Teach Compitum (Educator Guide)¶

Audience

Upper-undergraduate/graduate CS, data science, or AI ethics courses; technical managers learning cost-quality tradeoffs.

Learning Objectives

Interpret a routing certificate (utility components, constraints, boundary diagnostics, drift).
Explain utility U = performance - lambda * cost and willingness-to-pay (WTP).
Describe near-frontier behavior and why “close to optimal” can be valuable even without envelope wins.
Connect formal constraints to policy/compliance requirements.

Prerequisites

Comfortable with basic probability, optimization intuition, and Python. No deep ML required.

Before Class (10-15 min)

Read Mathematics: A Plain-Language Brief (plain-language summary).
Skim Certificate Schema and Peer Review Package (Routing Certificate section) to see what evidence looks like.
Optional: Watch/describe the media clip Media: tess.mp4 for intuition.

In-Class Activity (30-45 min)

Certificate walk-through (10 min)
- Run: compitum route --prompt "Sketch a proof for AM-GM inequality." --trace
- Identify fields: utility_components, constraints.feasible, constraints.shadow_prices, boundary_analysis.gap.
Cost-quality tradeoff (10-15 min)
- Define U = performance - lambda * cost. Discuss how increasing lambda penalizes cost.
- Show that different WTP slices (0.1 vs. 1.0) can change selections.
Constraints as safety/policy hooks (10 min)
- Map constraints to compliance (e.g., region limits). Interpret shadow prices: which limits “bind” the choice?
Near-frontier behavior (5-10 min)
- Discuss frontier gap with 95% CIs. Why being near-frontier can be enough when constraints are respected.
Control of error (5-10 min)
- Read: Pedagogy and Control of Error (first two sections). Connect “control of error” to the certificate.
- Prompt: “Which certificate fields make mistakes legible at the moment of choice?”
- Extension: Propose a small change to constraints or lambda and predict the effect; then test.

Assessment Ideas

Short quiz: define utility and WTP; interpret one certificate; explain shadow prices in one sentence.
Small assignment: change lambda and describe selection shifts.

Resources

Mathematics: A Plain-Language Brief - plain-language summary.
Certificate Schema - fields and JSON schema.
Peer Review Package - evidence pack and reproduction steps.
Media: tess.mp4 - optional video + text description.
RouterBench Fairness Notes - how we ensure fair evaluations.
Pedagogy and Control of Error - educator perspective linking “control of error” to mechanistic feedback.

Accessibility