Definition: A delusion is an incorrect belief.
A “belief” is an assessment of a statement with a truth value based on anecdotal evidence. For example, I believe that gravity will cause a thrown rock to return to the ground. This is an example of a correct belief. A delusion is a belief which is incorrect (although the colloquial usage tends only to describe delusions which are egregious or silly or both). For example, a man may believe he is actually a woman according to evidence and some definition of “woman”. If he were actually a woman, this would not be a delusion, it would be a correct belief.
(NB: A “conviction” is a belief which inspires action.)
Because delusion is a belief about a symbolic expression, it requires awareness. It would be a category error to suppose that a computer can express belief- rather, a computer is purely ding an sich.
Here is the tricky part that I will assume but I can’t prove: it is possible for two aware minds to communicate symbolically. This means that I can think up a novel idea and transmit it to your mind by using a mutual symbolic language. It requires some shared noumena (we must inhabit the same universe), and my mind must be able to manipulate some noumena in order to form the symbolic language you’re reading. In reality, it is pretty obvious that this more likely than the alternatives.
Given the definition, the first title statement is obviously true. It is common for lots of people to hold the same incorrect belief. It is unusual (but possible) for them to come to the same incorrect belief separately, so the more people believe something incorrect the more likely it is that this was accomplished by communication.
Definition: A hallucination is an incorrect perception.
This is philosophically tricky in two places. First, I am uncertain about the nature of perceptual processing- the way noumena become phenomena. However, even if perception is a black box, we can still make sense of “incorrect” perceptions as correct noumena which are processed incorrectly into incorrect phenomena.
An example would be a man who looks at a cat and sees a raccoon instead. This is a visual hallucination. If studies can be believed, auditory hallucinations are far more common. For instance, a man can listen to the wind and hear voices instead.
Alternatively it is possible that he may look at a cat, see a cat, and yet believe it is a raccoon. This would be a delusion again, and not a hallucination.
The second tricky part is another obvious thing that I can reasonably assume but I can’t prove: it is impossible to transmit noumena between minds. That is, it is possible to describe a sensation to someone using words or ESP, and they can emulate the sensation according to the quality of the description and their imaginative abilities, but this would not be the sensation itself. It is only a facsimile or at best a perfect copy. I believe it is possible to prove that a perfect copy cannot be communicated, but I haven’t done so yet.
Because noumena can’t be transmitted except as phenomena, it is impossible to share perceptions. A hallucination is a type of perception, and therefore cannot be shared. Further, it is impossible for two people to feel the exact same sensations. They would have to be in identical bodies in the same location at the same time- i.e. they would have to be the same person. So it is strictly impossible for two people to experience the same noumena as the same incorrect phenomena even if phenomena are shared, because it is strictly impossible to share noumena.
In practical terms, it is very unlikely for two people to perceive similar sensations incorrectly in the same way. This is because there are infinitely many more ways to be incorrect than there are to be correct. Similarly, it is very, very unlikely for many people to perceive similar sensations incorrectly in the same way. So it is obviously true that mass hallucination is also practically impossible even by a loose definition. It is quite possible for many people to believe they have done so after the fact, but this is an example of a mass delusion rather than mass hallucination. If this seems to have occurred, we would suspect that they talked amongst themselves and came to a consensus opinion, as with any other mass delusion.
Contrapositively, if many people report the same sensation and it can be demonstrated that they have not communicated, then it follows that they have perceived correctly.