How would you define "existential risk?"

I wrote a post last year basically trying to counter misconceptions about Ord's definition and also somewhat operationalise it. Here's the "Conclusion" section:

To summarise:

• Existential risks are distinct from existential catastrophes, extinction risks, and global catastrophic risks.
• [I'd say that] An existential catastrophe involves the destruction of the vast majority of humanity’s potential - not necessarily all of humanity’s potential, but more than just some of it.
• Existential catastrophes could be “slow-moving” or not apparently “catastrophic”; at least in theory, our potential could be destroyed slowly, or without this being noticed.

That leaves ambiguity as to precisely what fraction is sufficient to count as "the vast majority", but I don't think that's a very important ambiguity - e.g., I doubt people's estimates would change a lot if we set the bar at 75% of potential lost vs 99%.

I think the more important ambiguities are what our "potential" is and what it means to "lose" it. As Ord defines x-risk, that's partly a question of moral philosophy - i.e. it's as if his definition contains a "pointer" to whatever moral theories we have credence in, our credence in them, and our way of aggregating that, rather than baking a moral conclusion in. E.g., his definition deliberating avoids taking a stance on things like whether a future where we stay on Earth forever or a future with only strange but in some sense "happy" digital minds, or failing to reach such futures, would be an existential catastrophe. 

This footnote from my post is also relevant: 

I don’t believe Bostrom makes explicit what he means by “potential” in his definitions. Ord writes “I’m making a deliberate choice not to define the precise way in which the set of possible futures determines our potential”, and then discusses that point. I’ll discuss the matter of “potential” more in an upcoming post.

Another approach would be to define existential catastrophes in terms of expected value rather than “potential”. That approach is discussed by Cotton-Barratt and Ord (2015).

If we're being precise, I would just avoid thinking in terms of X-risk, since "X-risk" vs "not-an-X-risk" imposes a binary where really we should just care about losing expected value.

If we want a definition to help gesture at the kinds of things we mean when we talk about X-risk, several possibilities would be fine. I like something like destruction of lots of expected value.

If we wanted to make this precise, which I don't think we should, we would need to go beyond fraction of expected value or fraction of potential, since something could reduce our expectations to zero or negative without being an X-catastrophe (in particular, if our expectations had already been reduced to an insignificant positive value by a previous X-catastrophe; note that the definitions MichaelA and Mauricio suggest are undesirable for this reason), and some things that should definitely be called X-catastrophes can destroy expectation without decreasing potential. A precise definition would need to look more like expectations decreasing by at least a standard deviation. Again, I don't think this is useful, but any simpler alternative won't precisely describe what we mean.

We might also need to appeal to some idealization of our expectations, such as expectations from the point of view of an imaginary smart/knowledgable person observing human civilization, such that changes in our knowledge affecting our expectations don't constitute X-catastrophes, but not so idealized that our future is predictable and nothing affects our expectations...

Best to just speak in terms of what we actually care about, not X-risks but expected value.

(Borrowing some language from a comment I just wrote here.)

If an event occurs that permanently locks us in to an "astronomically good" future that is <X% as valuable as the optimal future, has an existential catastrophe occurred? I'd like to use the term "existential risk" such that the answer is "no" for any value of X that still allows for the future to intuitively seem "astronomically good." If a future intuitively seems just extremely, mind-bogglingly good, then saying that an existential catastrophe has occurred in that future before all the good stuff happened just feels wrong.

So in short, I think "existential catastrophe" should mean what we think of when we think of central examples of existential catastrophes. That includes extinction events and (at least some, but not all) events that lock us in to disappointing futures (futures in which, e.g. "we never leave the solar system" or "massive nonhuman animal suffering continues"). But it does not include things that only seem like catastrophes when a total utilitarian compares them to what's optimal.