Inversion

What it is

Inversion turns a decision round and asks the opposite question. Rather than asking how to make the plan work, you ask what you would do to make it fail, then treat the answer as a list of conditions to remove, reverse or watch. It is a search technique, not a mood. It earns its place when the forward search has stopped producing anything new.

Where it comes from

The maxim behind the method is "man muss immer umkehren", one must always invert. It is attributed to the German mathematician Carl Gustav Jacob Jacobi (1804–1851), who is said to have offered it to students choosing a research problem. The attribution is second-hand. Its earliest known appearance in print is a 1916 address by Edward B. Van Vleck to the American Mathematical Society: "The great mathematician Jacobi is said to have inculcated upon his students the dictum: Man muss immer umkehren." Van Vleck names no source, and his own "is said to have" shows he was not quoting a text. Jacobi's practice is better recorded than his slogan. He turned the elliptic integral inside out and obtained the theory of elliptic functions, published in 1829.

The move from mathematics into business decisions belongs to Charlie Munger. At the Harvard School commencement on 13 June 1986 he told the class he could not say how to be happy, so he would follow a speech by Johnny Carson and prescribe guaranteed misery instead: mood-altering chemicals, envy, resentment, unreliability, learning only from your own experience, staying down after a setback. "The great algebraist, Jacobi, had exactly the same approach as Carson," he said. Most business writing on inversion descends from that talk.

What it corrects

A forward question is scored on plausibility. The team proposes moves that sound reasonable in the room, and what sounds reasonable is what the room has already accepted, so the search keeps returning the same short list. Failure conditions nobody has named stay unnamed, because nothing in the forward question asks for them. Ordinary care does not fix this. Care makes people check the plan they hold more carefully against the risks they have already written down, which is the wrong set. Inversion changes what the question rewards. When failure is the goal, an unmentioned dependency becomes a good answer rather than an embarrassment, and the people who know where the weak joints are have a reason to point at them.

How it works

1. Write the failure state as an event with a date: what has happened, to whom, by when.
2. Ask the inverted question out loud: what would we do to make that failure close to certain?
3. Record the answers as actions, dependencies and incentives, not adjectives. "Weak ownership" becomes "no named owner after launch".
4. Mark each condition as inside or outside your control.
5. Take the largest controllable one and remove it, reverse it, or attach a tripwire to it.
6. Say what the inverted list added that the forward plan had missed.

Worked example

Bank supervisors turned this into a rule. Ordinary stress testing runs forward: pick a scenario, apply it, check whether capital survives. The European Banking Authority's Guidelines on institutions' stress testing (EBA/GL/2018/04), issued on 19 July 2018 and applying from 1 January 2019, add the other direction. A reverse stress test, in their definition, "starts from the identification of the pre-defined outcome (e.g. points at which an institution business model becomes unviable ...) and then explores scenarios and circumstances that might cause this to occur." Paragraphs 84 to 91 make it a standing duty rather than an exercise. Paragraph 90 is the part with teeth: where the risk of business model failure proves unacceptably high, the bank should plan measures and consider whether the business model itself has to change. The diagnostic is the size of the shock required. As the guidelines put it, "the plausibility of the parameter shifts required to reach the pre-defined outcome gives a first idea about possible vulnerabilities". A bank that needs a once-in-a-century event to fail stands differently from one that needs a bad quarter, and only the inverted question separates them. The EBA's own review of supervisors found how new the habit was: "very few competent authorities required reverse stress testing."

In a Business Case Weekly case

In the SEGA case you sit on the board in late 1994, with three live platforms, a fourth about to launch, and two divisions pulling in opposite directions. Asked forward, the question invites an answer about better coordination. Inverted, it reads differently: what would you install to make the new console fail on schedule, which reporting line, which incentive, which shared budget, and which of those do you already have? The list that comes back is about structure, which is what the second half of the question asks you to change.

In your answer

• "This decision fails predictably if …, and the shortest route to that failure is …"
• "To guarantee failure I would …; our present plan already does that in one respect, namely …"
• "Of those failure conditions, the ones we control are …; the ones we can only watch are …"
• "I would remove … now, and treat … as the signal that the uncontrollable one has started."

Common misuse

The counterfeit is a risk list in a darker voice: everything that could go wrong, ranked by how bad it would feel, and not one line of the plan changed. The opposite excess is trying to eliminate every condition on the list, including those no company could control. Inversion is finished when a specific decision is different. The test is one question: point at the sentence in your plan that changed because of the inverted list. If no sentence changed, you wrote pessimism.

References

• Edward B. Van Vleck, "Current tendencies of mathematical research", Bulletin of the American Mathematical Society 23(1), 1916, pp. 1–13 — the earliest known record of Jacobi's maxim, on page 3, with the mathematics that produced it.
• Charlie Munger, Harvard School commencement address, 13 June 1986 — the method performed rather than described, and short enough to finish tonight.
• European Banking Authority, Guidelines on institutions' stress testing (EBA/GL/2018/04), 19 July 2018 — section 4.6.5 and paragraphs 84 to 91 are inversion written as an obligation.