What is the situation called where a strong party uses logical reasoning based on a flawed foundation? I am interested in the  situation where two parties (people or organisations) differ in their commitment to exert power where party has more commitment to exert power than the other. The two parties have a dispute on some matter. The strong party builds an argument upon an erroneous point and with great rigour proceeds with some logical conclusions. The strong party is gladly involved in philosophical dispute concerning the validity of all links, but first. The initial point is sold as an axiom. 

My question is twofold:


does this situation have name?
What is the best strategy to deal with this situation for a weak party?
A partial solution:

As for the logical fallacy (unrelated to "strong" and "weak" parties), you seem to be describing a "Fallacy of Presumption," where one makes an argument based off of a false/questionable/undefended presumption. There are several more specific cases of this type of fallacy. A website that describes a few is listed below (found via a Google search).

http://www.philosophypages.com/lg/e06b.htm