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Not sure changing the payout schemes would help. The underlying issue which Tyler Cowen thinks is a problem is that making a bet freezes your position in time, so to say, and gives you a stake (if not monetary then a status stake) to defend. That does not depend on the details of how the bet is arranged. And you can't go around it because getting some skin into the game is precisely the purpose of betting from Robin Hanson's point of view.
I would contest that's the case insofar as you have to bet only on one side, if you gain / lose stakes from both positions, possibly the " rooting for one outcome over another, it makes the denouement of the bet about the relative status of the people in question" would be diminished?