Are random events expected to be small?

Abstract

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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Fig. 1

Graphs adapted from Random walk hypothesis (n.d.)

Fig. 2
Fig. 3
Fig. 4

Notes

  1. 1.

    We included on purpose functions that did not consistently favor small or primitive animals. For instance behavioral flexibility (learning) and finding a mate “by chance” could be advantageous for species at all levels of the evolution.

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Appendix

Appendix

See Figs. 5 and 6.

Fig. 5
figure5

Mean ratings of amount and ability for randomness of insects and birds, ordered according to size

Fig. 6
figure6

Mean ratings of amount and ability of randomness for mammals, ordered according to size

Approximate weights based on various internet sources (e.g., Wikipedia)

Insects and birds  
Mosquito 2.5 mg
Bee 113.3 mg
Hummingbird 3.6 g
Sparrow 32.5 g
Parakeet 35 g
Magpie 177.5 g
Crow 450 g
Eagle 4.4 kg
Pelican 7 kg
Swan 10.3 kg
Mammals  
House mouse 42.5 g
Brown Rat 320 g
Guinea pig 950 g
Rabbit 1.2 kg
Domestic cat 4.5 kg
Siberian tiger 147.2 kg
Pony 192.8 kg
Arabian horse 405 kg
Hippo 1400 kg
Indian elephant 3500 kg

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Teigen, K.H., Kanten, A.B. Are random events expected to be small?. Psychological Research 85, 133–150 (2021). https://doi.org/10.1007/s00426-019-01252-9

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