Assholiness charaterizes itself by complete contempt of those who are not assholes, and justifies their humiliation of those unfortunates with extreme prejudice. This attitude can only be dealt with by applying their (the assholes) own weapons against them. The Asshole Ambush is an effective technique.

Find an issue or situation in which you have all the advantages and all the knowledge, bring it up in a rational, dignified and courteous fashion, and when the asshole attempts to take advantage of your obvious weakness, demolish him with your meticulously prepared defense, as publicly and humiliatingly as possible. If the Asshole recovers, and counterattacks, refuse to engage him and walk away. No matter how effective his riposte, anything he says will be overshadowed by the audience's (assholes need an audience) glee at watching him get his deserved comeuppance.