CARE-AI: Pedagogical Risk Scoring Matrix (PRSM*) Calculator

1. Mathematical Model Formulation

The PRSM* index measures educational AI task vulnerability on a continuous non-linear scale $PRSM^* \in [0.0, 100.0]$. It avoids naive additive scoring by applying a convex power function ($\alpha = 1.5$) to model compounding risk acceleration when multiple risk vectors degrade simultaneously:

$$PRSM^* = \min\left(100.0, \;\Omega(X) \cdot 100 \cdot \left[ \sum_{i=1}^{4} w_i \cdot \left(\hat{x}_i\right)^{\alpha} \right]^{1/\alpha}\right)$$

2. Input Normalization ($\hat{x}_i$)

Raw user responses $x_1, x_2, x_3, x_4 \in \{1, 2, 3\}$ represent ordinal risk tiers. These are transformed into min-max normalized continuous metrics $\hat{x}_i \in [0.0, 1.0]$:

$$\hat{x}_i = \frac{x_i - 1}{2}$$

3. Analytic Hierarchy Process (AHP) Weighting ($w_i$)

Dimensional weights $w_i$ were derived using Saaty’s Analytic Hierarchy Process (Pairwise Comparison Matrix, Consistency Ratio $CR = 1.38\% < 10\%$). Priority is heavily weighted toward data privacy compliance and cognitive offloading integrity:

w₂ = 0.454 — Data Privacy (DPR) Weighted highest to enforce compliance with GDPR Art. 8 & EU AI Act Reg. 2024/1689 regarding minor PII handling.

w₁ = 0.282 — Cognitive Delegation (CDR) Evaluates the degree to which essential analytical synthesis and critical thinking are outsourced.

w₃ = 0.160 — Assessment Vulnerability (AV) Measures likelihood that unverified LLM output can pass assessment without student understanding.

w₄ = 0.104 — Social Equity Gap (SEG) Accounts for systemic disparities driven by dependencies on paid, proprietary model tiers.

4. Critical Penalty Multiplier ($\Omega$)

To ensure that high risk in a single dimension cannot be obscured by low scores in other dimensions, a single-factor multiplier $\Omega(X)$ applies a **+35% penalty escalation** if any dimension hits level 3 ($x_i = 3$):

$$\Omega(X) = \begin{cases} 1.35 & \text{if } \max(x_1, x_2, x_3, x_4) = 3 \\ 1.00 & \text{otherwise} \end{cases}$$

5. Statutory Data Privacy Hard Veto Override

Non-Negotiable Governance Safety Gate:

If Data Privacy Risk is rated at High Risk ($x_2 = 3$, e.g., open platforms ingesting student PII), the diagnostic engine engages an automatic **Hard Statutory Veto**. The assessment status is locked to **RED (HIGH RISK)** regardless of the composite numerical score.

6. Governance Stratification Thresholds

• GREEN (LOW RISK): PRSM* < 35.0 → Autonomous execution with disclosure.

• YELLOW (MODERATE RISK): 35.0 ≤ PRSM* < 65.0 → Conditional approval with process logs & oral defense.

• RED (HIGH RISK): PRSM* ≥ 65.0 OR Privacy Veto → Deployment prohibited; redesign required.

CARE-AI Governance Framework

Assignment Metadata

1. Cognitive Delegation Risk (CDR) (w₁ = 0.282)

2. Data Privacy Risk (DPR) (w₂ = 0.454)

3. Assessment Vulnerability (AV) (w₃ = 0.160)

4. Social Equity Gap (SEG) (w₄ = 0.104)

PRSM* Index Dashboard

Institutional Governance Protocol