If we communicate to influence others, then we are probably aiming to change their perception. If this is the goal of the conversation then we too should be open to the possibility of being influenced since doing otherwise would negate our intend to influence others in the first place. If the goal is to argue effectively and with purpose, we need to be comfortable with changing our beliefs/values, and trust that the conversation is aimed at something that’s of mutual benefit. This is important because thinking that the conversation favours only the other side then their facts would not be influential because they don’t improve our position. The possibility for change is also as important because it is the cause for all evolution, the relevant evolution being improvement in the way of thinking. Now, if you don’t believe in evolution then the only way for mutual understanding is convincing you that evolution is real, or you convincing me that it is not. Still, changing one’s beliefs/values is considered evolution. However, the level of understanding in the conversation would depend on the communicators’ ability to process information and that depends on their intelligence and common sense. I view intelligence as the amount of information that you know, how well you validate this information (truth from falsehood), how well you can link this information together, and how well you can recall it. This definition of intelligence may explain how arguments/ideas are limited to the amount of information that one possesses, how capable we are of using information (e.g. 1+1 equals 2 and not solely 1+1), and how the true result of the conversation can be influenced by our ability to recall all the relevant information in order for it be used in our interpretations. If a person does not have well developed forms of intelligence, then his understanding would be limited to his level of development.
Assuming that perception is relative to the individual, to effectively engage in conversation we would need common sense. Common sense can be characterised as the ability to mentally unite the information conveyed by the five physical senses. Then, to be able to talk about the information gathered, we labelled and named the things (common language) that are associated with it. That is common sense. Now we can say that without common sense, conversation would be meaningless and incomprehensible. For example, a trans-man is not a man unless he presents the biology of a man. Suggesting the opposite would mean that I am not using the five physical senses or that I am refusing the international label/name, thus there is no common sense. Of course common sense can be associated with intelligence because again, "If a person does not have well developed forms of intelligence, then his understanding would be limited to his level of development" and his perception would vary. However, if we choose to neglect the roots of common sense (physical senses + common language) then we should provide improved mechanisms for making sense of the world or humanity will regress due to lesser cognition.
Often, an atheist cannot convince a theist that his definition of God does not exist like the theist cannot convince the atheist that his God exists. The reason is that both sides expect to receive information that is related to their level of intelligence. However, if your aim in the communication is to really influence, then you can’t say things like “lack of knowledge leads to faith” or “if you don’t believe you will suffer” because this would destroy the conversation by corrupting mutual trust. Instead, we should communicate at a level that slightly exceeds the opposing side’s level of intelligence. For example, talk to babies like a baby and all they learn is baby talk. Talk to them like adults and they won’t understand a thing. The solution to this is finding the moderate where they mostly understand what you say but they are challenged at the same time. Then you would ask why would we want to challenge them? Because it opens them to the possibility of change and allows them to process information gradually.
Therefore, intelligence from both sides is the key to effective communications and common sense is the medium.