Weight of priors and weight of evidence in real life

In real life the situations are never so simple.
Not only priors can differ a lot from a person
to another. Also the probabilities that enter
the Bayes factor might not be the same for everybody.
Simply because they are probabilities, and
probabilities, meant as degree of belief,
have an intrinsic *subjective*
nature [10].
The very reason for this trivial remark
(although not accepted by everybody, because of
ideological reasons) is that probability depends
on the available information and
- fortunately! - there are no two identical brains
in the world, made exactly the same way and
sharing exactly the same information.
Therefore, the same event is not expected with the same
security by different subjects, and the same hypothesis
is not considered equally credible.^{18}

At most degrees of belief
can be *inter-subjective*, because in
many cases there are people or entire communities
that share the same initial beliefs (the same *culture*),
reason more or less
the same way (similar *brains* and similar *education*)
and have access to the *same data*.
Finally, there are stereotyped
`games' in which probabilities can even be *objective*,
in the sense that everybody will agree on its value.
But these situations have to be considered the exceptions rather than the rule
(and even when we state with great security that the probability
of head tossing a regular coin is exactly 1/2, we forget
it could remain vertically, a possibility usually
excluded but that I have personally experienced
a couple of times in my life.)

Therefore, although educational games with boxes and balls might be useful to learn the grammar and syntax of probabilistic reasoning, at a given point we need to move to real situations.

- Assessing subjective degrees of beliefs - virtual bets
- Beliefs versus frequencies
- Subjective evaluation of Bayes factors
- Combining uncertain priors and uncertain weights of evidence
- Agatha Christie's ``three pieces of evidence''
- Critical values for guilt/innocence - Assessing beliefs versus making decisions