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The Role of 'Prominent Numbers' in Open Numerical Judgment: Strained Decision Makers Choose from a Limited Set of Accessible Numbers

Numerate adults can represent an infinite array of integers. When a judgment requires them to "pick a number," how do they select one to represent the abstract signal in mind? Drawing from research on the cognitive psychology of number representation, we conjecture that judges who operate primarily in decimal systems simplify by initially selecting from a set of chronically accessible "Prominent Numbers" defined as the powers of ten, their doubles, and their halves [... 5, 10, 20, 50, 100, 200...]; then, when willing and able, refining from there. A sample of 3 billion stock trades reveals that traders' decisions reflect Prominent-Number clustering (Study 1) and a "natural experiment" reveals more clustering in rushed trading conditions (Study 2). Three sets of subsequent studies provide evidence consistent with an accessibility-based account of Prominent-Number usage: Experiments show that judges rely more on Prominent Numbers when they are induced to rush rather than take their time (Studies 3a and 3b), and when they are under high versus low cognitive load (Studies 4a, 4b, and 4c); and a final correlational study shows that Prominent-Number clustering is more apparent for judgments that require judges to scan a wider range of plausible values (Study 5). This work underscores the need to differentiate between Round Numbers and Prominent Numbers, and between representational properties of graininess and accessibility, in numerical judgment.