Demo 1 · The arithmetic of expected harm

Expected harm is the product of three factors — frequency N, per-event risk p, and severity S. The stylized population injects N = 1,000 times a year at p = 0.002 and S = 0.10, so baseline expected fatal overdoses are H = 0.20. Abstinence lowers N for the few who stop; harm reduction lowers p and S for everyone. The defaults reproduce the article’s worked example. Computed locally, not stored.

0.200Baseline0.180Abstinence0.048Harm reduction
Baseline H = 1000 × 0.002 × 0.10 = 0.200.
Abstinence acts on N only: 900 × 0.002 × 0.10 = 0.180 — a 10% cut, reaching only the 10% who stop.
Harm reduction acts on p and S for all: 1000 × 0.0016 × 0.030 = 0.048 — a 76% cut. The two cuts compound as 0.24.

Demo 2 · Same facts, opposite choice

A disease threatens 600 people. Two programs are offered. The sure program and the gamble are identical across the two framings — 200 saved is 400 lost, and the gamble’s odds never change. Only the wording moves between a gain frame and a loss frame, yet the majority choice flips. Shares are the classic results reported by Tversky and Kahneman (1981); computed locally, not stored.

200 saved under the sure program400 not saved
Program A: 200 people will be saved.
Program B: a 1-in-3 chance that all 600 are saved, and a 2-in-3 chance that no one is saved.
Typical choice under this frame:
sure 72%
gamble 28%
The gain frame pulls people toward the sure option; the loss frame — describing the very same outcomes as deaths — pushes the majority toward the gamble. Harm-reduction messaging frames a safer practice as a gain to secure rather than a loss to avoid.

Demo 3 · Who the program reaches

The transtheoretical model holds that change moves through stages and that most people are not in the action stage at any one moment. An abstinence-only program delivers benefit only to those in action or maintenance; harm reduction delivers benefit at every stage. Adjust the readiness distribution and watch the reach of each approach. The distribution is illustrative; computed locally, not stored.

Precontemplation40%Contemplation25%Preparation15%Action12%Maintenance8%
PrecontemplationContemplationPreparationActionMaintenance
Abstinence-only reaches the 20% of people in action or maintenance.
Harm reduction reaches 100% — a clean needle or a naloxone kit helps a person in precontemplation who has no intention of stopping, so benefit is delivered across the whole distribution of readiness.