Mayoclinic defines mental illness as such: "Mental illness refers to a wide range of mental health conditions — disorders that affect your mood, thinking and behavior. Examples of mental illness include depression, anxiety disorders, schizophrenia, eating disorders and addictive behaviors." This seems to be the standard definition.
The statistic of 1 in 5 that I used seems to pretty much only refer to diagnosed people with specific, named disorders. I don't think it was including "I feel sad sometimes" as a mental illness. And considering it was only used statistics based on diagnostics, it seems pretty clear to me that a LOT of people got left out. Many people can't get help. This also only covered the U.S.A., and statistics could vary widely in other areas of the world and based on methods.
If you like, we can taboo the "mental illness" phrase and instead use something like "badly defined and illogically based thinking patterns." That would cover the schizophrenic fantasy/reality disconnect, anxiety, depression, etc. Then it becomes pretty clear that "badly defined and illogically based thinking patterns" are really common and often not as specific as biases. I don't think anyone would claim mental illness is rare. According to the American Foundation for Suicide Prevention, 12.6 people out of 100,000 successfully committed suicide in 2013. That means over 41,000 people died, in one year, in the U.S. alone, not counting the suicides ruled as accidents or disappearances. The AFSP says it's not easy to get a good number for suicide attempts, but they believe based on self-harm caused hospitalizations that it easily exceeds 600,000 people a year. And that's just the people who want to die. Eating disorders are gaining attention as one of the more common kinds. Addictive disorders are so common almost everyone knows one or more people struggling. Depression, the same. There's a trend among students where anxiety and stress are causing serious issues.
Also, there's a difference between commonality and normality. Urine fetishes, for instance, are considered abnormal and uncommon. BDSM would be considered normal but uncommon (though 50 Shades of Grey seems to be making it a more common thing.) The urge to eat is normal and common. Mental illness, I would say, are considered common but abnormal.
Honestly, I can't think of a single definition of mental illness that would say it's uncommon. I may be misinterpreting your meaning, but it kind of seems like you're focusing on semantics when the problem here is that common diseased thinking patterns are killing, sickening, and limiting lives.
Mayoclinic defines mental illness as such: "Mental illness refers to a wide range of mental health conditions — disorders that affect your mood, thinking and behavior. Examples of mental illness include depression, anxiety disorders, schizophrenia, eating disorders and addictive behaviors." This seems to be the standard definition.
Actually, I think the "standard" definition is provided by the current DSM. The Mayo Clinic definition is way too vague and general to be of any use.
...If you like, we can taboo the "mental illness"
For a site extremely focused on fixing bad thinking patterns, I've noticed a bizarre lack of discussion here. Considering the high correlation between intelligence and mental illness, you'd think it would be a bigger topic.
I personally suffer from Generalized Anxiety Disorder and a very tame panic disorder. Most of this is focused on financial and academic things, but I will also get panicky about social interaction, responsibilities, and things that happened in the past that seriously shouldn't bother me. I have an almost amusing response to anxiety that is basically my brain panicking and telling me to go hide under my desk.
I know lukeprog and Alicorn managed to fight off a good deal of their issues in this area and wrote up how, but I don't think enough has been done. They mostly dealt with depression. What about rational schizophrenics and phobics and bipolar people? It's difficult to find anxiety advice that goes beyond "do yoga while watching the sunrise!" Pop psych isn't very helpful. I think LessWrong could be. What's mental illness but a wrongness in the head?
Mental illness seems to be worse to intelligent people than your typical biases, honestly. Hiding under my desk is even less useful than, say, appealing to authority during an argument. At least the latter has the potential to be useful. I know it's limiting me, and starting cycles of avoidance, and so much more. And my mental illness isn't even that bad! Trying to be rational and successful when schizophrenic sounds like a Sisyphusian nightmare.
I'm not fighting my difficulties nearly well enough to feel qualified to author my own posts. Hearing from people who are managing is more likely to help. If nothing else, maybe a Rational Support Group would be a lot of fun.