  Classification is the task of predicting the class labels of objects based on
the observation of their features. In contrast, quantification has been defined
as the task of determining the prevalences of the different sorts of class
labels in a target dataset. The simplest approach to quantification is Classify
& Count where a classifier is optimised for classification on a training set
and applied to the target dataset for the prediction of class labels. In the
case of binary quantification, the number of predicted positive labels is then
used as an estimate of the prevalence of the positive class in the target
dataset. Since the performance of Classify & Count for quantification is known
to be inferior its results typically are subject to adjustments. However, some
researchers recently have suggested that Classify & Count might actually work
without adjustments if it is based on a classifer that was specifically trained
for quantification. We discuss the theoretical foundation for this claim and
explore its potential and limitations with a numerical example based on the
binormal model with equal variances. In order to identify an optimal quantifier
in the binormal setting, we introduce the concept of local Bayes optimality. As
a side remark, we present a complete proof of a theorem by Ye et al. (2012).
