For a world to be consistent when the observed laws of physics can change basically on demand, there would still need to be a set of laws that define how this power can, and more importantly can't, act on the world. Were it that any one person can change the world for everybody, then reality would essentially just be a chaotic mess and life would likely die as it it would only take one person to end it all by stating that there is no atmosphere or something and killing everyone.
As such, what is needed is a set of rules that would keep the world in a somewhat consistent state even as several being are basically trying to twist reality with their words.
Warning: Twisting reality with your beliefs can be dangerous. Take care to avoid the strangely unaffected high school student and more importantly his right arm. And whatever you do, don't believe that the kid is a monster -- it will not end well for you.
The World "Computer"
Looking at the universe from a programming perspective, pretend that it stems from the base class of Plane. The Universe object has a set of parameters that defines its physical constants. Declare the Universe object with the proper parameters, and boom -- the universe was created.
This will make a lot of people very angry and will widely be regarded as a bad move. References aside, there's more to declare.
The celestial objects -- stars and planets may be their own objects derived from the Universe object. From there, a Planet may have Life, and Life can extend into say Human. Each Human is its own object with its own set of parameters and processes.
Basically, Object-Oriented Programming, but for the universe.
Your reality warping powers works by changing the various variables of the objects of the world. As those variables and/or flags are changes, the affects on the world change. Ideally, this can only work on individual objects but occasionally there's a person that has higher rights and might be able to affect a superclass or a group of objects.
Depending on the strength of the reality warper, they will have specific access to affect changes in the programming values of the various objects of the universe. Of course, like any good systems, there are forces that are there to prevent malicious or undesirable changes to the code.
The sysadmins of this reality program should be checking into malicious changes, but they are busy with their sister and her boyfriend.
The Laws of Reality
As stated, there needs to be some laws to keep reality working properly. To keep the programming metaphor going, you can't change reality in such a way to create a syntax error in reality and crash everything. As such, there are four rules that this reality changing power adheres to in order to not break anything with a description to follow.
- Law of Paradox Prevention -- No statement can change reality in such a way as to create a paradox
- Law of Awareness -- For a statement to change your reality, you both have to perceive the statement and have it make sense
- Law of Subjective Reality -- What you perceive is not what somebody else may perceive
- Law of Collective Reality -- The belief of the multitudes is stronger than the belief of one
Law of Paradox Prevention
This rule prevents things that would cause a paradox in reality trying to resolve it. As a rule, it's pretty straight forward -- you can't kill somebody yesterday by stating it today.
From a programming perspective, it's about using data validation to ensure that your programmed changes in reality don't cause an error in the system and crash it. Whether the validation is on the data of reality as a whole or on a person, the point is that what you say is vetted to not crash the system.
Error checking is very important when it runs reality.
Law of Awareness
If a tree falls in the forest and nobody hears it, does it make a sound? That, but applied to reality warping.
Basically for reality to change, somebody has to perceive it. In the context of the question: Joe can say that the sky is black, but if nobody hears it, then really only Joe is affected by the statement. Should other people hear him, they will believe the sky is black
Going back to the programming metaphor, you have to not only have access to a Person object to change their reality, you have to know about that Person object in order to affect it. After all, you can't change code that you don't know where it is. The same would be true no matter what entity you're referring to -- the floor, a rock, a tree, etc.
Law of Subjective Reality
As it says -- Reality is subjective. What I see may not be the same as what somebody else would see. For a more literal example, compare the vision of a colour blind person compared to an average person (trichromatic) or a tetrachromatic person.
Alternatively, using the 1 + 1 = 3 example, there are multiple ways to resolve this statement. One could always see an third item where there are supposed to be two as per the question. Alternatively, one could resolve that statement by the reversal of 2 and 3. There are absolutely a host of side effects with that interpretation, but there was nothing in the assertion that denies that perception of the new reality
Programming-wise using the sky is black statement, the Person object could have a colourIsSky variable. It could be black for Joe and those he has told, but for the rest of the world, it is blue. The variable values are different for different Person objects.
Law of Collective Reality
In short, many people believing something will make it harder to change by an individual. Consider the idea that Joe says that the sky is black. By telling me, one could argue that I will now perceive that the sky is black. But I believe that the sky is blue, as does common knowledge believe that the sky is blue.
Using the programming metaphor, there's two things in action here. The first is that multiple people are trying to change the same variable in the same object. One way around it is to consistently change the value, but it is taking the other way and locking the value in until the conflict in the changes is resolved.
For things believed by the masses, the variable that was once editable is not a constant value and unable to be changed by the average person -- one needs higher permissions to change a constant value.