Fake Reviews on Amazon, Baye’s Rule, and Sequential decision-making and cascades
Amazon, as one of the most popular and well-known retail companies in the US, is a very likely primary choice for the general public for shopping. Without previous purchases, many customers rely on the review section of a certain product as a reliable indicator of quality. However, not all the reviews are actually written by verified customers, which means that certain sellers may pay individuals to post five-star reviews to promote the rating of their product and therefore improve the sales volume. According to Taylor, “while 71% of the items on the first page of search results had five-star reviews, almost 90% of those reviews were unverified.” Although not all unverified reviews are fake, the large percentage could indicate the potential pervasiveness of the problem. To prove the unreliability of these reviews, Baye’s Rule needs to be applied.
As stated on page 431 in the Network, Crowds, and Markets: Reasoning About a Highly Connected World, Baye’s Rule is the equation. Pr[A] and Pr[B] respectively means the probability of the occurrence of event A and B. The probability of A given B is denoted as and vice versa. Supposed that there is an ordinary product on sale. With the assumption that only 10% of the 90% unverified five-star reviews are fraudulent, Pr[Fraudulent|Five-star review] = 0.09. Following the data given by Talyor, Pr[Five-star review] = 0.7, and Pr[Five-star review| Fraudulent] = 1 as everyone who is paid to write will write a five-star review. With this information, the probability of a review written by a “water army”, Pr[Fraudulent], can be calculated as follows:
Therefore, even if only 6.3% of the reviewers are water army, they could lead to a result of a five-star review rate of 70%, regardless of the value of Pr[Five-star Review|not Fraudulent], which reveals the actual quality of the product. Such a fact reflects the ease for sellers on Amazon to promote the rating of his/her products – the number of “water army” that they need to hire can be very small.
Of course, a high rating and a large number of positive comments would help sellers succeed in seizing potential buyers. Additionally, these reviews can also benefit the seller when the verified customers judge the product. This can be explained by the theory of sequential decision making and cascades. In the context of Amazon, when a verified customer of a certain product sees the reviews, he/she will:
Follow his/her own judgment of the product if the number of positive reviews is the same as that of negative reviews, or the difference between these two numbers is only one.
Follow the earlier majority and ignore his/her own judgment of the product or if the difference between these two numbers is more than one.
Thus, a dominant number of positive reviews will theoretically lead a customer to judge the product as of high quality, even if he/she is not satisfied with it. Following this theory, if the majority of existing comments are five-star, the next customer would also write a positive comment, and so do the future reviewers, which leads to a cascade and result in an even higher rating of the product. Eventually, more potential consumers will be attracted and the sales volume will be promoted. Of course, the actual condition is quite different from the theoretical prediction, as human beings would not necessarily give up their own judgments. Yet, the theory of sequential decision-making and cascades do explain the importance of the quality indicators. Given that positive reviews and high ratings can provide sellers with considerable profits and are not difficult to fake, the phenomenon of hiring a water army becomes a challenging problem faced by the Amazon platform, and must be tackled before the company loses the trust of customers.
Sources:
https://www.cnbc.com/2019/04/16/amazon-flooded-with-thousands-of-fake-reviews-report-claims.html
https://www.tandfonline.com/doi/full/10.1080/0960085X.2021.1886613
Easley, David, and Jon Kleinberg. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press, 2017.