Inversion

What it is

Suppose you are planning a product launch. Instead of asking how to make it work, you ask what you would do to make it fail. Then you remove, reverse or watch each cause. That is inversion: turning the question upside down. It helps most when asking how to succeed brings no new ideas.

Where it comes from

The method rests on a saying, "man muss immer umkehren": one must always invert. It is credited to the German mathematician Carl Gustav Jacob Jacobi (1804–1851). He is said to have given this advice to students choosing a research problem. But the story is second-hand. The earliest known record is a 1916 speech by the mathematician Edward B. Van Vleck to the American Mathematical Society. He said: "The great mathematician Jacobi is said to have inculcated upon his students the dictum: Man muss immer umkehren." Van Vleck names no source. His "is said to have" means he was retelling a story, not quoting a text. How Jacobi worked is better recorded. He turned the elliptic integral inside out and got the theory of elliptic functions, published in 1829.

The investor Charlie Munger brought the idea into business. On 13 June 1986 he spoke at the graduation of the Harvard School, a school in Los Angeles. He told the class he could not say how to be happy. So, as the TV host Johnny Carson once did in a speech, he would describe how to be sure of misery. His recipe: mood-altering chemicals, envy, resentment, being unreliable, learning only from your own experience and staying down after a setback. "The great algebraist, Jacobi, had exactly the same approach as Carson," he said. Most business writing on inversion goes back to that talk.

What it corrects

Ask a team how to make a plan work, and people suggest moves that sound reasonable. Things sound reasonable when people in the room already agree with them, so the same short list keeps coming back. Nobody asks how the plan could fail, so nobody names the ways it could.

Working harder does not fix this. Careful people check the plan more closely against the risks already written down, but the dangerous ones were never written down. Turn the question round, and different answers count as good. When the goal is failure, pointing out something the plan quietly relies on is a good answer, not an embarrassment. And those who know the plan's weak spots get a reason to say so.

How it works

1. Write the failure as an event with a date: what happened, to whom, by when.
2. Ask the upside-down question out loud: what would we do to make that failure almost certain?
3. Write the answers as actions, dependencies and rewards, not adjectives. "Weak ownership" becomes "nobody named as owner after launch".
4. Mark each failure condition as inside or outside your control.
5. Take the biggest one you control. Remove it, reverse it or set a tripwire on it: a warning sign agreed in advance.
6. Say what you found this way that your first plan had missed.

Worked example

Bank supervisors made inversion a rule. A normal stress test runs forward: pick a bad scenario, run the bank through it, check whether its capital lasts. The European Banking Authority (EBA) added the reverse test in guidelines EBA/GL/2018/04, issued on 19 July 2018 and applying from 1 January 2019.

In these guidelines, a reverse stress test "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." Put simply: decide what failure looks like, then look for its causes. Under paragraphs 84 to 91, banks must do this regularly, not once. Paragraph 90 goes furthest. If the risk of the bank's business model failing is unacceptably high, it should plan its response and consider changing the model itself.

What matters is the size of the shock needed to break the bank. In the guidelines' words, "the plausibility of the parameter shifts required to reach the pre-defined outcome gives a first idea about possible vulnerabilities". One bank fails only in a once-in-a-century crisis, another after one bad quarter. You can tell them apart only by asking the upside-down question. In the 2018 guidelines the EBA recalls its 2013 review of national supervisors: "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. SEGA has three game platforms on sale and a fourth about to launch. SEGA's American and Japanese divisions pull in opposite directions. Ask how to make this work, and the obvious answer is better coordination. Then turn it upside down. What would you set up to make sure the new console fails? Who reports to whom, what are people rewarded for, which budget do they share? Which do you already have? The answers are about how SEGA is organised. The second half of the case's question asks you to change exactly that.

In your answer

• "This decision fails predictably if …, and the quickest way there is …"
• "To make it fail, I would …; our plan already does this in one way: …"
• "Of these failure conditions, we control …; we can only watch …"
• "I would remove … now, and treat … as the sign that the one we cannot control has started."

Common misuse

The usual mistake is an ordinary list of risks, written more gloomily. You rank everything that could go wrong by how bad it would feel, and change nothing in the plan. The opposite mistake is trying to remove every condition on the list, even ones no company could control. You are done when a specific decision has changed. To check, point to the sentence in your plan that changed because of the upside-down list. If none changed, you have written pessimism.

References

• Edward B. Van Vleck, "Current tendencies of mathematical research", Bulletin of the American Mathematical Society 23(1), 1916, pp. 1–13 — Jacobi's saying on page 3, with the mathematics behind it.
• Charlie Munger, Harvard School commencement address, 13 June 1986 — the method used, not described; short enough to read 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 make inversion a duty.