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.