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Yes, there is: https://manifold.markets/

People's bets are publicly viewable. The website is very popular with these "rationality-ists" you refer to.

I wasn't in fact arguing that giving a prediction should make people more trustworthy, please explain how you got that from my comment? I said that the main benefit to making such predictions is as practice for the predictor themselves. If there's a benefit for readers, it is just that they could come along and say "eh, I think the chance is higher than that". Then they also get practice and can compare how they did when the outcome is known.