It’s a Small World!
A cognitive bias where people underestimate the likelihood of random encounters or coincidences because they fail to account for the vast number of possible combinations of people, places, and times.
THE IDEA
It’s a Small World!
A similar misconception of probabilities arises from the random encounters one may have with relatives or friends in highly unexpected places. “It’s a small world!” is often uttered with surprise. But these are not improbable occurrences—the world is much larger than we think. It is just that we are not truly testing for the odds of having an encounter with one specific person, in a specific location at a specific time. Rather, we are simply testing for any encounter, with any person we have ever met in the past, and in any place we will visit during the period concerned. The probability of the latter is considerably higher, perhaps several thousand times the magnitude of the former.
When the statistician looks at the data to test a given relationship, say, to ferret out the correlation between the occurrence of a given event, like a political announcement, and stock market volatility, odds are that the results can be taken seriously. But when one throws the computer at data, looking for just about any relationship, it is certain that a spurious connection will emerge, such as the fate of the stock market being linked to the length of women’s skirts. And just like the birthday coincidences, it will amaze people.
When to use it
Interpreting everyday coincidences with a more realistic sense of probability.
Evaluating claims of extraordinary correlations in scientific or business data analysis.
When interpreting a coincidence, distinguish a particular event specified in advance from any event that would have felt remarkable.
Teaching statistical literacy to avoid overinterpreting chance occurrences.
FROM THEORY TO EVERYDAY LIFE
In practice
Unexpected Reunion in a Distant City
You meet a former colleague in a town abroad. The encounter feels surprising, but the relevant comparison is broader than meeting that particular person there: any encounter with anyone you know could have prompted the same reaction.
Data Mining Spurious Correlation
Imagine a researcher searching a large dataset for any striking relationship and finding an association between stock performance and skirt length. Searching many possibilities increases the chance of a spurious finding. The researcher would need further evidence, such as a test on new data.
A MOMENT TO REFLECT
Put it to work.
Recall a time you exclaimed 'It's a small world!' after an unexpected encounter. How many different people, locations, and times could have produced a similar feeling of surprise?
When you see a surprising correlation in a news article or dataset, what steps can you take to determine whether it is a genuine relationship or just a coincidence?
How does the 'small world' bias affect our perception of meaningful coincidences, such as those often cited in support of psychic phenomena?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Fooled by Randomness The Hidden Role of Chance in the Markets and in Life (Nassim Nicholas Taleb)