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- Reviews or Ratings: Quantifying Information Loss from CoarseningMatthew J. H. Murphy2025
This paper quantifies the amount of information that is lost from coarsening signals, in a rate of learning sense. I show how a platform seeking to learn an unknown state should trade off between the informativeness and frequency of submission of reviews (signals). As is the case in many online platforms, I model signals as the realized utility of past consumers, where their average utility is dependent on the unknown quality of a product (state). I study how taste heterogeneity for the product impacts the performance of these systems, especially binary review systems. Information loss from coarsening is increasing in the homogeneity of the population (in terms of their idiosyncratic taste shocks). Moreover, optimal asymmetry of review systems follows the same pattern: as homogeneity increases the platform increasingly isolates extreme signals on one side of the distribution. Regardless of the degree of homogeneity, when the optimal threshold is used a binary review is preferred to a full signal if it is at least 3.25 times as frequent. Finally, I illustrate how information loss can be visualized in posterior space.