[MaxWeiss]

The wording of your question and teh way you asked similar questions in this thread is very awkward to me. There are only two levels to your yes/no question.

The first is the gathering of all available and relevant information and utilizing it correctly through deduction and logically reasoning. There are no "levels of logic". An argument is either logical or not, assuming the same amount of knowledge. I think what you are getting into with your "levels of logic" is the second part of the question, which is simply knowing your opponent.

The problem is that these two things--gather evidence and knowing your opponents are completely independent of one another, although the final answer does incorporate both. Once all information is obtained and optimally used, there is some percent chance of yes versus no. With 100% information, you can tell 100% yes or no. There is no debate or "logic levels" about the event--it can be determined by evidence and logic. And one can make logical or illogical arguments, but logic is an absolute term, there are no varying degrees of it--there is only the addition of new evidence.

For the second part, you are trying to determine the likelihood of the yes/no answer based on another type of evidence--how well you know the other person. You are determining if he will do something. There only exist about 3 "levels of logic" in a two-sided situation such as your yes/no question. Once you pass level three, it just loops back to one. He knows that I know that he knows that---and so you just pick what you would have originally picked. With more variables or answers the levels might increase, but any further and you unnecessarily and erroneously complicate it.

But again, this is an entirely different situation. Either the yes/no is answered with evidence and logical argument or it is an estimation of another person based on what you know, or some combination thereof, but there is certainly a distinct probability of yes or no depending on what each factor says, and it certainly may not be 50/50.

I don't communicate well and I know this post might have been confusing but if you take anything away from it, let it be that an argument is logical or it is not. The rest is just knowing yourself and the other guy better than he knows himself and you.

Also, the probability of an event you described where each succeeding level of "he knows that I know" type of situation does in fact have a 50/50 chance if each smarter person continues to go opposite. That is simply the definition of limits in mathematics. However that would NOT happen in the situation you described where there is a 100% right answer. Person number two or three, or anybody capable of logical argument and proper use of deduction and inference, would immediately get the right answer (assuming they have all the evidence) as would each of the rest of the people.