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Black swans
The limits of probabilistic modelling


The term “black swan” was used in 16th century discussions of impossibility (all swans known to Europeans at the time were white). Explorers arriving in Australia discovered a species of swan that is black. The term is now used to refer to events that occur though they had been thought to be impossible. In risk analysis, these are also called “unexampled events” or “outliers”.

Black swan They are more likely when your risk models include “fat tailed” probability distributions, where extreme events (in the tails of the distribution) have higher probabilities than a normal probability distribution. Fat-tailed distributions are infrequent in most measures of physical populations, but can be caused by mechanisms such as preferential attachment in social networks and “winner takes all” mechanisms. They can also be caused by correlation between different risk categories, which lead to systemic risks.

Methods for coping with black swans include stress tests, horizon scanning exercises, improving your “safety imagination”, logics of precaution, and increasing system resilience.

This submodule is a part of the risk management module.

Course material

Black swans, or the limits of probabilistic modelling

Lecture slides (PDF)

Some characteristics of a black swan event:

  • it is an outlier (it lies outside the realm of regular expectations, and nothing in the past can convincingly point to its possibility)

  • it carries an extreme impact

Examples include the September 2001 terrorist attacks in New York, the 2009 avian flu pandemic, the Covid-19 pandemic in 2020, the “discovery” of America by Europeans for the native population (of whom 80 to 90% died following arriving of settlers), the outbreak of bovine spongiform encephalopathy or “mad cow disease” in the UK in the early 1990s and the 1992 collapse of the European Monetary System. Note that:

  • in spite of its outlier status, it is often easy to produce an explanation for the event after the fact;

  • a black swan event may be a surprise for some, but not for others; it’s a subjective, knowledge-dependent notion;

  • warnings about the event may have been ignored because of strong personal and organizational resistance to changing beliefs and procedures;

  • black swan events overturn some fundamental assumptions in classical risk management, such as the assumption that hazards can be identified exhaustively, the probability of future events and their consequences can be estimated, and that risk controls can be put in place to reduce unacceptable risks;

  • our ability to plan for predictable surprises and increase our disaster preparedness is affected by multiple cognitive biases, including normalcy bias (our tendency not to react in the face of danger), herd instinct or social conformity (we tend not to react if we see other people not reacting), and egotistical optimism bias (“it won’t happen to me”).

One coping technique that can help limit the impact of black swan events is to increase the resilience of the system, its ability to adjust its functioning prior to, during, or following events (changes, disturbances, and opportunities), and thereby sustain required operations under both expected and unexpected conditions. Characteristics of resilient organizations include the ability to:

  • respond to variability, disturbances and opportunities

  • monitor what is going on and identify threats and interpret them

  • anticipate possible future outcomes and their potential

  • learn from experience

Unfortunately, many of the organizational and structural features that provide resilience, such as organizational slack (spare capacity that enhances reflexive capability and learning) and discussion spaces that allow people to understand how other parts of the system work, can be seen as unproductive and destroyed in cost-cutting drives and interventions that aim to increase efficiency.

Other resources

We recommend the following sources of further information on this topic:

  • Book The Black Swan: The Impact of the Highly Improbable by N. Taleb (ISBN: 978-0812973815)

  • Book Managing the Unexpected: resilient performance in an age of uncertainty, Karl E. Weick & Kathleen M. Sutcliffe, 2007 (ISBN: 978-0787996499)

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