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Are random events expected to be small?

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People’s intuitions about mathematical and statistical concepts often include features that are not a part of the formal definitions. We argue that randomness and related concepts (events happening “accidentally”, “coincidentally” or “by chance”) are typically assumed to occur in a context of small rather than large events. Five experiments were designed to test the hypothesis of an association between perceived randomness and size. In Experiment 1 and 2, statements describing small outcomes as due to chance were judged to be more natural and to make better sense than corresponding statements about large outcomes (or about small outcomes not due to chance). Experiment 3 showed that people imagine that stories about randomness in daily life should preferably start with small events, even when they eventually turn out to be consequential (e.g., stories about an apparently random meeting ending with marriage). Experiment 4 demonstrated that small changes in a graph of a random walk were seen as random, whereas large changes were perceived as potentially nonrandom. Finally, Experiment 5 showed that small animals are believed to display more random behavior than larger ones. This applied also to fictional creatures with nonsense names, where size was implicitly suggested by the names’ phonetic qualities. Analogical instances can be found in the history of science, all the way back to Lucretius’ doctrine of the tiny “swerves” of atoms. The pervasive association between smallness and randomness might be partly due to real-world observations and partly to cognitive and motivational constraints.
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Psychological Research (2021) 85:133–150
https://doi.org/10.1007/s00426-019-01252-9
ORIGINAL ARTICLE
Are random events expected tobe small?
KarlHalvorTeigen1 · AlfBørreKanten2
Received: 21 May 2019 / Accepted: 24 September 2019 / Published online: 30 September 2019
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
People’s intuitions about mathematical and statistical concepts often include features that are not a part of the formal defini-
tions. We argue that randomness and related concepts (events happening “accidentally”, “coincidentally” or “by chance”)
are typically assumed to occur in a context of small rather than large events. Five experiments were designed to test the
hypothesis of an association between perceived randomness and size. In Experiment 1 and 2, statements describing small
outcomes as due to chance were judged to be more natural and to make better sense than corresponding statements about
large outcomes (or about small outcomes not due to chance). Experiment 3 showed that people imagine that stories about
randomness in daily life should preferably start with small events, even when they eventually turn out to be consequential
(e.g., stories about an apparently random meeting ending with marriage). Experiment 4 demonstrated that small changes in
a graph of a random walk were seen as random, whereas large changes were perceived as potentially nonrandom. Finally,
Experiment 5 showed that small animals are believed to display more random behavior than larger ones. This applied also
to fictional creatures with nonsense names, where size was implicitly suggested by the names’ phonetic qualities. Analogi-
cal instances can be found in the history of science, all the way back to Lucretius’ doctrine of the tiny “swerves” of atoms.
The pervasive association between smallness and randomness might be partly due to real-world observations and partly to
cognitive and motivational constraints.
Introduction
Most people want their world to be predictable and orderly,
especially when it comes to the major events in life. Scien-
tists are no exceptions. They hunt for regularities, and, like
Einstein, shudder at the thought of God playing dice with
the universe. Yet all of us encounter events that cannot be
controlled or predicted and seem to happen “for no obvious
reason”. We speak in such cases of outcomes that seem to
occur randomly, haphazardly, accidentally, or by chance.
Randomness can be formally defined in terms of process,
by which all outcome elements have the same probability
of occurring and are sequentially independent, leading to
irregular, uncontrollable, unpredictable and incompressible
(complex) patterns, as with lotteries or a string of tosses of a
coin (e.g., Nickerson, 2002, Falk & Konold, 1997). But not
all such patterns will be perceived from a subjective point
of view as equally random. People expect, for instance, that
a random binary sequence should contain an approximate
equal number of elements of each kind, and be character-
ized by frequent alternations (Scholl & Greifeneder, 2011;
Yu, Gunn, Osherson & Zhao, 2018). This would make each
part a “representative” sample of its parent population, as
well as reflecting salient features of the processes by which
it is generated (Kahneman & Tversky, 1972; Teigen, 2017).
Randomness is typically “negatively” defined to denote
events that are not intended and cannot be predicted or con-
trolled. Such events have alternatively been said to happen
fortuitously, accidentally, incidentally, by chance or “by
sheer luck”. Although these terms may apply to slightly dif-
ferent contexts and highlight different aspects of an irregu-
lar happening (for example, “incidental” suggests a non-
intended side-effect, and “luck” is mainly used about events
that have a valenced—positive or negative—outcome), they
are in many cases used interchangeably. In a discussion of
the distinction between “random” and “by chance”, Eagle
(2018) concludes that in ordinary language (and sometimes
in textbooks) people use these two terms as synonyms.
Intuitive notions of randomness can be expected to have
connotations that go beyond the formal definitions. The
* Karl Halvor Teigen
k.h.teigen@psykologi.uio.no
1 Department ofPsychology, University ofOslo, Oslo,
Norway
2 Bjørknes University College, Oslo, Norway
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... It also appears that people are more willing to accept small events as random, compared to large ones (Teigen & Kanten, 2021). For instance, winning with a small margin, or arriving for an interview five minutes late, were much more often described as random, or accidental, than corresponding large events (winning by a large margin, arriving 60 minutes late). ...
... Statement pair #9 suggests that people think that beginnings are more strongly associated with chance events than endings are, in line with Hypothesis 3. Chance is also more strongly related to counterfactual endings, what 'could' have happened, than what actually happened, as shown by answers to item #10, as suggested by conceptual and empirical analyses of what constitutes a 'lucky' event (Pritchard & Smith, 2004;Teigen, 2005). The two last pairs were based on Teigen and Kanten's (2021) finding of an association between smallness and chance, but yielded in the present study weaker and more inconsistent effects. ...
... Participants in the Chance condition (n ¼ 98) received eight pairs of statements, including careers ('My career as a tech consultant began [came to an end] purely by chance'), partnerships ('The two musicians started [ended] their collaboration by coincidence'), and external events ('The riots started [ended] by a coincidence'). For the full list of statements see Appendix C. Both positive, ambiguous, and negative events were included, and a varied set of terms (by chance, accidental, coincidental, and arbitrary) were used to describe chance events, as these have been shown to be interchangeable in lay descriptions of randomness (Eagle, 2018;Teigen & Kanten, 2021). ...
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