Glazer and Rubinstein on debates

There's a really funny and interesting paper in Game Theory and Pragmatics about the pragmatics of debate (chapter 9, by Jacob Glazer and Ariel Rubinstein). I think their results might benefit both from being reformulated in a information-theoretical language and in epistemic logic, but I'm not quite sure how.

In their model, a debate is a game played by three people; debater 1, debater 2, and listener. The debaters can refer to one witness each to support their case, and the goal of listener is then to guess whether a majority of the pool of possible witnesses actually support the case of debater 1 or the case of debater 2. The task of the listener is to devise a guessing pattern such that debater 1 has a winning strategy if a majority of the witnesses support his case, and debater 2 has a winning strategy if the majority supports her case.

Maybe this can be seen as a cryptography problem? Listener doesn't know the state of the world, and the preference of the debaters is, in a sense, to keep it things way. But in cryptography, there is only an encoder and a spy, and the map from states of the world to messages must be injective. In the debating game, arguments do not need to be different in different states of the world, but there are other constraints such as truthfulness and length. I don't know exactly how far this metaphor can be pushed.