Black Swans Upend Logic - So We Rethought Decision Models

We developed a model of decision making that combines theory-based and case-based reasoning.

When evaluating the probability of an outcome, our decision maker looks at the probabilities of this outcome according to each theory she entertains, but also looks at similar past cases in which this outcome has occurred.

The relative weight placed on theory-based compared to case-based reasoning depends on several factors, including the past success of the theories the agent entertains and the similarity of past cases to the present case. Also, the balance between the two modes of reasoning may be a personal trait, depending on cognitive style and education.

In a hypothetical example, a team of entrepreneurs seeks funding from a venture capital firm for a new cancer treatment.

When considering the proposal, the potential investors do so from different perspectives. John examines the efficacy of the treatment, possible competitors, possible delays and costs of clinical trials, the amount insurers will pay for the treatment and expected profits. He finds the potential investment quite promising.

Sarah, who is more experienced, is skeptical. Though she admits that John’s analysis has merit, she has seen few projects that have been successful in the past. Rachel, who has little experience, is also skeptical of the project, noting that even the most careful calculations might not have captured all of the relevant possibilities and weighted them appropriately; she urges caution with “fantastic new technologies.”

In this case, Sarah has a larger database of past cases in her memory than John. They may agree on the probability of success of the enterprise and may have the same cognitive style, but Sarah’s experience has made her more skeptical. John and Rachel both have little information about past cases, yet have different cognitive styles, with Rachel being more cautious about trusting theories.

Different people may analyze the same situation by placing different emphases on case-based and theory-based reasoning and arrive at different conclusions.

In times of great uncertainty, case-based reasoning is particularly relevant.

Currently, for example, people are making analogies between the Russia-Ukraine war and other wars. The COVID-19 pandemic spurred an interest in the 1918 flu epidemic.

There is evidence that this approach is relevant and sometimes successful: during the financial crisis of 2007-2008, governments learned from the past and acted so that it did not become another Great Depression.

Similarly, in the aftermath of 9/11, financial experts learned from past crises to predict market behavior. “All eyes will be on the market Monday morning,” a Barron’s columnist wrote in the first issue of the publication after the 2001 terrorist attack.

In the same issue, another columnist was reassuring, noting that share prices were resilient following events such as the fall of France in 1940, Pearl Harbor, the Kennedy assassination and the Gulf War.

We argue that theory-based reasoning is an excellent way of making decisions when there is a bounty of data - when it’s business as usual.

Yet we find that this mode of reasoning is insufficient, even useless, in the face of a black swan - and the world is filled with black swans.

In times of surprise, decision makers may naturally put less weight on their probabilistic reasoning and rely more on past analogies.

Methodology

By employing the axiomatic approach, we translate the abstract mathematical model to observable behavior in concrete situations, in the hope of better understanding what the model implies.

Applications

We believe that scientists in economics, finance, political science and related fields can benefit from using such a model, and we hope that our axiomatic results would convince them that this is a reasonable model to use when trying to understand human behavior, as well as when making recommendations for individuals and organizations.