  Disagreement is an essential element of science and life in general. The
language of probabilities and statistics is often used to describe
disagreements quantitatively. In practice, however, we want much more than
that. We want disagreements to be resolved. This leaves us with a substantial
knowledge gap which is often perceived as a lack of practical intuition
regarding probabilistic and statistical concepts.
  Take for instance the R\'enyi divergence which is a well-known statistical
quantity specifically designed as a measure of disagreement between
probabilistic models. Despite its widespread use in science and engineering,
the R\'enyi divergence remains a highly abstract axiomatically-motivated
measure. Certainly, it offers no practical insight as to how disagreements can
be resolved.
  Here we propose to address disagreements using the methods of financial
economics. In particular, we show how a large class of disagreements can be
transformed into investment opportunities. The expected financial performance
of such investments quantifies the amount of disagreement in a tangible way.
This provides intuition for statistical concepts such as the R\'enyi divergence
which becomes connected to the financial performance of optimized investments.
Investment optimization takes into account individual opinions as well as
attitudes towards risk. The result is a market-like social mechanism by which
funds flow naturally to support a more accurate view. Such social mechanisms
can help us with difficult disagreements (e.g., financial arguments concerning
the future climate).
  In terms of scientific validation, we used the findings of independent
neurophysiological experiments as well as our own research on the equity
premium.
