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California Freight Cleanup → Investigation 6-4

Which portfolio holds its value no matter what?

Consensus: Q_nsga_2 (5/5 robustness lenses) — CAVEAT: ISRM validation AMBIGUOUS (see Investigation 6-9)

Eleven portfolio candidates tested against six robustness criteria: a simple cost-per-death ratio, expected-value maximization, a chance constraint on minimum net benefit, the average in the worst 5% of draws (CVaR), a parametric adversarial stress test, and an info-gap horizon. 5,000-draw Monte Carlo, seed 2026.

Earlier stages ranked portfolio candidates by expected net benefit — a mean that silently assumes the dose-response function, cost, and effectiveness parameters are known well enough that the average is a reliable guide. Phase 2 quantified the actual uncertainty: dose-response CV around 16%, effectiveness CV around 30%, cost CV around 25%. This investigation asks the decision-relevant question: when those uncertainties are taken seriously, does the expected-value ranking hold, or does a different portfolio win?

Anyone presenting a $2B recommendation must be able to say not only “this performs best on average” but also “this choice is defensible if key assumptions shift by realistic amounts.” If the robust winner and the expected- value winner are the same portfolio, the case is straightforward. If they diverge, the decision-maker must choose a risk posture explicitly — not absorb it as a hidden assumption.

Six robustness criteria applied in sequence. The first (L0) is a simple VSL-independent cost-per-death ratio. The remaining five use a 5,000-draw Monte Carlo envelope across eleven portfolio candidates: the six named portfolios from the frontier investigation (Investigation M-1), the best sequential policy from the adaptive planning investigation (Investigation M-2, annualized over 10 years), and five NSGA-II Pareto-optimal candidates from Investigation M-3 (labeled Q_nsga_1 through Q_nsga_5).

L0 — Cost-effectiveness ($M per death avoided; VSL-independent)

Deterministic ratio of cost ÷ deaths avoided. Zero-cost portfolios rank first by definition. The NSGA-II candidates (Q_nsga_1–5) dominate all paid Phase 1 portfolios: Q_nsga_5 achieves $2.44M/death, vs. $16.6M/death for B_transport_2B and $69.3M/death for F_maximum. The primary differentiator for visitor-facing narrative; uses the metric CARB and EPA employ to defend SIP measures, with an historical acceptance band of roughly $10–30M/death for major air-quality rules.

L1 — Expected-value maximization

5,000-draw MC over the full uncertainty envelope. Net benefit = monetized deaths avoided (California VSL $11.6M) minus cost. Q_nsga_2 wins with mean NB = $+5.92B (SD $3.05B). A_free_lunch earns $+0.67B; B_transport_2B and all other Phase 1 paid portfolios show negative expected NB under this CRF and VSL.

L2 — Chance-constrained programming (Charnes & Cooper 1959)

Require P(NB ≥ $1.0B) ≥ 0.90. Q_nsga_2 achieves P = 0.989 (feasible). Q_nsga_1 achieves P = 0.969 (feasible). All Phase 1 paid portfolios fail (P < 0.13). L2 best: Q_nsga_2 (mean NB = $+5.89B among feasible candidates).

L3 — CVaR0.05 tail risk (Rockafellar & Uryasev 2000)

Expected net benefit in the worst 5% of draws. Q_nsga_2: CVaR = $+1.45B (worst-5% average still positive). Q_nsga_4: $+1.05B. A_free_lunch: $+0.30B. All Phase 1 paid portfolios have negative CVaR, meaning a bad draw wipes out the investment entirely.

L4 — Parametric adversarial envelope (DRO-lite)

Worst-case mean NB over a 4×4 grid of mean-shift (0–30%) × sigma-inflation (1.0–1.6), with cost axis inflated by the Investigation M-2 half-normal cost-overrun factor (1.160). Q_nsga_2 worst-corner NB = $+2.72B (corner: −30% mean, ×1.0 sigma). A_free_lunch worst-corner = $+0.48B. All Phase 1 paid portfolios go negative at the worst corner.

L5 — Info-gap horizon (Ben-Haim 2006)

Largest α-multiplier on base CVs at which the 10th-percentile NB stays above $0.5B. Q_nsga_2 critical α = 1.91 (tied with Q_nsga_4). This means Q_nsga_2 remains viable even when all uncertainty parameters are inflated to 1.91× their base values. Phase 1 portfolios saturate at the search ceiling α = 0.50, indicating they cannot maintain positive NB under any meaningful uncertainty expansion.

Cost-effectiveness ladder: Q_nsga candidates at $2–5M/death vs Phase 1 paid portfolios at $17–69M/death
L0 cost-effectiveness ladder. The five NSGA-II candidates (Q_nsga_1–5) achieve $2.44–$5.26M/death, well within EPA’s historical $10–30M/death acceptance band. A_free_lunch (zero cost) dominates the paid options by definition. F_maximum at $69M/death is the only portfolio unambiguously outside the EPA band.
Robustness consensus across L1–L5: Q_nsga_2 wins all five lenses
Robustness consensus across L1–L5. Q_nsga_2 wins all five lenses (5/5 votes). A_free_lunch is the zero-cost L0 winner and maintains positive NB at all lenses, but does not win any of L1–L5 against the NSGA candidates. F_maximum is the only portfolio dominated on every criterion.
Lens Winner Key metric
L0 (free)A_free_lunch$0 cost
L0 (best paid)Q_nsga_5$2.44M/death
L1 EVQ_nsga_2Mean NB +$5.92B
L2 Chance-constrainedQ_nsga_2P(NB ≥ $1B) = 0.989
L3 CVaR0.05Q_nsga_2Tail floor +$1.45B
L4 Adversarial envelopeQ_nsga_2Worst-corner NB +$2.72B
L5 Info-gapQ_nsga_2Critical α = 1.91
ConsensusQ_nsga_25/5 votes, robust = EV pick

Robust and EV picks agree: robust_matches_ev = true. The same portfolio that maximizes expected benefit also maximizes resilience to uncertainty. This is not just an average-case result—it holds across all five robustness lenses.

A_free_lunch (zero cost, T1+B1+DTE retire) avoids 53.8 deaths/yr with mean NB $+0.67B and a CVaR tail floor of $+0.30B. It is the conservative production recommendation while Q_nsga_2’s ISRM validation remains AMBIGUOUS. Its cost-effectiveness is dominant by definition, but its absolute health impact (54 deaths/yr) is roughly 12× smaller than Q_nsga_2’s surrogate-predicted 631 deaths/yr.

FieldValue
Investigation23_portfolio-robust
TierTier 1
Run timestamp2026-05-04T07:46:21
results.json sha256cab2edc05333
MC draws5,000 (seed 2026)
Upstream: Investigation M-1sha256 145dbfd826d0 (named portfolios)
Upstream: Investigation M-2sha256 ff6e97fe9760 (sequential BO policy)
Upstream: Investigation M-3sha256 59656b02ceb7 (NSGA-II Pareto frontier)
MethodsCVaR (Rockafellar & Uryasev 2000), Info-gap (Ben-Haim 2006), Chance-constrained (Charnes & Cooper 1959)
ISRM validationAMBIGUOUS — see Investigation 6-9 (Q_nsga_2 ISRM validation)