  The amount of training-data is one of the key factors which determines the
generalization capacity of learning algorithms. Intuitively, one expects the
error rate to decrease as the amount of training-data increases. Perhaps
surprisingly, natural attempts to formalize this intuition give rise to
interesting and challenging mathematical questions. For example, in their
classical book on pattern recognition, Devroye, Gyorfi, and Lugosi (1996) ask
whether there exists a {monotone} Bayes-consistent algorithm. This question
remained open for over 25 years, until recently Pestov (2021) resolved it for
binary classification, using an intricate construction of a monotone
Bayes-consistent algorithm.
  We derive a general result in multiclass classification, showing that every
learning algorithm A can be transformed to a monotone one with similar
performance. Further, the transformation is efficient and only uses a black-box
oracle access to A. This demonstrates that one can provably avoid non-monotonic
behaviour without compromising performance, thus answering questions asked by
Devroye et al (1996), Viering, Mey, and Loog (2019), Viering and Loog (2021),
and by Mhammedi (2021).
  Our transformation readily implies monotone learners in a variety of
contexts: for example it extends Pestov's result to classification tasks with
an arbitrary number of labels. This is in contrast with Pestov's work which is
tailored to binary classification.
  In addition, we provide uniform bounds on the error of the monotone
algorithm. This makes our transformation applicable in distribution-free
settings. For example, in PAC learning it implies that every learnable class
admits a monotone PAC learner. This resolves questions by Viering, Mey, and
Loog (2019); Viering and Loog (2021); Mhammedi (2021).
