LogicalMANIPULATIVE

Ludic Fallacy

What it is

Treating real-world uncertainty as if it were the well-defined, known-odds uncertainty of a casino game — modeling risk with tidy probability distributions and then trusting the model where the world does not follow its rules.

How it works

Taleb (2007) coined the term (from ludus, game) for the error of basing the study of chance on the narrow world of games and dice: in a casino the rules are known, the odds are stated, and the distribution of outcomes is fixed; in markets, wars, and epidemics the rules are unknown and change, the distributions have fat tails, and the largest outcomes are the ones the model never contained. His illustration is Dr. John, who reasons that a fair coin has a fifty-percent chance of heads after ninety-nine heads in a row, and Fat Tony, who concludes the coin is loaded. Knight (1921) had already separated measurable risk from unmeasurable uncertainty, and Ellsberg (1961) showed that people treat the two differently. The ludic fallacy becomes a persuasion device when a model's precision is offered as evidence of its reliability — a value-at-risk figure to three decimals, a “one in ten thousand years” event, a confidence interval computed from data that exclude the event in question. The honest version is a modeler who forgets that the model's assumptions are part of the model. The knowing version uses the mathematics as a credential and sells the tail risk to someone else. The tell is a precise probability attached to an event whose generating process nobody can specify.

Real-world examples

  • •Long-Term Capital Management, staffed by Nobel laureates, lost most of its capital in 1998 when correlations its models treated as stable broke during the Russian default; Lowenstein (2000) describes events the models had priced as effectively impossible.
  • •In August 2007 Goldman Sachs's chief financial officer said the firm was seeing “25-standard-deviation moves, several days in a row”; under the assumed distribution such a move should not occur in the life of the universe, which shows that the distribution, not the world, was wrong.
  • •Taleb (2007) notes that a casino's largest losses in one period came not from the tables, whose odds are fully specified, but from a tiger mauling a performer in its show and from an employee's failure to file tax forms — risks outside the model entirely.
  • •Economic and epidemiological forecasts issued during 2020 carried confidence intervals computed from prior data that contained no comparable pandemic; the intervals were mathematically correct for the model and uninformative about the world, and were cited across the political spectrum as though they were the second.
  • •Retail structured products are sold with back-tested probabilities of loss derived from a decade of calm markets; the buyer receives the model's odds and the seller retains the world's.

Ethical guidelines

  • ●State the assumptions under which your probability holds, and say what happens to the estimate if they fail.
  • ●Do not present model precision as evidence of model reliability; a number to three decimals from a wrong model is wrong to three decimals.
  • ●Distinguish risk from uncertainty in your own communication; where the generating process is unknown, say so rather than manufacturing odds.
  • ●Do not sell tail risk to people who cannot see it; if your product's losses occur outside the back-test, the back-test is a misrepresentation.

How to defend against it

  • ►Ask what generated the probability: “Where does this number come from, and what would have to be true for it to hold?” A probability with no generating process is a decoration.
  • ►Ask about the tails: “What is the worst case the model contains, and what happens outside it?” Then ask who bears the loss outside it.
  • ►Apply Fat Tony's test: when a model says something you observe is nearly impossible, suspect the model before the observation.
  • ►Prefer robustness to precision for decisions that cannot be undone: ask what choice survives the model being wrong, not what choice is optimal if it is right.
  • ►Look for the missing data: a back-test or confidence interval built from a calm period says nothing about a period unlike it; ask what the sample excludes.

References

  1. Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House
    The coinage of the ludic fallacy, the Fat Tony and Dr. John illustration, and the casino example.
  2. Knight, F. H. (1921). Risk, Uncertainty and Profit. Houghton Mifflin
    The distinction between measurable risk and unmeasurable uncertainty on which the fallacy turns.
  3. Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75(4), 643-669
    Experimental evidence that people treat known-odds risk and ambiguous uncertainty differently.
  4. Lowenstein, R. (2000). When Genius Failed: The Rise and Fall of Long-Term Capital Management. Random House
    The LTCM example of model-priced impossibilities occurring.
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