No, I think concepts like "belief in belief" or "belief in self-deception" have more to do with people who are slightly on the autism spectrum having difficulty understanding neurotypical brains than anything else. Yes, I am specifically thinking EY here.
Basically neurotypical brains are way more social. A religion is professed and that means there are statements repeated aloud, in company, basically like a password for gaining social acceptance. When done early enough from childhood and often enough, you learn to repeat them also inward, inside your brain. It becomes part of your inner voice. It also has a certain emotional effect, maybe reassuring, or frightening.
But at no point in the process does truth play much of a role. You don't believe it in the sense you believe things that require immediate action. You just hear this inner voice saying it. And you repeat it aloud for other people.
The best parallel is probably music. Like song lyrics stuck in your ear. Do you really wonder what is the probability that Rick Astley is never gonna give her up? No, it is just a chain of words heard outside from the radio or inside your brain with a certain emotional effect.
People who are slightly autistic tend to think beliefs are private, you really, seriously decide if X is true or false. But for neurotypicals beliefs aren't private and thus they are not really beliefs in this sense, they do not carry a big stamp putting "this is true" on their beliefs, it is passwords, word-memes repeated aloud for a social function and also heard inward. Since they do not require immediate action, they also do not require actually deciding if they are true.
This is why "I believe people are nicer than they actually are" makes perfect sense. It means "I enjoy hearing an inner voice telling me people are nice. I know it is not really true. But I enjoy this tape so I keep playing it. I will also say it aloud so that others can also enjoy hearing it."
Human intelligence evolved as social intelligence. We are far better equipped to win political debates and get elected than to find truth. This is why Newton type truth-finders tend to be slightly autistic, having Asperger, you need to turn off the social in order to be really interested in truth.
Disagree -but up voted for the Rick Astley reference. And for a plausible and interesting hypothesis.
I am not sure that it is productive to tell certain people that they do not really believe what they claim to believe, and that they only believe they believe it. I have an alternative suggestion that could possibly be more useful.
Binary Beliefs
It seems that human beings have two kinds of beliefs: binary beliefs and quasi-Bayesian beliefs. The binary beliefs are what we usually think of as beliefs, simple statements which are true or false like "Two and two make four," "The sun will rise tomorrow," "The Messiah is coming," and so on.
Binary beliefs are basically voluntary. We can choose such beliefs much as we can choose to lift our arms and legs. If I say "the sun will rise tomorrow," I am choosing to say this, just as I can choose to lift my arm. I can even choose the internal factor. I can choose to say to myself, "the sun will rise tomorrow." And I can also choose to say that the sun will NOT rise. I can choose to say this to others, and I can even choose to say it to myself, within my own head.
Of course, it would be reasonable to respond to this by saying that this does not mean that someone can choose to believe that the sun will not rise. Even if he says this to himself, he still does not act as though the sun is not going to rise. He won't start making preparations for a freezing world, for example. The answer to this is that choosing to believe something is more than choosing to say it to oneself and to others. Rather, it is choosing to conform the whole of one's life to the idea that this is true. And someone could indeed choose to believe that the sun will not rise in this sense, if he thought he had a reason to do so. If he did so choose, he would indeed begin to make preparations for a dark world, because he would be choosing to conform his actions to that opinion. And he would do this voluntarily, just as someone can voluntarily lift his arm.
Quasi-Bayesian Beliefs
At the same time, human beings have quasi-Bayesian beliefs. These are true degrees of belief like probabilities, never really becoming absolutely certain of the truth or falsity of anything, but sometimes coming very close. These are internal estimates of the mind, and are basically non-voluntary. Instead of depending on choice, they actually depend on evidence, although they are influenced by other factors as well. A person cannot choose to increase or decrease this estimate, although he can go and look for evidence. On account of the flawed nature of the mind, if someone only looks for confirming evidence and ignores disconfirming evidence, this estimate in principle can go very high even when the objective state of the evidence does not justify this.
Belief in Belief
It seems to me that what we usually call belief in belief basically means that someone holds a binary belief together with a quasi-Bayesian belief which conflicts with it. So he says "The Messiah is coming," saying it to himself and others, and in every way acting as though this is true, even though his internal Bayesian estimate is that after all these thousands of years, the evidence is strongly against this. So he has a positive binary belief while having a very low estimate of the probability of this belief.
The reason why this often happens with religion in particular is that religious beliefs very often do not have huge negative consequences if they are mistaken. In principle, someone can choose to believe that if he jumps from the window of the tenth story of a building, he will be ok. In practice, no one will choose this on account of his non-voluntary Bayesian estimate that he is very likely to be hurt if does so. But a person does not notice much harm from believing the Messiah is coming, and so he can choose to believe it even if his internal estimate says that it is likely to be false.
A cautionary note: one might be tempted to think that religious people in general have belief in belief in this sense, that they all really know that their religions are unlikely to be true. This is not the case. There are plenty of ways to distort the internal estimate, even though one cannot directly choose this estimate. I know many very religious people who clearly have an extremely high internal estimate of the truth of their religion. They REALLY BELIEVE it is true, in the fullest possible sense. But on the other hand I also know others, also extremely devout, who clearly have an internal estimate which is extremely low: they are virtually certain that their religion is false, and yet in every way, externally and internally, they act and think as though it were true.