Retrieval check (from lesson 6, new setting). A support-ticket triage system scores pending tickets by priority = credibility × value ÷ cost — credibility that the ticket is genuinely urgent, value of resolving it (customers affected, revenue at risk), cost (engineer-hours to investigate). Three tickets: T1 (credibility 0.8, value 0.9, cost 2), T2 (credibility 0.9, value 0.2, cost 1), T3 (credibility 0.5, value 0.6, cost 1.5). Which ticket gets worked first? (This is the correct use of the formula — all three terms genuinely present, unlike lesson 14’s zero-value trap.) Work it out; the solution confirms it.
Two heuristics, one machinery consequence
A heuristic is a mental shortcut — a fast, usually-good-enough rule for judgment under uncertainty, substituting an easy question for a hard one. Two of the best-studied, from Tversky and Kahneman’s research program:
- Availability: judging how probable or frequent something is by how easily examples come to mind — not by actual frequency. Plane crashes feel more common than they are because they’re vivid and heavily covered; routine car trips don’t make the news, so their much higher actual risk feels less available to recall.
- Representativeness: judging how probable something is by how well it matches a mental stereotype or pattern — not by the actual base rates involved. A description that “sounds like” a category member gets rated as more probably a member of that category than the numbers justify.
Representativeness has a specific, checkable failure mode: the conjunction fallacy. For any two events A and B, the probability that both happen (A and B) can never exceed the probability that just one of them (A alone) happens — if you’re a member of set A∩B, you’re necessarily also a member of set A. This is pure arithmetic (P(A∩B) ≤ P(A), always), not a matter of judgment. But when a conjunction “sounds like” a better-fitting story than the plain event alone, representativeness reliably makes people rate the conjunction as more probable — a description that fits a specific narrative can feel more believable than the bare category it’s a strict subset of.
The puzzle
A hiring pool’s résumés include this profile: quiet, detail-oriented, uses precise technical language, was a musician for several years before switching careers. From this team’s actual hiring data:
- P(software engineer) = 0.15 (15% of this résumé pool are software engineers, full stop)
- P(plays in a band | software engineer) = 0.05 (among software engineers in this pool, 5% also currently play in a band)
The description above “sounds like” the second, more specific story — engineer and still-a-musician — more than it sounds like “software engineer” alone, which is exactly the setup representativeness exploits. Compute the actual joint probability, P(software engineer AND plays in a band), from the base rates given, and compare it to P(software engineer) = 0.15 alone.