Decision-Making Under Uncertainty

DECISION-MAKING UNDER UNCERTAINTY expected value says one thing — we reliably do another. the math of the 'rational' choice, and the psychology of the real one. 1 · THE RATIONAL BASELINE — Expected Value EV = Σ ( probability × payoff ) A coin flip offered to you: heads (50%): win +$150 tails (50%): lose -$100 EV = .5(+150) + .5(-100) = +$25 → a POSITIVE-EV bet. a pure calculator takes it every time. …yet most people REFUSE it. the loss of $100 looms larger than the bigger $150 gain. EV is the NORMATIVE model (what's optimal); we need a DESCRIPTIVE one. 2 · HOW WE ACTUALLY CHOOSE — Prospect Theory value gains → ← losses reference point (your status quo) concave in gains → risk-AVERSE convex + STEEPER in losses → loss aversion (~2×) → risk-SEEKING to dodge a loss you value CHANGES from a reference point, not absolute wealth — and the loss arm is ~twice as steep. 3 · PROBABILITY WEIGHTING — π(p) 0 stated p → π(p) 'rational' OVER-weight rare events (lottery, plane crash, jackpot) UNDER-weight likely ones (the 90% that usually happens) certainty effect: a SURE thing (p=1) gets a bonus — we overpay to remove the last 1% of risk. 4 · DIMINISHING MARGINAL UTILITY (Bernoulli) utility wealth → $0→1M: huge $4→5M: meh the 2nd million matters less than the 1st. a concave curve = risk aversion — and why buying INSURANCE (paying a premium ABOVE EV to erase a rare ruinous loss) is perfectly rational. 5 · THE FOURFOLD PATTERN LOW probability HIGH probability GAINS LOSSES risk-SEEKING buy the lottery ticket (chase the jackpot) risk-AVERSE take the sure $ (bird in hand; settle a lawsuit) risk-AVERSE buy INSURANCE (pay to avoid rare ruin) risk-SEEKING gamble to dodge a SURE loss (double-or-nothing) same person flips between bold & timid depending on the quadrant — value curve × weighting, combined. 6 · RISK vs UNCERTAINTY vs AMBIGUITY RISK — odds are KNOWN dice, roulette. you can COMPUTE the EV. this is the easy case. UNCERTAINTY (Knightian) — odds UNKNOWN a new product launch, a novel outage. no reliable probabilities to plug in. AMBIGUITY (Ellsberg) — we AVOID unknown odds prefer a known 50/50 urn over an unknown one, even when it costs us. 'ambiguity aversion' — we pay extra just to know the odds. THIS IS RISK ENGINEERING (shop / Agent) • 'risk = probability × impact' (the risk matrix / heat map) IS expected value. An SLO error budget is an EV call: spend reliability on features. • Redundancy (multi-AZ, backups, DR) = INSURANCE: paying a premium above raw EV to erase a rare catastrophic loss — rational via the utility curve. • 'Should we go multi-region?' = P(region outage) × cost-of-outage vs cost-of-multi-region, PLUS your loss-aversion premium. Name the premium so it's a choice. • Beware OUTCOME BIAS: judge a decision by whether it was +EV given what you KNEW, not by how it turned out. A good bet can still lose; a lucky call is still reckless. JARGON, DECODED expected value — Σ probability × payoff expected utility — EV weighted by diminishing value reference point — the status quo you measure from prospect theory — the descriptive model of real choice probability weighting — over-rate rare, under-rate likely certainty effect — a sure thing gets a premium risk / uncertainty / ambiguity — known / unknown / avoided odds outcome bias — judging the bet by the result, not the odds satisficing — pick 'good enough', don't optimise (Simon)