Yes. The winner of rationality-contest can not be decided by subjective judges. Instead, the winner must be confirmed by reality. This, of course, limits the amount of possible questions, because at some point, real data ist needed.

Contestants could be asked to judge if a precition for the future will happen or not.

Example: stock market rises from 2015 to 2017. The current president gets reelected.

They discuss, choose a position, the event happens or does not happen, and THEN the winner is decided.

Or they might come from research papers, which the contestants do not know. In that case the contestants would be presented an experiment and can test their rationality by predicting the outcome. Which is read after everyone has made a prediction.

Of couse, different from a debate, all contestens may provide the same answer.