Confidence judgments during ratio comparisons reveal a Bayesian bias.

Area of Science:

• Cognitive Psychology
• Decision Science
• Numerical Cognition

Background:

• Humans frequently err in comparing rational numbers, often using flawed whole number strategies.
• The underlying cause of this bias, particularly the reliance on numerator/denominator magnitude, remains unclear.

Purpose of the Study:

• To investigate the Bayesian hypothesis that a bias towards larger numbers in ratio estimation results from increased confidence in large samples.
• To understand the cognitive mechanisms behind human ratio comparison and the large number bias.

Main Methods:

• Two experiments were conducted using non-symbolic proportion comparisons (arrays of colored dots).
• Confidence measures were collected explicitly (Experiment 1) and implicitly (Experiment 2).
• Fraction discernibility, cardinality, and congruency were manipulated to control difficulty and test ratio perception.

Main Results:

• Subject confidence in ratio comparisons was significantly influenced by the numerical magnitude of fraction components.
• Results align with a Bayesian model of relative ratio perception.
• A strong correlation was observed between component magnitude and confidence.

Conclusions:

• The human bias towards large numbers in ratio estimation may originate from a Bayesian process involving greater confidence in larger samples.
• This finding sheds light on the cognitive underpinnings of numerical cognition and decision-making biases.