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This article investigates how different decisions can be reached when decision makers consult a binary rating system and a scale rating system. Since typically decision makers use rating information to make binary decisions, it is particularly important to compare the scale system to the binary system. We show that the only N-point scale system that reports a rater's opinion consistently with the binary system is one where N is odd and N-1 is not divisible by 4. At the aggregate level, however, we illustrate that inconsistencies persist regardless of the choice of N. In addition, we provide simple tools that can determine whether the systems lead decision makers to the same decision outcomes.
Bargagliotti, Anna E., and Lingfang (Ivy) Li. “Decision Making Using Rating Systems: When Scale Meets Binary.” Decision Sciences, vol. 44, no. 6, Dec. 2013, pp. 1121–1137. doi:10.1111/deci.12049.