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Inherent in your question it seems to me is the thesis that all Empires fall for pretty much the same reasons. I don't think that's right at all. Empires by their very nature are exceptional things, and thus inherently unstable in the long run.
I think the Anna Karenina principle applies to societies as well as families: Successful societies are all alike; every failed society fails in its own way. In other words, a whole lot of things have to go right, and keep going right, for a very successful society to stay that way.
So you could maybe come up with a grand unified theory for how they come into existence, but not for how they fall.
As fate would have it, while I'm typing this answer, Jared Diamond is on NPR delivering his critique of a new book on exactly this topic. The book is Why Nations Fail, by Daron Acemoglu and James Robinson. Diamond was fairly critical, but still you might consider checking it out. Otherwise, you could consider reading his own book on the subject: Collapse: How Societies Choose to Fail or Succeed.
Upvote:2
My suggestion is to read what Nassim Nicholas Taleb has to say about Black Swan events and fragility. The idea expressed in the video you mentioned is an example of this. As empires get larger, they usually become more fragile and thus vulnerable to the "Black Swan" while smaller, simpler, units typically are less vulnerable to these unexpected events.
Taleb notes that there are ways to avoid fragility, in business and government. He also thinks that our system is on the edge of collapse. You can take his ideas and see how they apply when a complex society fails.
As T.E.D. noted, the reasons for a collapse and the results are usually quite different on the surface. However, when you start examining these events, you'll find some kind of fragility was at the core.
Upvote:3
One other book that offers a lot of insight is named 'Balance - from Ancient Rome to Modern America'.
When I see books that expound at length on the fate of the US, the first thing I use to figure out whether it's a hack job is to look at how quickly the content turns into invective. I've found books that start on page one by blaming some group of evil people in the midst of a conspiracy, and it doesn't stop - ever. This is not one of those books.
One point made in this book is that Rome never 'fell', it simply dissolved. It wasn't replaced by some other empire, as it fell apart it simply deteriorated into isolated chunks. However, there is a purported natural disaster that occurred around 535 AD, this is presumably a 'dark age' as the result of a volcanic eruption, probably in Sumatra. The few years after this event were known for starvation, cannibalism, mass migration, and other evidence of serious ecological disturbance.
One point the book makes is that governments tend to get in debt, which simply gets worse over time. True for Rome, France at the time of the Revolution, most 'Western' countries today, and others. Generally the trends (as the book points out) are that government benefits become more generous, groups split up into more and more assertive special interest groups intent on protecting their privileges, and the sovereign state turns 'inward' - building walls instead of roads, excluding foreigners and expelling 'undesirables' instead of absorbing fresh blood from afar.
As the US debt approaches the capacity of taxpayers to keep up, the credibility of the central government declines. In short, if you know someone that has cash, you believe them when they say they're going to do something. If you know someone is broke but can borrow money, you suspect they aren't going to attempt anything as ambitious as someone with money. If you know someone that is not only broke but in such hock that no one will loan them any more, you know they're basically trapped, and not going anywhere. This is the likely fate of most modern democracies. At some point people will simply quit believing government has the capacity to act. One would expect this to lead to moral decline, but other institutions tend to spring up to take it's place, and often these are religious.