Let's take a look at three examples that illustrate the key challenges in deciding when to trust ratings on Amazon. First, given that different products have a different number of reviews, as we've said, it's harder to determine which has the best quality. So, we can refer back to the original example between the two HD TVs, that we had looked at before. And as we saw there, one product has four stars and 95 reviews as opposed to 4.5 stars and eight reviews. So there's a trade-off between the average review and the total number of people who have reviewed it. Which it makes it not exactly clear which of the products is the better one to buy. And so that trade-off is something that is kind of subjective. There's no true objective answer to help you, to guide you in that decision. Second is review variation. So let's consider two flashlights on Amazon, a Maglite and a Fenix. So when we look at these they have roughly the same price. And additionally, so the price isn't shown here, but the prices are, roughly, the same. And additionally, we can't say as, last time, we can't say that there's any difference between the average customer review, or the number of reviews because they're, they're, roughly, on the same order. This is a about 4.5 stars. This is also about 4.5 stars and 183 reviews versus 260 reviews. It isn't that large, it not an order of, order of magnitude difference or anything. So roughly the same number of reviews, roughly the same average customer review. So, it's not clear which one is the product that you should buy, but, you know, if you look at, the ratings, what's interesting is that for the Maglite, you see, there's 169 of these reviews have five stars, and 20 of them have one star. So that, that corresponds to 65% being five stars and, 7.6% being one star reviews. For the Fenix, we have 62.3% giving five stars, and 2.2% give it one star. So on the one hand, the number of five star ratings, the fraction of five star ratings is higher for this flashlight than it is for this one. But, the fraction of one star ratings is also higher on this side than it is on this side. So, again, the question is, does a larger variation make the average more or less trustworthy? And so do you go by the fact that this has, higher fraction of five stars, or that is has a higher fraction of one stars, in deciding which, which of these two flashlights you should buy? Again, the answer to that question is pretty subjective. Third, we can look at possible recent changes that have occurred. So, here we're comparing the most recent, the 60 most recent ratings for an iPod Touch. And the 60 most helpful ratings over all time for this same iPod Touch. The most helpful ratings has an average of 4.4 right here. So if we, we take the average of the most, the 60 most helpful ratings over all time, that's going to have an average of 4.4. But if we look at the most recent ratings clearly the there's a lot of variation going on. And average is actually down at 3.6. So the question is just this trend, this, this recent increase in variation, this recent decrease in the average value indicate something that really happened with the product and something that we need to factor and take into account, displaying the average review? again, there's no subjective way of determining that. Whether the Ipod started to have some defect, or something else is going on, or if it was just some random fluctuation that is not necessarily indicative of anything having to do with the product. The question is, is the most recent, or the most helpful a better fit for the average? Again, this as well as the previous two questions don't really have any clear answers. Their answers are subjective, and that's what makes rating aggregation and choosing what to buy a product kind of difficult on Amazon in any of these three cases.