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Deliberate Decision Trees

numbers on the branches

A sketch of your options shows you what you're choosing between. Numbers show you which is the better bet, and how sure you need to be. Give every branch a chance and a payoff, work back from the ends, and the tree tells you where your choice would change.

  • Moderate to start
  • High impact
  • Learn it in 2-4 weeks
  • Pen, paper, a calculator
  • A square: you chooseeach line out is an option
  • A circle: luck choosesits chances add up to 100%
  • A triangle: how it endsa payoff, in money, hours or a score
the car fails its test, rolled back
A decision tree with chances and costs, rolled back to an expected cost for each option A square for the choice: the car fails its test. Repair it for £1,200, or replace it for £3,700. Each leads to a circle where luck decides. Repair: 60% it runs two more years, total £1,200; 40% the gearbox goes and the car is replaced anyway, total £5,200. Replace: 85% no trouble, £3,700; 15% it needs £800 of repairs, £4,500. Rolled back, repair is expected to cost £2,800 and replace £3,820, so the replace branch is struck through. Repair wins unless the gearbox is more than 65% likely to go. the car fails its test Repair · £1,200 Replace · £3,700 60% 40% £1,200 runs two more years £5,200 gearbox, then replace £2,800 85% 15% £3,700 no trouble £4,500 £800 of repairs £3,820 £2,800 where it flips Repair wins unless the gearbox is more than 65% likely to go.

£4,000 for a used car, less £300 for the old one, is the £3,700. The two short strokes on the replace line are the old notation for a branch you've rolled back and dropped.

Rolling back

Multiply, add, keep the best.

At each circle, multiply every payoff by its chance and add them up. That's what the branch is worth on average, its expected value. At the square, keep the best one.

OptionChance × cost, addedWorth
Repair 0.6 × 1,200 + 0.4 × 5,200 £2,800
Replace 0.85 × 3,700 + 0.15 × 4,500 £3,820

But look at the worst leaf. Repair is £1,020 cheaper on average, and it also holds the most expensive ending on the tree, £5,200. If you couldn't find that money in a bad year, the average isn't the whole answer.

On a choice that matters

Five moves, one sheet of paper.

Draw it left to right. The numbers will be guesses, and that's fine: a guess you've written down can be checked, argued with and improved.

  1. Square, then options

    Draw a square on the left for the choice. Draw a line out of it for each real option, labelled with what it costs or takes up front.

  2. Circles where luck decides

    Where something outside your control happens next, draw a circle and a line for each thing that could happen. Their chances must add up to 100%.

  3. A number on every branch

    Write a chance on each line out of a circle and a payoff at each end. Use money, hours, or a 0 to 10 score, but the same unit everywhere.

  4. Roll back from the right

    At each circle, multiply and add. At each square, keep the best branch and strike the rest. Then look at the worst ending on the branch you kept.

  5. Find where it flips

    Take the chance you're least sure of and move it until the answer changes. If the flip is far from your guess, decide. If it's close, find out more first.

Try it on yours

Find your flip point.

Two options, each with a good ending and a bad one. It starts with the car; change any number, and watch the strip below show how sure you'd need to be before the answer changes.

The payoffs are
Option A
Option B

Why a number, not a word

“Likely” means different things to different people.

“a serious possibility”

The hatched span is how far apart the readers were. Kent's own reading is the mark.

In 1951 an American intelligence estimate said a Soviet attack on Yugoslavia was “a serious possibility”. When Sherman Kent, who helped write it, asked his colleagues on the board what odds they'd had in mind, the answers ran from about 20% to about 80%. He had meant something like 65%. He told the story in a 1964 essay, Words of Estimative Probability.

A tree with “likely” on its branches hides that disagreement. A tree with 60% on it invites someone to say “I'd have put that at 30”, and that's the conversation you want before you decide. Putting numbers on chances is also a skill that improves with practice: in the Good Judgment Project, a short training in probabilistic reasoning made forecasters more accurate (Mellers and colleagues, 2014).

The idea

Why it works.

In your head, a decision gets judged by its most vivid ending: the gearbox story you heard last week, the friend who loved their new car. On paper, every ending is weighed by how likely it is, so a vivid but rare outcome counts for what it's worth.

The flip point is the most useful number on the tree. Most of your guesses won't matter, because the answer stays the same however you move them. The one that does matter tells you exactly what to find out next.

Keep the numbers honest

Habits that help.

  • Start from how often it happens. How do cars like this usually do? Then adjust for yours.
  • Avoid 0% and 100%. If you're that sure, it isn't a circle. Draw it as a straight line.
  • Count what money can't. Score time, stress or a relationship 0 to 10 if that's what's really at stake.
  • Average, then worst case. Choose the better bet only if you could live with its worst leaf.

Go deeper

Keep going.

Practise this in HourLife.

In Decisions: Options with leanings. Write down a decision, weigh the options, mark the one you chose, and come back later to record how it turned out.

Download on the App Store Download on the Mac App Store How Decisions works in HourLife