Repeating numbers reduces results: Violations of the identity axiom in mental arithmetic

Martin H. Fischer, Samuel Shaki

Research output: Contribution to journalArticlepeer-review


Even simple mental arithmetic is fraught with cognitive biases. For example, adding repeated numbers (so-called tie problems, e.g., 2 + 2) not only has a speed and accuracy advantage over adding different numbers (e.g., 1 + 3) but may also lead to under-representation of the result relative to a standard value (Charras et al., 2012, 2014). Does the tie advantage merely reflect easier encoding or retrieval compared to non-ties, or also a distorted result representation? To answer this question, 47 healthy adults performed two tasks, both of which indicated under-representation of tie results: In a result-to-position pointing task (Experiment 1) we measured the spatial mapping of numbers and found a left-bias for tie compared to non-tie problems. In a result-to-line-length production task (Experiment 2) we measured the underlying magnitude representation directly and obtained shorter lines for tie- compared to non-tie problems. These observations suggest that the processing benefit of tie problems comes at the cost of representational reduction of result meaning. This conclusion is discussed in the context of a recent model of arithmetic heuristics and biases.

Original languageEnglish
Article number2453
JournalFrontiers in Psychology
Issue numberDEC
StatePublished - 5 Dec 2018


  • AHAB
  • Cognitive bias
  • Mental arithmetic
  • Numerical cognition
  • Operational momentum
  • Tie problems


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