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Decision Making Using Rating Systems: When Scale Meets Binary

Bargagliotti, Anna E. and Li, Lingfang (Ivy) (2009): Decision Making Using Rating Systems: When Scale Meets Binary.

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Abstract

Rating systems measuring quality of products and services (i.e., the state of the world) are widely used to solve the asymmetric information problem in markets. Decision makers typically make binary decisions such as buy/hold/sell based on aggregated individuals' opinions presented in the form of ratings. Problems arise, however, when different rating metrics and aggregation procedures translate the same underlying popular opinion to different conclusions about the true state of the world. This paper investigates the inconsistency problem by examining the mathematical structure of the metrics and their relationship to the aggregation rules. It is shown that at the individual level, the only scale metric (1,. . . ,N) that reports people's opinion equivalently in the a binary metric (-1, 0, 1) is one where N is odd and N-1 is not divisible by 4. At aggregation level, however, the inconsistencies persist regardless of which scale metric is used. In addition, this paper provides simple tools to determine whether the binary and scale rating systems report the same information at individual level, as well as when the systems di®er at the aggregation level.

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