Typical Ranges as Scale-Specific Benchmarks: When and Why Percentages Amplify Relative Magnitudes and Their Differences

Business managers and policymakers must often communicate magnitudes. Yet conveying large relative magnitudes without desensitizing people to further increases can be challenging because of diminishing sensitivity to large numbers. In this research, we propose that percentage expressions not only make large relative magnitudes (e.g., 500%) appear larger than equivalent non-percentage expressions but also make large increases in relative magnitudes (e.g., from 500% to 600%) appear larger. We posit an explanation: percentages typically have values between 0% and 100%, so when percentages and percentage-point differences reach 100% or more, they seem unusually large. This hypothesis is supported by data scraped from New York Times articles and a series of online experiments employing both management-relevant scenarios and incentive-compatible decisions. Existing theories of magnitude perception either cannot predict all the results of these studies (e.g., numerosity and unitosity) or need further specification to do so (e.g., decision-by-sampling and range-frequency theory). We discuss implications for the theory of magnitude and difference perception and the practice of communicating large magnitudes and changes. This paper was accepted by Yuval Rottenstreich, behavioral economics and decision analysis. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.02646 .