Hum, I'm skeptical about all that. It might be part of the evolutionary process behind humor, yes, but I don't think it really qualifies modern humor.
You can very well laugh when you actually expect something bad. Like, all the "hotline jokes" about people calling hotline because their computer doesn't work and after a while admitting that they didn't plug the cable, well, we (people working in IT) do expect that level of "lameness" from some users, and yet we still find them funny.
There are many cases where this formula is true, but where it doesn't generate humor. Like, if someone bakes a cake to me, and the cake isn't very good while I was expecting it to be, it would rarely lead to humor.
Something which doesn't have to do with failure or bad quality would also lead to humor. Like if during a causual conversion with a friend, he would suddenly start using a very elaborated language, it would likely make me smile, even if there is no failure or lower quality than expected, in fact, it's because of higher quality than expected that humor will raise.
Anxiety, like many other negative feelings (anger, tiredness, pain, ...) can make humor (and other positive feelings) harder, but it's not as clear cut as you display it. Many people (and myself too, sometimes) actually use humor as a shield against anxiety. Like a friend of mine recently had to undergo surgery, she was anxious, I did a few silly jokes and while it didn't lower much her anxiety, it did help a bit and make her smile.
I honestly don't think humor can be summarized with such a simple formula, humor is a very complicated cluster in thingspace, different people having different boundaries to it, and lots of different things can contribute positively or negatively to it. Trying to summarize all of humor by such a single formula seems like trying to summarize all of human values by a single explanation ("humans want wealth" or whatever) and then creating ad-hoc twisted justification for people sacrificing themselves for a loved one or altruism, instead of acknowledging that human values are complicated, because "we are godshatter".
Wrong spot.
Alrighty, with the mass downvoters gone, I can make the leap to posting some ideas. Here's the Humor Theory I've been developing over the last few months and have discussed at Meet-Ups, and have written two SSRN papers about, in one page. I've taken the document I posted on the Facebook group and retyped and formatted it here.
I strongly suspect that it's the correct solution to this unsolved problem. There was even a new neurology study released in the last few days that confirms one of the predictions I drew from this theory about the evolution of human intelligence.
Note that I tried to fit as much info as I could on the page, but obviously it's not enough space to cover everything, and the other papers are devoted to that. Any constructive questions, discussion etc are welcome.
A "Holy Grail" Humor Theory in One Page.
Plato, Aristotle, Kant, Freud, and hundreds of other philosophers have tried to understand humor. No one has ever found a single idea that explains it in all its forms, or shows what's sufficient to create it. Thus, it's been called a "Holy Grail" of social science. Consider this...
In small groups without language, where we evolved, social orders were needed for efficiency. But fighting for leadership would hurt them. So a peaceful, nonverbal method was extremely beneficial. Thus, the "gasp" we make when seeing someone fall evolved into a rapid-fire version at seeing certain failures, which allowed us to signal others to see what happened, and know who not to follow. The reaction, naturally, would feel good and make us smile, to lower our aggression and show no threat. This reaction is called laughter. The instinct that controls it is called humor. It's triggered by the brain weighing things it observes in the proportion:
Humor = ((Qualityexpected - Qualitydisplayed) * Noticeability * Validity) / Anxiety
Or H=((Qe-Qd)NV)/A. When the results of this ratio are greater than 0, we find the thing funny and will laugh, in the smallest amounts with slight smiles, small feelings of pleasure or small diaphragm spasms. The numerator terms simply state that something has to be significantly lower in quality than what we assumed, and we must notice it and feel it's real, and the denominator states that anxiety lowers the reaction. This is because laughter is a noisy reflex that threatens someone else's status, so if there is a chance of violence from the person, a danger to threatening a loved one's status, or a predator or other threat from making noise, the reflex will be mitigated. The common feeling amongst those situations, anxiety, has come to cause this.
This may appear to be an ad hoc hypothesis, but unlike those, this can clearly unite and explain everything we've observed about humor, including our cultural sayings and the scientific observations of the previous incomplete theories. Some noticed that it involves surprise, some noticed that it involves things being incorrect, all noticed the pleasure without seeing the reason. This covers all of it, naturally, and with a core concept simple enough to explain to a child. Our sayings, like "it's too soon" for a joke after a tragedy, can all be covered as well ("too soon" indicates that we still have anxiety associated with the event).
The previous confusion about humor came from a few things. For one, there are at least 4 types of laughter: At ourselves, at others we know, at others we don't know (who have an average expectation), and directly at the person with whom we're speaking. We often laugh for one reason instead of the other, like "bad jokes" making us laugh at the teller. In addition, besides physical failure, like slipping, we also have a basic laugh instinct for mental failure, through misplacement. We sense attempts to order things that have gone wrong. Puns and similar references trigger this. Furthermore, we laugh loudest when we notice multiple errors (quality-gaps) at once, like a person dressed foolishly (such as a court jester), exposing errors by others.
We call this the "Status Loss Theory," and we've written two papers on it. The first is 6 pages, offers a chart of old theories and explains this more, with 7 examples. The second is 27 pages and goes through 40 more examples, applying this concept to sayings, comedians, shows, memes, and other comedy types, and even drawing predictions from the theory that have been verified by very recent neurology studies, to hopefully exhaustively demonstrate the idea's explanatory power. If it's not complete, it should still make enough progress to greatly advance humor study. If it is, it should redefine the field. Thanks for your time.