Introduction

Government AI investment appraisals typically ignore AI-specific technical risks. We contribute a Monte Carlo simulation tool with: (1) a tiered algorithmic risk model scaled to project size, (2) retraining-aware degradation, and (3) a decision framework mapping simulation outputs to investment actions. Core code is provided in-paper.

Risk Taxonomy

Government Project Risks

AI-Specific Risks

Tiered algorithmic risk (costs scaled as percentage of investment, not hardcoded):

Scaling costs as percentages of investment ensures the model works across currencies, project scales, and contexts without hardcoded constants.

Retraining-aware degradation:

Other AI risks:

Simulation Code

Complete, runnable, with all costs scaled to user inputs:

import numpy as np

def simulate(investment, annual_benefit, opex, discount_rate,
             n_sims=5000, horizon=10, defund_prob=0.05):
    """Monte Carlo for government AI investment with 9 risk factors.
    All monetary inputs in same units (e.g., millions). Output in same units."""
    np.random.seed(42)
    results = []

    for _ in range(n_sims):
        overrun = np.random.uniform(1.1, 1.6) if np.random.random() < 0.45 else 1.0
        delay = int(np.random.uniform(0.5, 2.5))
        adopt_ceil = np.random.uniform(0.65, 0.85)
        talent_mult = np.random.uniform(1.2, 1.8)
        degradation = 1.0
        npv = -investment * overrun
        defunded = False

        for year in range(1, horizon + 1):
            if defunded or np.random.random() < defund_prob:
                defunded = True; continue

            # Retraining: pay to reset degradation, or let it decay
            retrain_cost = 0
            if np.random.random() < 0.30:
                retrain_cost = opex * np.random.uniform(0.15, 0.30)
                degradation = 1.0
            else:
                degradation *= np.random.uniform(0.93, 0.98)

            # Adoption S-curve with procurement delay
            eff_year = max(0, year - delay)
            adoption = min(adopt_ceil,
                          adopt_ceil / (1 + np.exp(-0.8 * (eff_year - 3.5))))

            # Tiered bias cost (scaled to investment, not hardcoded)
            bias_cost = 0
            r = np.random.random()
            if r < 0.005:    # Catastrophic
                bias_cost = investment * np.random.uniform(0.5, 10.0)
            elif r < 0.055:  # Moderate
                bias_cost = investment * np.random.uniform(0.01, 0.10)
            elif r < 0.255:  # Minor
                bias_cost = investment * np.random.uniform(0.001, 0.005)

            benefit = adoption * annual_benefit * degradation
            cost = opex * talent_mult + retrain_cost + bias_cost
            npv += (benefit - cost) / (1 + discount_rate) ** year

        results.append(npv)

    results.sort()
    n = len(results)
    pos = sum(1 for x in results if x > 0)
    return {
        'median': results[n // 2],
        'p5': results[int(n * 0.05)],
        'p25': results[int(n * 0.25)],
        'p75': results[int(n * 0.75)],
        'p95': results[int(n * 0.95)],
        'prob_positive': round(pos / n * 100, 1),
        'mean': sum(results) / n
    }

# Example: Brazil tax administration (all values in BRL millions)
brazil = simulate(investment=450, annual_benefit=1700, opex=85,
                  discount_rate=0.08, defund_prob=0.05)
print(f"Brazil: Median NPV={brazil['median']:.0f}M, "
      f"P(NPV>0)={brazil['prob_positive']}%, "
      f"P5={brazil['p5']:.0f}M, P95={brazil['p95']:.0f}M")

# Example: Saudi Arabia municipal services (all values in SAR millions)
saudi = simulate(investment=280, annual_benefit=470, opex=55,
                 discount_rate=0.06, defund_prob=0.03)
print(f"Saudi:  Median NPV={saudi['median']:.0f}M, "
      f"P(NPV>0)={saudi['prob_positive']}%, "
      f"P5={saudi['p5']:.0f}M, P95={saudi['p95']:.0f}M")

Decision Framework

Simulation outputs map to investment actions:

Using P5/P95 for decision-making: The P5 value represents the worst plausible outcome (5th percentile). If P5 exceeds the negative of total investment, even worst-case scenarios don't result in total loss. The P95-P5 range shows total outcome uncertainty — a narrow range suggests the decision is robust to parameter uncertainty; a wide range indicates the decision depends heavily on assumptions that should be validated before commitment.

Sensitivity-driven validation: The tool's sensitivity ranking tells analysts which assumptions to validate first. If adoption ceiling dominates (as in both examples), the priority is operational: will departments actually use the system? If benefit estimates dominate, the priority is analytical: are the benchmark comparisons realistic?

Example Outputs

Brazil Tax Administration

Inputs: Investment 450M, annual benefit 1,700M, opex 85M, discount 8%.

Saudi Arabia Municipal Services

Inputs: Investment 280M, annual benefit 470M, opex 55M, discount 6%.

Limitations

1. No retrospective validation against completed government AI projects. The necessary outcome data is sparse but growing.
2. Tier probabilities are estimates, not derived from systematic meta-analysis. They improve on single-distribution approaches but should be updated as incident databases grow.
3. Multiplicative decay is a simplification. Real concept drift varies by data type, policy environment, and model architecture. The tool accepts custom decay parameters.
4. Two examples demonstrate the tool, not the viability of those specific investments.

Conclusion

We contribute a Monte Carlo tool for government AI investment appraisal with tiered algorithmic risk (scaled to project size), retraining-aware degradation, and a decision framework mapping outputs to investment actions. Complete executable code is provided in-paper.

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