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<p>Many consequential decisions involve rare outcomes, yet most research focuses on probabilities above 1%. The present studies (total <i>N</i> = 4611) examined decision-making for <i>microscopic</i> probabilities (0 &lt; <i>p</i> ≤ .01) in the domain of losses. Participants made a single hypothetical investment decision involving a constant payoff structure, while we manipulated the probability of loss across different formats. In Study 1 (<i>n</i> = 1367), we replicated prior findings: expressing probabilities as fractions (e.g., “1-in-X”) produced higher rates of risk-avoidant choices than equivalent percentages. Study 2 (<i>n</i> = 3244) extended these findings by varying the digits used to express probabilities. Again, fractions produced higher perceived risk overall, but a distinct “digit effect” emerged, where larger digits within the probability phrase (e.g., “5” vs. “1”) led to more risk-avoidant decisions, even when the actual difference in probability was negligible. For example, 19.23% of participants chose the risk-avoidant option when the probability was “0.005%,” whereas only 10.94% did so for “0.01%,” despite the latter denoting a larger risk. These results show that superficial numeric features—such as digit magnitude and formatting—can systematically distort judgments of probability. The findings underscore the need for decision-making models to incorporate such biases and highlight the practical implications of numeric phrasing for risk communication.</p>

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“Less is… more?” The influence of digit magnitude and formatting on probability weighting

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Mark LaCour,
  • Zebulon Bell

摘要

Many consequential decisions involve rare outcomes, yet most research focuses on probabilities above 1%. The present studies (total N = 4611) examined decision-making for microscopic probabilities (0 < p ≤ .01) in the domain of losses. Participants made a single hypothetical investment decision involving a constant payoff structure, while we manipulated the probability of loss across different formats. In Study 1 (n = 1367), we replicated prior findings: expressing probabilities as fractions (e.g., “1-in-X”) produced higher rates of risk-avoidant choices than equivalent percentages. Study 2 (n = 3244) extended these findings by varying the digits used to express probabilities. Again, fractions produced higher perceived risk overall, but a distinct “digit effect” emerged, where larger digits within the probability phrase (e.g., “5” vs. “1”) led to more risk-avoidant decisions, even when the actual difference in probability was negligible. For example, 19.23% of participants chose the risk-avoidant option when the probability was “0.005%,” whereas only 10.94% did so for “0.01%,” despite the latter denoting a larger risk. These results show that superficial numeric features—such as digit magnitude and formatting—can systematically distort judgments of probability. The findings underscore the need for decision-making models to incorporate such biases and highlight the practical implications of numeric phrasing for risk communication.