A sophist hopes that no one will realize that their arguments are invalid and will believe them anyway based upon how strongly the argument appears to be valid.
The only truly effective means of combating sophistry is a clear understanding of logic and reasoning yourself. When you know how arguments need to be structured in order to be valid and how the various fallacies work, then you will also understand when an argument being offered is simply unacceptable. You cannot prevent a person from trying to use sophistry, but you can demonstrate that their attempts won’t work because you know more than they are giving you credit for.
In addition, you could always publish the reasoning behind their decisions together with a detailed analysis of all the fallacious arguments and flawed logic they have used in order to arrive at their perverse conclusions.