  We introduce distributed NLI, a new NLU task with a goal to predict the
distribution of human judgements for natural language inference. We show that
by applying additional distribution estimation methods, namely, Monte Carlo
(MC) Dropout, Deep Ensemble, Re-Calibration, and Distribution Distillation,
models can capture human judgement distribution more effectively than the
softmax baseline. We show that MC Dropout is able to achieve decent performance
without any distribution annotations while Re-Calibration can give further
improvements with extra distribution annotations, suggesting the value of
multiple annotations for one example in modeling the distribution of human
judgements. Despite these improvements, the best results are still far below
the estimated human upper-bound, indicating that predicting the distribution of
human judgements is still an open, challenging problem with a large room for
improvements. We showcase the common errors for MC Dropout and Re-Calibration.
Finally, we give guidelines on the usage of these methods with different levels
of data availability and encourage future work on modeling the human opinion
distribution for language reasoning. Our code and data are publicly available
at https://github.com/easonnie/ChaosNLI
