It's unfortunately varying from case to case. In most cases, the code for the old personalities will still be active doing the same things as it did, leading to potential contradictions with ruler personalities. In some other cases, new code depending on ruler personalities is supplanted by old personalities if DLC isn't present. Overall, I don't think it's more than a flavor issue though, with maybe some exception.
When it comes to numerical modifiers (particularly internal computations, rather) it can indeed be the case that additions or multiplications cancel out each other from contradictory personalities.
When it comes to numerical modifiers (particularly internal computations, rather) it can indeed be the case that additions or multiplications cancel out each other from contradictory personalities.
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