In this paper, the authors analyze the problem of poor performance of Bayesian model averaging under model misspecification using new second-order PAC-Bayes bounds. And they use their tools to suggest an alternative model to handle misspecification. Three of four reviewers are excited about the novelty of the approach and its important practical contribution. That being said, the authors need to be careful to follow up on their promises (in the author feedback) for clarification throughout the paper. And the authors need to make sure to correct the error in the author feedback flagged by Reviewer 1 (please see revised review).