We really have nothing to say about extreme solipsism other than it's unprovable and untestable. Fine, I accept that. However, doesn't the razor imply solipsism? If I can get away with one observer (me), what basis do I have for more than one? Or is there a mathematical argument for multiple observers? I'm looking for a formal, mathematical reason that implies multiple observers, not a colloquial one. Are multiple observers necessary for QM? Is there a reason, internal to QM, to think that there are multiple observers, or is that simply assumed by most thinkers because their senses tell them so? Look outside the window, the world is CLEARLY FLAT, not round. That sense deduction didn't hold up. Why are we assuming multiple observers other than because we don't want to insult each other? I accept I can not convince holo-deck characters they are on the holo-deck, but that doesn't mean they aren't.
No, there are no physical reasons, in QM or any other theory, to believe that there is more than one observer (nor that there are any observer actually) because this is not a physical question at all. However there are philosophical reasons to do so.
For example the way physical theories are tested presupposes that there are objective measurement outcomes, which in turn presupposes that there are more than one observer (measurement outcomes should not be conflated with mental phenomena)
Trying to answer this question in physics alone is not a good strategy. Physics cannot answer a question if the question cannot be formulated in the language of physics. The term "observer" in the sense I think you are using it (meaning "conscious observer") is not a term used by physicists. What physicists usually mean by "observer" is "reference frame", i.e. the choice of spatio-temporal coordinate, and sometimes "measurement apparatus". If you are clear about the differences in meaning, it will be obvious that physics has no answer for you.
Your question seems to imply that you take physics too seriously. Quantum Mechanics is not a theory of everything, but the best way we, human beings, represent what happens at very small scales. There is still lots of room for interpretation.
I have a similar, but somewhat different, answer to quen_tin —
To the best of our knowledge, no piece of mathematics, nor theory of phenomena, can ever prove to you that you are not the only sapient being. Mathematics are just symbols, and if you're inclined to doubt the existence of other intelligent beings, then you should be doubtful of any interpretation you have been taught to impose on those symbols — though no interpretation of those symbols that I know of have anything to say on the subject.
Quantum mechanics is no more special than Newtonian mechanics in this respect. A lot of emphasis is put on "observers" in popular and elementary presentations of quantum mechanics, but there is no reason to believe that a tape recorder is any different from a human as regards "observation".
What is it that is important about a so-called 'observer', to you? Reacting to physical occurances? But that is something that all matter does; only the reaction of some matter is more predictable than others. Is it that they have some inherent special property, such as a soul? But quantum mechanics — being a theory of physics — has no room nor patience for distinctions such as essences and accidents: properties of all things — yourself included — are emergent from dynamics, and beneath this is nothing more than motion and the void. Of course, the dynamics are so absurdly complex that to consider calculating what those reactions might be is a ridiculous conceit, but the point remains — if you take QM seriously, you should accept that you are a mode of a standing wave, as is everything else that you perceive. Nor should this seem to you to be more nihilistic than if you were an animated piece of clay, as the old tales have it, albeit subject to the laws of physics: either way, you are a piece of matter which is acting as matter will act, however elaborate the action.
No matter what laws of physics you acknowledge, you are drawn to Descartes' question: is everything you see really just a cleverly constructed illusion, designed to fool you into assuming things which are false?
What is important to you about the notion of 'observer' in this case? Discarding the conceit of extracting metaphysics from quantum mechanics, perhaps you are really asking whether you have peers. Are you in some fundamental sense alone?
Yes, of course you are. You have a singular viewpoint, don't you? Of course, that singular viewpoint is the result of an aggregate of activity in millions of neurons, so perhaps any cohesive perceptive system (hypothetical or otherwise) is bound to notice a separation between itself and the parts of its environment with which it lacks cohesion. So is it really any deep insight that you might feel a sort of solitude?
No, of course you aren't. What sort of arrogance do you have to discount the reality of the rocks and grass and chairs that you encounter in your life? Well, okay, maybe there are important qualitative differences between you and a chair. But chairs (and rocks, and grass, and animals, and people) form an important part of your sensory experience, don't they? Do they not form a useful, narrative, and often predictive role in your perceptions? Maybe you can never have absolute certainty about the finest, or even the coarsest, elements of the world that you experience; but that does not mean that you know nothing, unless you adopt a trivializing notion of knowledge which in itself denies the very nature of your experience. And if your experience includes experience of objects which you are inclined to treat as peers, does this not suggest that, singular as you are, you are truly not alone?
Occam's Razor is much abused for intellectual self-mutilation. What is important is to remove the parts of a theory which serve no purpose. Do you find it extravagant to suppose that you are not alone? Do you find it an unnecessary complication to acknowledge the complexity of behaviour of the people around you? — Either way, you have your answer: and Occam's razor either does, or does not, recommend solopsism.
Occam's razor is not much use as a principle. Good science and philosophy involves searching for explanations. One way to improve an explanation is to eliminate parts of the theory that do no explanatory work. But the existence of other people does explanatory work. For example, you can't understand or predict the content of my answer before I give it because I am a person independent of you with my own ideas. You could try to label me as part of your imagination but that label plays no role in any explanation, and so should be eliminated.
Also, quantum mechanics is a physical theory that explains a lot about how the world works. It is not a decoration for mystical woo woo. For explanations of quantum mechanics see "The Fabric of Reality" by David Deutsch, Chapters 2,9,11. You should also read Chapter 4 of that book since it argues against some of your misconceptions about solipsism.