We give here a comparison of the expected outcome theory, the expected utility theory, and the Bayesian decision theory, by way of a simple numerical toy problem in which we look at the investment willingness to avert a high impact low probability event. It will be found that for this toy problem the modeled investment willingness under the Bayesian decision theory is minimally three times higher compared to the investment willingness under either the expected outcome or the expected utility theories, where it is noted that the estimates of the latter two theories seem to be unrealistically low.

1.
Jaynes
E.T.
:
Probability Theory; the Logic of Science
.
Cambridge University Press
, (
2003
).
2.
Lindgren
B.W.
:
Statistical Theory
,
Chapman & Hall, Inc.
,
New York
, (
1993
).
3.
van Erp
H.R.N.
,
Linger
R.O.
, and
van Gelder
P.H.A.J.M.
:
Fact Sheet on the Bayesian Decision Theory
, arXiv, (
2015
).
4.
Bernoulli
D.
:
Exposition of a New Theory on the Measurement of Risk
.
Translated from Latin into English by Dr Louise Sommer from ‘Specimen Theoriae Novae de Mensura Sortis’
,
Commentarii Academiae Scientiarum Imperialis Petropolitanas
,
Tomus V
,
175
192
, (
1738
).
5.
van Erp
H.R.N.
,
Linger
R.O.
, and
van Gelder
P.H.A.J.M.
:
An Outline of the Bayesian Decision Theory
,
Bayesian Inference and Maximum Entropy Methods in Science and Engineering-35ᵗʰ International Workshop
,
Potsdam, New York
, (
2016
).
This content is only available via PDF.