Well if the OP’s question has “been answered to a reasonable degree” then I may add that the worst and to me most suspicious LWS (Low Stock Warning) is the one used by the airlines. I have been on flights with more free seats than were on sale on the website more often than not.
Look at where the airlines are today and enjoy with me the concept of schadenfreude. 
(Sorry for their employees though. And their investors.)
Pssst. . . . This is not 1995 anymore. You don’t have to warn people that they’re about to click on a PDF.
As an Amazon seller who fulfills our own orders, we only put a couple units in Amazon inventory at a time. Amazon has this stupid system where someone can have an item sitting in their shopping cart for hours or days before going through checkout and completing the purchase even after other people have depleted the available stock. This means we risk selling stock we don’t have on hand and canceling completed orders. Amazon then penalizes us for canceled orders and customers get pissed off. By just putting a few in Amazon inventory at a time, we will always have a reserve for when Amazon’s stupid system oversells what we have put in their inventory.
Now that’s a perverse situation I would not have expected. Thank you for sharing.
You essentially need to hold back stock equal to the unknowable number of units sitting in all the unbought shopping carts. A number that Amazon probably knows perfectly well, plus has a good idea of the statistical conversion rate that you also don’t have any way to compute.
What a sleazy racket!
Noted, but I’m happy to take two extra seconds to be polite. Manners aren’t about what you have to do; they’re about what you ought to do.
It has nothing to do with 1995. There are many platforms out there with varying capabilities. On my tablet, if I tap on a link that turns out to be a PDF, the browser can’t display it and it initiates a download. If I was only casually interested in it, I then have to navigate to a utility that deletes the unwanted PDF. If I know it’s a PDF, I usually won’t tap on it on the tablet at all. On a PC of course it just opens another browser tab so no issue. As @Johnny_Bravo said, the PDF notice is just simple courtesy.
Agreed.
The company I worked for was a large Amazon vendor (as opposed to Amazon Seller). Amazon placed orders with us for a couple dozen of their distribution centers every Tuesday, pretty much the same standing orders every week. So they could easily show a product with only 2 left in stock, even though more are expected within a day or so.
So take it with a grain of salt. Products sold by Amazon (versus “fulfilled” by Amazon) will likely be restocked within days, as that’s how their cycle works. Products “fulfilled” by Amazon could go either way, but likely are also going to be quickly available, as @Elmer_J.Fudd described.
Said another way, what Amazon actually truly has internally is something akin to this:
We have 12 in stock nearby you for delivery this afternoon, we have 120 in stock in your country that we can deliver tomorrow, and we have an arrangement with our supplier(s) to deliver 1200 within a week. But could ramp that by 4x on 2 weeks’ notice if demand warranted.
Right now of those 3 “buckets” of goods we know there are 5, 43, and 172 respectively sitting unbought in somebody’s shopping cart. Of which 40%, 30%, and 22% will probably convert to actual purchases in the relevant timeframes.
And knowing all that they show us buyers “6 in stock; better hurry!”
Thanks, everyone. I think I understand how it works. When it says “only 2 left in stock” that usually means for immediate shipment versus delayed shipment. The fact that they don’t spell that out tells me they hope you will think there are only 2 left on the planet, and that people will be motivated to buy now versus waiting. Whether doing that is cricket is up to interpretation.
A related question. If I put something in my cart and don’t purchase it immediately is it guaranteed to be there for some period of time, or can someone who wants to buy it right now take it from my cart. Don’t my cart items free up after some period of time not matter what?
We’ve been trying to get clarification on that from Amazon for years now, with no success. All I know is that we can put 5 units in inventory that will sell out in a couple of days and then a day later get an order for a 6th unit that we never added to inventory.
Is your answer here ?
All that does is confirm that an item isn’t deducted from inventory when it is added to a shopping cart. Which is the problem if that purchase is allowed to be completed after the inventory has been depleted.
Amazon must have some way to manage this or there would be a lot of pissed off customers.
When customers are pissed off, it’s the seller’s problem, not Amazon’s. They take responsibility for nothing in the three-way relationship between the seller, the buyer, and themselves. They just play referee - always in favor of the buyer.
Any idea how Amazon’s inventory management (IMS) handles multiple orders processed at the exact same time – meaning: if you have one item remaining in inventory at the time, can their IMS create a ‘remaining’ quantity of -1 (negative one) ?
Our IMS used to do that during seasonal peaks where hourly order volume was sky high.
Which sucked.
It was probably a business decision made somewhere along the line: better to take the order and substitute something on the back end than to interrupt the customer with an “out-of-stock” message when they had reason to believe there was sufficient inventory.
I’m wondering if Amazon’s IMS might allow a negative, but then treat it as a back order that gets passed along to you.
Do they, though? I’ve never interpreted it that way, and no one I’ve talked to about this outside this thread has either.
If you are in a store and there is just one of an item on the shelf, unless it is a seasonal item that is known to only be there for a limited time (say Halloween decorations in early November), do you assume that the store will never sell this item again? 
Yes. The shortfall is reflected in negative numbers - yet somehow, it’s still the sellers responsibility to cancel the order or pull stock out of their ass. High volume during the holidays exasperates the problem. We are lucky in that we are a manufacturer with a turnaround of less than 24 hours. It’s very disruptive to our production efficiency but we can fill those orders. Retailers with empty shelves, on the other hand, are screwed.
I think it’s a problem they could solve if they wanted to. I am a Prime customer and expect 2 day delivery, but a lot of the time I don’t care if it takes a week or two weeks since it’s something I don’t need urgently. If they said there are only 2 left that we can ship immediately, but we have 53 that we can ship in a week, and 263 that we can ship in 2 weeks, I think that’s a very different message than saying there’s only 2 left in stock, which tells me nothing about what I can get in greater than 2 days, assuming that’s what that means. It’s misleading at best.
But IME that’s exactly how it works - when an item is out of stock the system tells me “out of stock until DATE”.