Given OR and assuming entities either exist or they don’t exist there is no circumstance where two theories are equally accurate and differ in terms of simplicity. In order to demonstrate this let us suppose that some theory, T1 is more complicated than another theory, T2. The only way for T1 to be more complicated than T2 (given OR) is for T1 to postulate more entities than T2. This means that T1 says that the entities not mentioned within T2 are present within the world. The number of entities that they postulate has to be different in order for one theory to be more or less complicated than another.

Let us consider the most basic case possible where one theory is more complicated than another, T1 postulates only 1 entity and T2 postulates 0 entities. This means T1 is more complicated than T2. How could T1 and T2 be equally accurate? T1 postulates only 1 entity and in order for T1 to be accurate that entity has to exist. T2 postulates no entities and so if T1 is accurate then there is no way that T2 can also be accurate (since the world would contain only 1 entity and no entities). If T2 is accurate then there is no way for T1 to be accurate.

Considering the next possible case, T1 postulates only 2 entities and T2 postulates only 1 entity. The same situation is present, T1 postulates only 2 entities and either those entities exist or they don’t. T2 postulates only 1 entity and so if T1 is accurate then there is no way that T2 can also be accurate. If T2 is accurate then there is no way for T1 to also be accurate. This can be shown no matter how many entities are postulated in T1 or T2. It is not possible for two theories to differ in terms of simplicity and be equal in terms of accuracy.