's PASS/FAIL is the output of the founder reading the distribution, not a substitute for it. In Bayesian terms: stages 1–3 build and display the posterior; stage 4 applies the loss function. The most-improvable gap today is that RDCO's collapse threshold is implicit. The web's sharpest finding is that the loss function owns the collapse point — so the deploy gate should make its cost asymmetry explicit (what does a wrong paper-trade deploy cost vs a missed one?) and set the threshold from that, rather than collapsing at a default midpoint. For an investing/paper-trade page where a false deploy burns capital and credibility while a missed deploy is a foregone-upside option, the asymmetry argues for a high conviction bar to flip to deploy — a deliberately conservative threshold, which also hedges the inherited overconfidence ceiling from [[2026-06-16-multi-agent-ensembles-conviction-calibration]].

One guardrail carries through from the prior two briefs and must not be lost in the plumbing: none of this manufactures calibrated conviction. Preserving the distribution to stage 3 makes the founder's judgment better-informed about where the independent seats fracture; it does not let the pipeline size a position on the number. The point estimate is a navigation aid; the spread is the signal; the deploy collapse is a human-owned, cost-asymmetric, late-binding action. Build the pipeline so the distribution is cheap to carry (it already exists per-seat) and the collapse is loud, explicit, and singular.

Open follow-ups

• Does the live /decisions/ page actually render per-seat spread today, or does it already collapse to a single number before the founder sees it? (cheap UI/template audit — the concrete first fix if it collapses early)
• What is the explicit cost asymmetry for a paper-trade deploy gate (cost of wrong-deploy vs missed-deploy), and can it be written into [[verify-strategic-output]] / the deploy classifier as a named threshold rather than an implicit midpoint?
• Should the /decisions/ deploy gate expose a third "abstain / insufficient-independence" outcome when panel spread is wide AND seats are homogeneous — i.e. refuse to collapse when the distribution is fake-tight or genuinely uninformative?
• Can RDCO retro-test on the paper-trade decision log whether a late-collapse + explicit-cost-threshold gate would have changed any past deploy/no-deploy call vs the current implicit collapse?
• Does surfacing the full spread to the founder worsen confidence-alignment contamination (a confident-looking band importing unwarranted conviction), the open risk flagged in [[2026-06-16-multi-agent-ensembles-conviction-calibration]]?

Related

• [[binary-decision-around-continuous-probability]]
• [[2026-06-16-multi-agent-ensembles-conviction-calibration]]
• [[2026-06-18-probability-aggregation-scoring-rules-panel]]
• [[2026-05-20-verify-stack-two-gate-pass-fail-architecture]]
• [[verifier-as-epistemology]]
• [[2026-06-12-agentic-targeting-conviction-calibrated-confidence]]
• [[brier-score]]
• [[feedback_targeting_system_prioritization_filter]]
• [[feedback_paper_trade_deploy_authorization]]

Sources

• Vault: [[binary-decision-around-continuous-probability]] — ~/rdco-vault/06-reference/concepts/binary-decision-around-continuous-probability.md (the anti-pattern + "collapse as late as the pipeline allows" operational rule)
• Vault: [[2026-06-16-multi-agent-ensembles-conviction-calibration]] — ~/rdco-vault/06-reference/research/2026-06-16-multi-agent-ensembles-conviction-calibration.md (seeding brief; spread-as-asset, calibration ceiling, this question as open follow-up)
• Vault: [[2026-06-18-probability-aggregation-scoring-rules-panel]] — ~/rdco-vault/06-reference/research/2026-06-18-probability-aggregation-scoring-rules-panel.md (geo-mean-of-odds for the summary; reinvest budget in spread)
• Vault: [[2026-05-20-verify-stack-two-gate-pass-fail-architecture]] — ~/rdco-vault/02-sops/2026-05-20-verify-stack-two-gate-pass-fail-architecture.md (verify-strategic-output two-gate collapse surface)
• Vault: [[verifier-as-epistemology]] — ~/rdco-vault/06-reference/concepts/verifier-as-epistemology.md (independence precondition — fake-tight distributions)
• Vault: [[brier-score]] — ~/rdco-vault/06-reference/concepts/brier-score.md (proper scoring; measurability at low volume)
• Web: Bayes estimator — https://en.wikipedia.org/wiki/Bayes_estimator (posterior untouched in inference; loss function sets the collapse point; mean/median/mode by loss)
• Web: Bath MA40189 ch.4, Decision Theory — https://people.bath.ac.uk/masss/ma40189/_book/ChapDecTheo.html (minimize posterior expected loss at action-selection)
• Web: Between accurate prediction and poor decision making: the AI/ML gap — https://arxiv.org/pdf/2310.02029 (collapse needs probability AND utility; only at the final decision step)
• Web: Calibration and Sharpness (Tichy, on Gneiting et al) — https://medium.com/@maltetichy/calibration-and-sharpness-fd8270b71f07 (maximize sharpness subject to calibration; ship the distribution so the consumer sets the threshold)
• Web: Evidence-accumulation collapsing boundaries — https://pmc.ncbi.nlm.nih.gov/articles/PMC8857294/ (the collapse boundary is a function of cost structure, can move over time)