Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic - Fischer, Martin H.; Shaki, Samuel (Frontiers in Psychology, 2018)
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 novel 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.