What causes failure to apply the Pigeonhole Principle in simple reasoning problems?

ABSTRACT

The Pigeonhole Principle states that if n items are sorted into m categories and if n > m, then at least one category must contain more than one item. For instance, if 22 pigeons are put into 17 pigeonholes, at least one pigeonhole must contain more than one pigeon. This principle seems intuitive, yet when told about a city with 220,000 inhabitants none of whom has more than 170,000 hairs on their head, many people think that it is merely likely that two inhabitants have the exact same number of hair. This failure to apply the Pigeonhole Principle might be due to the large numbers used, or to the cardinal rather than nominal presentation of these numbers. We show that performance improved both when the numbers are presented nominally, and when they are small, albeit less so. We discuss potential interpretations of these results in terms of intuition and reasoning.

KEYWORDS:

• Pigeonhole Principle
• framing
• cardinality
• fallacious inference

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Dan Sperber's work was supported by a grant from the European Research Council [grant number ERC–2013- SyG], Constructing Social Minds: Communication, Coordination and Cultural Transmission, ERC [grant agreement number 609619].