While it is good to look at these sorts of mathematically rigorous algorithms, I think I would be frustrated if it was used everywhere. Or, well, maybe not me perhaps, but a non technical user.
The beauty of the second algorithm for rating products is that it is straightforward. Having never seen it before I can deduce that 5 stars come before 4 stars and more reviews come before fewer. If I want to skip ahead to the 4 stars I know what to do. I can internalize the sorting algorithm easily. And as a user, understanding the order items are presented to me is important.
If Amazon were to use the last algorithm and present items in that order (assuming we accounted for the 5 star vs positive/negative issue), it would like a random order to most users and would be frustrating.
So I guess what I am saying is that this algorithm is very clever, but in some cases, it may be too clever. Sometimes you just want to keep it Simple Stupid.
The beauty of the second algorithm for rating products is that it is straightforward. Having never seen it before I can deduce that 5 stars come before 4 stars and more reviews come before fewer. If I want to skip ahead to the 4 stars I know what to do. I can internalize the sorting algorithm easily. And as a user, understanding the order items are presented to me is important.
If Amazon were to use the last algorithm and present items in that order (assuming we accounted for the 5 star vs positive/negative issue), it would like a random order to most users and would be frustrating.
So I guess what I am saying is that this algorithm is very clever, but in some cases, it may be too clever. Sometimes you just want to keep it Simple Stupid.