Executive Summary
We formulate the talent-to-job matching problem as a min-cost max-flow optimization with tiered job nodes and ensemble slot allocation, departing from the Gale-Shapley stable matching paradigm that dominates the matching market literature. Our formulation exploits a structural feature of brokered hiring platforms: because the platform computes compatibility scores centrally rather than eliciting preference rankings from participants, the strategy-proofness constraint that drives much of mechanism design becomes irrelevant. This frees the optimizer to pursue welfare-weighted global optima subject to fairness constraints encoded directly in the flow network.
In simulation (1,000 candidates x 200 jobs, 50 random seeds), the MCF-Tiered engine achieves 95.3% company satisfaction versus 24.5% for the greedy per-job strategy that approximates current industry practice, with all advantages significant at p < 10-20. On 8,000 human-labeled resume-job description pairs, MCF achieves a 90.8% match quality rate versus 74.9% for greedy (p = 0.039). On 851 GPT-4o-scored resume-JD pairs, MCF-Tiered achieves 87.3% job coverage versus 40.0% for greedy at 2:1 ratio (p < 0.001).
Key Contributions
- Network flow formulation: Many-to-one hiring match with native capacity constraints, quality floors, and equitable distribution achieved through flow network structure rather than ad hoc post-processing.
- Adaptive tiered nodes: Premium bonus β = 0.7σ(S) ensures scale-invariant equity distribution regardless of scoring function precision. Eliminates regression on low-precision scorers while preserving the full advantage on high-precision ones.
- Hiring-science-informed scoring: Component weights derived from Sackett et al. (2022) meta-analytic validity coefficients. 72% top-1 disagreement with cosine similarity — picks fundamentally different candidates.
- Ensemble slot allocation: 2 welfare + 2 equity + 1 exploration per job per cycle. Fills 94.2% of jobs over 15-week lifecycle versus 90.9% for pure optimization (p < 0.001).
- Scorer independence: MCF-Tiered advantage over greedy ranges from +63.5 to +71.8 percentage points across three different scoring functions. Greedy stays at ~20% regardless of scorer quality. The allocation algorithm is the bottleneck, not the scoring function.
Key Findings
- 95.3% vs 24.5%: Company satisfaction at 1.5:1 ratio — MCF-Tiered versus greedy (p < 10-20)
- Cold-start advantage: At 1:1 ratio on real data, MCF-Tiered achieves 62.2% job coverage versus greedy's 20.0% — a threefold advantage at the condition every new platform faces
- 96.9% fill rate: Large-scale synthetic lifecycle (2,000c x 400j, 30 seeds) versus 88.5% for greedy and 94.9% for Gale-Shapley
- Adaptive β: Strict dominance across all tested conditions. Eliminates TF-IDF regression (p=0.002 → ns) while preserving hiring-science advantage (+21.9 filled, p < 0.001)
- Three datasets, one direction: Synthetic simulation, 8K human-labeled pairs, 851 GPT-4o-scored pairs — consistent directional findings under different labeling methodologies
Key References
College Admissions and the Stability of Marriage. American Mathematical Monthly, 69(1), 9-15.
Network Flows: Theory, Algorithms, and Applications. Prentice Hall.
Revisiting Meta-Analytic Estimates of Validity in Personnel Selection. Journal of Applied Psychology, 107(11), 2040-2068.
The Economics of Matching: Stability and Incentives. Mathematics of Operations Research, 7(4), 617-628.
Fair Prediction with Disparate Impact: A Study of Bias in Recidivism Prediction Instruments. Big Data, 5(2), 153-163.