“Numerical Category Bias in Legal Decision-Making”
Julian Marchionda, University of Michigan
Abstract
It’s both reasonable and common to make decisions based on numerical thresholds. For example, using a thermometer before deciding whether to call in sick to work, evaluating student performance with letter grades, and driving based on the speed limit all involve comparing a number to a given numerical boundary. While such boundaries can provide clear decision rules, placing an undue emphasis on arbitrary numerical boundaries can also lead to erroneous reasoning and decision-making. Here, we explore how numerical boundaries shape judgment and decision-making in the context of law. This context is particularly important given that legal decisions have high stakes and frequently reference numerical cutoffs (e.g., blood alcohol content and speed limits). Across seven experiments (N = 1476), participants evaluated pairs of numbers with equal differences that either straddled or did not straddle a legal cutoff. Our analyses provide evidence that participants perceive differences in intoxication, risk of recidivism, culpability, and intellectual disability as greater when presented with values that crossed a given numerical cutoff than when values did not, though this effect was not consistent across all experiments. This study provides insight into ways in which heuristic thinking can influence numerical reasoning and subsequent judgments.
Keywords: numerical cognition, decision-making, numerical reasoning, law
Project Summary
Introduction
Numerical boundaries are used in many facets of life: to identify a fever, to determine letter grades in school, and others. However, legal boundaries play a particularly important role, as they’re used to make decisions that can affect individuals’ liberties, finances, and careers. Although legal statutes such as speed and BAC limits are informed partly by scientific evidence, the exact boundaries for many of these are ultimately arbitrary. The present study investigates the influence of legal cutoffs such as .08% BAC (i.e., the cutoff for driving purposes in the U.S.), cutoffs used in risk assessment tools, and IQ score cutoffs on relevant judgments such as levels of impairment, responsibility, and intellectual disability across three experiments and two follow-ups.
Methods
A total of N = 1476 participants across all experiments were recruited online from Prolific, and paid for completing a survey. Each survey included a vignette describing a legal scenario in which participants compared two fictional characters, given some relevant measure (e.g., BAC) and a legal cutoff (e.g., .08%). Additionally, participants were assigned to one of three conditions (between-subjects): an above-cutoff group compared two numbers above the presented cutoff, a below-cutoff group compared two numbers below the cutoff, and a crossing-cutoff group compared numbers that straddled the cutoff. In all three groups, the difference between the two numbers presented were identical. Group responses were compared using one-way ANOVAs for each dependent measure and Tukey’s HSD post-hoc tests when appropriate.
Results
For three experiments, we evaluated responses in reference to DUI-related BAC limits, risk assessment classifications, and IQ thresholds. Across these legal domains, we found that participants perceived numerically equivalent differences as more significant when those differences straddled a legal cutoff. While some of these effects were not demonstrated in initial experiments where participants made comparative judgments, we found that follow-up experiments using absolute judgments on slider scales revealed that crossing-cutoff groups perceived equal differences as more significant than those in below and above-cutoff groups for multiple dependent measures.
Discussion
While not observed in every condition, the results of these experiments provide some evidence that legal boundaries can significantly shape how people perceive numbers, making equivalent differences appear larger when they cross a cutoff. For example, even small differences in BAC, such as .002%, were perceived as more significant when differences straddled a legal cutoff (i.e., .08%), suggesting that people may treat numerical boundaries as meaningful rather than arbitrary when forming judgments and making decisions about numbers. These findings support our hypothesis that people use arbitrary boundaries to categorize continuous data, perceiving information differently across them.
Impact Statement
People may treat numerical boundaries as psychologically meaningful, influencing how they perceive and evaluate quantitative information on continuous scales. In legal contexts, this suggests that judges, juries, and others interpreting scores, thresholds, or risk assessments may place undue weight on cutoffs when forming judgments. Recognizing this effect may inform how numerical information can be better presented to reduce misinterpretation and improve legal decisions.
