The manuscript analyzes various properties of loss functions for probabilistic estimation, and provides a number of results on properness and calibration. As pointed out by the reviewers, the strengths of the manuscript include the novelty and timeliness of the problem of interest, clarity of writing, and novelty of the results. The reviewers also point out some weaknesses, included limited generality of the the main results -- particularly related to properness. There were also very limited empirical motivation. The primary empirical result on outliers behavior of log losses for language tasks was unclear -- if this was an complete experiment by the authors, and if so why a more thorough evaluation was not provided. Overall, the reviewers and AC agree that this is an interesting submission, that has some potential to encourage new theoretical and applied work on loss functions, and thus may be of general interest.