When you shop on Amazon, what impacts your decision of what to buy? You might have a favourite brand, or a specific style that you prefer, but what might have a dominating influence of all is how Amazon ranks the products are displayed to you. The rankings usually play a good role as it puts the product with the highest review and the most purchase on the top to benefit more people. However, if the perfect product for you ends up in a low rank, you might not even get the chance to see it. Therefore, it will be nice if ranking can always do a good job and ranks the product as how they suit your interest. So… can we ever get this ideal ranking? Or even better, can the rankings on Amazon eventually stop changing and stabilise to your ideal ranking? The latter question is what I wish to answer through my project.

The way to answer this question is in two steps. We should explore how to make sure the rankings will stabilise in the end and observe the possible rankings that we can settle on to see if any of those is our ideal rank.

Let’s first think about, what kind of rankings are the ones we can possibly stabilise to? A bad scenario would be a ranking that has the lowest quality product ranked top. We will for sure leave this ranking since that product will get bad reviews and less purchases and eventually become lower ranked. Hence, a good ranking that we can settle on should be one where the higher ranked product gets more good reviews and purchases on average, and the lower ranked products gets fewer good reviews and purchases on average. Therefore, to guarantee stability, we need to first ensure we have this kind of good ranking that we can settle on!

The next question to worry about is, is there a case where we don’t eventually transition to one of the good rankings? It turns out that the only possible case is when the Amazon system gets stuck in cycles, transitioning from one bad ranking to another bad one and never stops. Hence, we see that to guarantee stability, we also need to set an extra restriction that this kind of behaviour cannot happen.

Now that’s it! We can conclude that if Amazon can avoid itself from getting stuck in the cycles of bad rankings, and have some ordering of the products that can be considered good rankings, then the ranking will stabilise for sure! To answer the question if Amazon will stabilise to your ideal rank, we observe that the criterion of a good ranking is simply one where the higher ranked product gets more purchases and good reviews on average. And the reason why a product gets more purchases and good reviews can be attribute to two reasons:

  • The product itself is good. For example, the product has high quality and appeals to most people
  • Other factors. For example, the product went viral on the internet, or because the product was in a high rank before, it keeps staying in the high rank because of the boost from being ranked high.

Therefore, if a product that is ranked high is getting lots of purchases and good reviews on average mainly because of “other factors”, then it is possible for it to stay in the high rank forever, which is not ideal! So, through the project we can discover that, although in some way doing rankings is a good mechanism to encourage higher quality product, it might also work in a way that we don’t want sometimes.

Kate Zhang
The University of Melbourne

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