Paper DAG¶
The directed acyclic graph of the paper's argument: how the institutional premise flows through the award-layer construct, the decomposition that disciplines it, and the reach-and-limits map that is the contribution. Each node is a claim or object; each arrow is "supports / leads to."
flowchart TD
%% ---------- Premise ----------
P0["Cartel enforcement must allocate costly<br/>proof-producing effort <b>before</b> proof exists"]:::premise
P1["Two observability layers:<br/><b>award</b> (cheap, routine) vs<br/><b>bid</b> (costly LANCES recovery)"]:::premise
P0 --> P1
%% ---------- Construct ----------
subgraph CON["Award-layer construct"]
direction TB
C1["Always-losers (win-rate = 0)<br/>16,843 firms"]:::obj
C2["Frequent-loser score<br/>s = log(1 + T), T = tender-item participations"]:::obj
C3["FL14 = T ≥ 14 (median + 1.5·IQR)<br/><i>administrative implementation, not structural</i>"]:::obj
C1 --> C2 --> C3
end
P1 --> C1
%% ---------- Validation target ----------
V1["Validation target: 651 <b>cobidders</b><br/>(adjudication-anchored exposure,<br/>non-circular label, <i>not</i> cartel members)"]:::target
V2["Direct CADE defendants =<br/>legal anchors (win-heavy)"]:::target
C2 --> V1
V2 -. anchors .-> V1
%% ---------- Decomposition: the method ----------
subgraph DEC["Decomposition — the contribution"]
direction TB
D1["Hold procurement <b>opportunity</b> fixed<br/>raw ROC 0.761; label-blind opportunity 0.553 → within-stratum 0.471 (≈chance)<br/><b>fragile increment +0.010</b> (p=0.013, not robust)"]:::method
D2["<b>Timing</b>: orders firms retrospectively<br/>among incumbents; full-universe ROC ≈ 0.474 (below chance);<br/>sequential strict-timing infeasible"]:::limit
D3["<b>Single-case</b>: leave-largest-case-out<br/>PR-AUC 0.143 → 0.090 (−37%);<br/>one case ≈ 32% of positives"]:::limit
D4["<b>Scope</b>: binary AUC ≈ 0.49 vs direct defendants<br/>— by design (continuous score 0.66–0.70)"]:::limit
D5["<b>Armor battery</b> (anchor-agnostic):<br/>label-blind opportunity 0.553; positive control 0.953;<br/>perm power 0.97 @ 0.55; label-frozen timing 0.713"]:::method
D6["<b>Over-crediting bias as an estimable object</b> (LEAD; Prop., App. C; full grid in Online Supplement):<br/>Δ = AUC_raw − AUC_opp-adj is a size-bias gap;<br/>SIGNS only — ↑ in CV(T), ↓ in base rate (no closed form);<br/>magnitude from a synthetic surface anchored at one point per platform (not an estimated curve);<br/>CV(T) is a pre-bid-file <i>leading-order sufficient statistic</i> / diagnostic, not a fix"]:::model
end
V1 --> D1
D1 --> D2
D1 --> D3
V1 --> D4
V2 --> D4
D1 --> D5
D1 --> D6
%% ---------- Architecture ----------
subgraph ARC["Division of labor between layers"]
direction TB
A1["Award ranks <b>where to look</b>;<br/>bid evaluates <b>what is found</b>"]:::arch
A2["Bid benchmark: bid RF 0.717 / award 0.760 /<br/>combined PR 0.188 random-CV but 0.103 case-grouped<br/>— conditional complementarity, case-fragile"]:::arch
A3["Cost-recall frontier: at K1=2000,<br/>firm pool −88% but bid-row footprint −33%;<br/>K1=1000 beats K1=2000 — no optimal cutoff"]:::arch
A4["<b>Enforcer stopping rule</b> (modest; Prop., App. B):<br/>standard cost–benefit (MB=MC) tangency — descend ranking until V·ρ(K)=c·φ(K) ⇔ ρ/φ=c/V;<br/>sweep c/V → locus of budget-dependent optima.<br/><i>No fixed cutoff — the optimum moves with the budget; the frontier is its image</i>"]:::model
A1 --> A2 --> A3
A4 -. image .-> A3
end
D1 --> A1
C3 --> A3
%% ---------- Price (scope) ----------
PR1["Price = <b>scope</b>, not damages:<br/>broad +0.064 → overlap-cell ATT −0.097 →<br/>Q4 +0.041 only; mechanism <b>not identified</b>"]:::scope
D4 --> PR1
%% ---------- Conclusion ----------
Z1["<b>Map of reach and limits</b>:<br/>cheap records order forensic priority<br/>within a bounded, retrospective, incumbent reach"]:::concl
Z2["Liability remains in the<br/>richer bid-level record"]:::concl
D1 --> Z1
D2 --> Z1
D3 --> Z1
D5 --> Z1
A3 --> Z1
PR1 --> Z1
Z1 --> Z2
classDef premise fill:#1f2a44,stroke:#3b4a6b,color:#fff;
classDef obj fill:#27384f,stroke:#3e5c79,color:#eaf2fb;
classDef target fill:#34425a,stroke:#5b6f93,color:#eaf2fb;
classDef method fill:#1f4d3a,stroke:#2e7d5b,color:#eafaf0;
classDef limit fill:#5a3a2a,stroke:#9a5b3b,color:#fbeee6;
classDef arch fill:#2d3f5c,stroke:#4a679a,color:#eaf2fb;
classDef scope fill:#4a3a5c,stroke:#6f4a9a,color:#f2eafb;
classDef concl fill:#143b4a,stroke:#1f6f8b,color:#eafaf8;
classDef model fill:#13313a,stroke:#2a7d8b,color:#e6fbfa;How to read it
The green nodes are the paper's methodological core — the opportunity decomposition that strips mechanical co-participation exposure from the raw award-layer score (0.761) and finds that almost nothing survives: genuine label-blind opportunity ranks the label at only 0.553, the within-stratum AUC is ≈ chance (0.471), and the only positive is a fragile +0.010 increment that is not robust across designs. The armor battery (anchor-agnostic) decides the deflationary verdict: a planted positive control recovers 0.953 (falsifiability), the permutation test has power 0.97 at within-AUC 0.55, and label-frozen timing (0.713) shows generic contact forecasting, not cartel-specific prediction. The ranking by observed contact (0.905) is mechanical label encoding, not a winning model. The brown nodes are the limits the same decomposition exposes (below-chance out-of-time ordering, single-case dependence, the direct-defendant scope boundary). The two teal nodes are the reframe's positive modeled objects, led (v25) by the over-crediting bias \(\Delta\) (a size-bias characterization of the deflation, stated as signs only — increasing in \(\mathrm{CV}(T)\), decreasing in the base rate, no closed form, magnitude read from a synthetic surface anchored at one empirical point per platform rather than an estimated curve, with \(\mathrm{CV}(T)\) a pre-bid-file leading-order sufficient statistic / diagnostic). The second object is the enforcer stopping rule, stated modestly as a standard cost–benefit (MB = MC) tangency, whose image is the cost-recall frontier — the absence of a fixed cutoff follows from the optimum being budget-dependent. The contributions are these two modeled objects plus a disciplined audit protocol — not a deployable cartel detector.
Second platform: the same DAG re-run on federal ComprasNet (§5)
The entire decomposition branch above (raw award score → label-blind opportunity → within-stratum residual → armor battery) was re-run unchanged on the federal ComprasNet platform (2013–2019, pure Pregão) against the same family of CADE anchors, and reaches the same verdict: the deflation replicates. Federally the raw award-layer ROC is 0.744, label-blind opportunity ranks the label at 0.611, the within-stratum residual falls to ≈ chance (0.462), the nested increment is null (+0.005, \(p = 0.191\)), and the negative controls return the surviving order to generic opportunity/volume geometry. The strict full-universe prospective collapse carries too (ROC 0.489 federal / 0.474 BEC). The construct ports and deflates; it does not break. This is a second-platform demonstration of the protocol, provisional — partially overlapping legal anchors (the 7 federal cases are the same cartels as the BEC portfolio, establishment-anchored), not a promotion to "Confirmed." Full battery in §5 and Appendix G; see the Changelog v23 entry.