  Given a classification problem and a family of classifiers, the Rashomon
ratio measures the proportion of classifiers that yield less than a given loss.
Previous work has explored the advantage of a large Rashomon ratio in the case
of a finite family of classifiers. Here we consider the more general case of an
infinite family. We show that a large Rashomon ratio guarantees that choosing
the classifier with the best empirical accuracy among a random subset of the
family, which is likely to improve generalizability, will not increase the
empirical loss too much. We quantify the Rashomon ratio in two examples
involving infinite classifier families in order to illustrate situations in
which it is large. In the first example, we estimate the Rashomon ratio of the
classification of normally distributed classes using an affine classifier. In
the second, we obtain a lower bound for the Rashomon ratio of a classification
problem with a modified Gram matrix when the classifier family consists of
two-layer ReLU neural networks. In general, we show that the Rashomon ratio can
be estimated using a training dataset along with random samples from the
classifier family and we provide guarantees that such an estimation is close to
the true value of the Rashomon ratio.
