I think you missed the fact that choosing arbitration is a
voluntary act. How does letting other people choose to be governed by Islamic law when in pertains to disputes
between then makes me "live under these laws"? I don't want to be subject to Islamic law, but I don't see why I should prevent others to submit themselves to it, as long as they have the choice not to.
Say you and I sign a contract where we both agree that a local alderman will serve as arbiter in case of a dispute. Do you think that make every US citizen suddenly have to follow rulings issued by that person?
I think you missed the fact that choosing arbitration is a voluntary act. For now.
Ever hear the word "incrementalism"?
Ever hear the phrase "camel's nose under the tent"?
What do you think those terms describe?