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Open AccessArticle

Optimal Number of Choices in Rating Contexts

1
Ganzfried Research, Miami Beach, FL 33139, USA
2
School of Computing and Information Sciences, Florida International University, Miami, FL 33199, USA
*
Author to whom correspondence should be addressed.
Big Data Cogn. Comput. 2019, 3(3), 48; https://doi.org/10.3390/bdcc3030048
Received: 19 May 2019 / Revised: 6 August 2019 / Accepted: 22 August 2019 / Published: 27 August 2019
(This article belongs to the Special Issue Computational Models of Cognition and Learning)
In many settings, people must give numerical scores to entities from a small discrete set—for instance, rating physical attractiveness from 1–5 on dating sites, or papers from 1–10 for conference reviewing. We study the problem of understanding when using a different number of options is optimal. We consider the case when scores are uniform random and Gaussian. We study computationally when using 2, 3, 4, 5, and 10 options out of a total of 100 is optimal in these models (though our theoretical analysis is for a more general setting with k choices from n total options as well as a continuous underlying space). One may expect that using more options would always improve performance in this model, but we show that this is not necessarily the case, and that using fewer choices—even just two—can surprisingly be optimal in certain situations. While in theory for this setting it would be optimal to use all 100 options, in practice, this is prohibitive, and it is preferable to utilize a smaller number of options due to humans’ limited computational resources. Our results could have many potential applications, as settings requiring entities to be ranked by humans are ubiquitous. There could also be applications to other fields such as signal or image processing where input values from a large set must be mapped to output values in a smaller set.
Keywords: recommender system; ranking; survey design; decision analysis; applied probability; quantization recommender system; ranking; survey design; decision analysis; applied probability; quantization
MDPI and ACS Style

Ganzfried, S.; Yusuf, F.B. Optimal Number of Choices in Rating Contexts. Big Data Cogn. Comput. 2019, 3, 48.

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