Introduction

Government analysts preparing AI investment cases lack tools that model AI-specific risks alongside standard procurement risks. We contribute an open-source Monte Carlo tool with two improvements over standard approaches: (1) a tiered algorithmic risk model that distinguishes routine model maintenance from catastrophic failure, and (2) a retraining-aware degradation model where investing in retraining resets performance decay — capturing the lifecycle tradeoff between maintenance cost and benefit preservation.

The tool incorporates nine risk factors (four government, five AI-specific) with user-configurable distributions. We provide the core simulation code directly in this paper for immediate reproducibility.

Risk Taxonomy

Standard Government Project Risks

AI-Specific Risks

Tiered Algorithmic Risk Model. Prior work (including earlier versions of this paper) modeled algorithmic bias as a single distribution calibrated from extreme cases. Reviewers correctly noted this overestimates risk for routine applications. We now use a three-tier model:

This tiered approach produces a more realistic expected annual bias cost than a flat 8% probability derived solely from catastrophic cases. For a typical government AI deployment, the expected annual algorithmic risk cost is dominated by Tier 1 (routine audits), not Tier 3 (scandals).

Retraining-Aware Degradation. ML models degrade as data distributions shift (Lu et al., IEEE TKDE 31(12), 2019). Our earlier model applied continuous decay without accounting for retraining. The updated model couples retraining investment with degradation:

• Each year, model accuracy decays by factor $d \sim \text{Uniform}(0.93, 0.98)$
• If retraining occurs (Bernoulli(0.30) per year), degradation resets to 1.0
• Retraining cost: 15-30% of annual model operating budget
• Net effect: organizations that invest in retraining preserve benefits; those that don't see compounding accuracy loss

This creates a realistic lifecycle tradeoff absent from standard ROI calculators.

Remaining AI-Specific Risks:

Core Simulation Code

The complete Monte Carlo engine is provided below for immediate reproducibility:

import numpy as np

def simulate_govai(investment, annual_benefit, opex, discount_rate,
                   n_sims=5000, horizon=10, defund_prob=0.05):
    np.random.seed(42)
    results = []

    for _ in range(n_sims):
        # Government risks
        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)

        # Track degradation with retraining resets
        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 decision
            retrain_cost = 0
            if np.random.random() < 0.30:
                retrain_cost = opex * np.random.uniform(0.15, 0.30)
                degradation = 1.0  # Reset on retrain
            else:
                degradation *= np.random.uniform(0.93, 0.98)

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

            # Tiered bias cost
            bias_cost = 0
            r = np.random.random()
            if r < 0.005:
                bias_cost = np.random.uniform(100, 5000)  # Catastrophic (M)
            elif r < 0.055:
                bias_cost = np.random.uniform(5, 50)      # Moderate (M)
            elif r < 0.255:
                bias_cost = np.random.uniform(0.5, 2)      # Minor (M)

            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()
    pos = sum(1 for x in results if x > 0)
    return {
        'median': results[len(results)//2],
        'p5': results[int(len(results)*0.05)],
        'p95': results[int(len(results)*0.95)],
        'prob_positive': round(pos / n_sims * 100, 1)
    }

Example Outputs

Example 1: Brazil Tax Administration

Inputs: Investment BRL 450M (estimated from comparable tax technology procurements: HMRC Connect GBP 100M+, ATO analytics AUD 200M+, scaled for Brazil). Annual benefit BRL 1,700M at full adoption (benchmark-discounted from HMRC Connect results, UK NAO HC 978, 2022-23). Discount rate 8%.

Example 2: Saudi Arabia Municipal Services

Inputs: Investment SAR 280M (comparable municipal digitization scales, OECD 2023). Annual benefit SAR 470M (benchmarked against Singapore BCA, Annual Report 2022/23). Discount rate 6%.

Note: Monte Carlo outputs are approximate and will vary slightly across runs due to the tiered bias model's heavy tail. The code above can be executed to reproduce results with seed 42.

Discussion

Contribution

Three elements: (1) a tiered algorithmic risk model distinguishing routine maintenance from catastrophic failure, (2) a retraining-aware degradation model capturing the ML lifecycle maintenance tradeoff, and (3) executable code provided in-paper for immediate reproducibility. The tool is configurable — all distributions can be overridden by users with domain-specific estimates.

Adoption Ceiling Variance

The default Uniform(0.65, 0.85) applies to non-mandatory government services. Mandatory services (tax filing, license renewal) may achieve higher adoption; experimental or niche services may achieve lower. Users should set this parameter based on the specific service type and delivery channel. The tool accepts any value in [0, 1].

Limitations

1. No ex-post validation against completed government AI projects. This requires outcome data that is currently sparse.
2. Tiered bias probabilities are estimates. The three-tier structure improves on single-distribution approaches, but the specific probabilities (20%/5%/0.5%) should be calibrated as more incident data becomes available.
3. Two example configurations demonstrate the tool but do not constitute empirical evidence about government AI investments.
4. The code provided is a simplified core. A full implementation would include visualization, sensitivity analysis, and parameter configuration interfaces.

Conclusion

We present an open-source Monte Carlo tool for government AI investment appraisal with two modeling improvements: tiered algorithmic risk (distinguishing routine audits from catastrophic failures) and retraining-aware degradation (where maintenance investment resets performance decay). The complete simulation code is provided in-paper for immediate reproducibility. All default risk distributions are user-configurable and grounded in documented incidents and published literature.

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