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The
'Law of Small Number' is the fact that investors have a tendency
to infer probabilities from a small series of recent historical
data |
Belief
in the Law of Small Numbers, Tversky and Kahneman, 1971
"People have erroneous intuitions about the laws of chance.
In particular, they regard a sample randomly drawn from a population
as highly representative". |
Inference
by Believers in the Law of Small Numbers, Rabin, 2000
"A person exaggerates the likelihood that a short sequence
of i.i.d. signals resembles the long-run rate at which those signals
are generated. The model predicts that people may pay for financial
advice from 'experts' whose expertise is entirely illusory. Other
economic applications are discussed". |
[RYAN]
D-Day invasion at Normandy, 1944. "All along the chain of German
command the continuing bad weather acted like a tranquilizer. The
various headquarters were quite confident that there would be no
attack in the immediate future. Their reasoning was based on carefully
assessed weather evaluations that had been made of the Allied landings
in North Africa, Italy and Sicily. In each case conditions had varied,
but (German) meteorologists had noted that the Allies had never
attempted a landing unless the prospects of favorable weather were
almost certain. To the methodical German mind there was no deviation
from this rule; the weather had to be just right or the Allies wouldn't
attack. And the weather wasn't just right". |
[BEN-ZVI]
Operation Barbarossa, the German Invasion of Russia, 1941. "One
example of an assumption of strategic possibility is reflected in
Stalin's brief that Hitler must issue an ultimatum before was would
break out. The fact that prior to April 8, 1941, Germany had made
ultimate demands before undertaking military action convinced Stalin
that this pattern would continue in the future". The sample
size on which this was based was less than five. |
[Wohlstetter]
The Cuban Missile Crisis, 1962. "...(a failure of intelligence
evaluation) was the predisposition of the intelligence community
to the philosophical conviction that it would be incompatible with
Soviet policy. Khrushchev had never put medium or long-range missiles
in any satellite country and, therefore, it was reasoned, he certainly
would not put them on an island 8,000 miles away from the Soviet
Union, and only 90 miles away from the United States, when this
was bound to provoke a sharp American reaction". The sample
size on which this was based was less then five. |
The
`Conjunction Fallacy' Revisited: How Intelligent Inferences Look
Like Reasoning Errors, HERTWIG and GIGERENZER, 1999
People's apparent failures to reason probabilistically in experimental
contexts have raised serious concerns about our ability to reason
rationally in real-world environments. One of the most celebrated
of these failures is the conjunction fallacy, in which people violate
what is widely considered the 'simplest and most fundamental qualitative
law of probability' (Tversky and Kahneman), the conjunction rule.
Stich, for instance, saw major implications of the conjunction fallacy
for people's assessment of technological risks: 'It is disquieting
to speculate on how large an impact this inferential failing may
have on people's assessments of the chance of such catastrophes
as nuclear reactor failures'. Kanwisher argued that the conjunction
fallacy might underlie 'flawed arguments' that 'often recur in debates
on U.S. security policy... Strategic priorities have in the past
become distorted by overemphasizing the most extreme scenarios at
the expense of less flashy but more likely ones'. Finally, based
on the conjunction fallacy, Gould concluded more generally that
'our minds are not built (for whatever reason) to work by the rules
of probability'. |
The
"Hot Hand" syndrome
"It is no great wonder if in the long process of time, while
fortune takes her course, hither and thither... numerous coincidences
should spontaneously occur"
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