The Bayesian decision theory is neo-Bernoullian in that it proves, by way of a consistency derivation, that Bernoulli’s utility function is the only appropriate function by which to translate, for a given initial wealth, gains and losses to their corresponding utilities. But the Bayesian decision theory deviates from Bernoulli’s original expected utility theory in that it offers up an alternative for the traditional criterion of choice of expectation value maximization, as it proposes to choose that decision which has associated with it the utility probability distribution which maximizes the mean of the expectation value and the lower and upper confidence bounds.

1.
Cox
R.T.
:
Probability, Frequency and Reasonable Expectation
,
American Journal of Physics
,
14
,
1
13
, (
1946
).
2.
Knuth
K.H.
and
Skilling
J.
:
Foundations of Inference
, arXiv:1008.4831v1 [math.PR], (
2010
).
3.
Tversky
A.
and
Kahneman
D.
:
Advances in Prospect Theory: Cumulative Representation of Uncertainty
,
Journal of Risk and Uncertainty
,
5
:
297
323
, (
1992
).
4.
Kahneman
D.
:
Thinking, Fast and Slow
,
Penguin Random House
,
UK
, (
2011
).
5.
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
).
6.
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
).
7.
Masin
S.C.
,
Zudini
V.
, and
Antonelli
M.
:
Early Alternative Derivations of Fechner’s Law
,
Journal of Behavioral Sciences
,
45
,
56
65
, (
2009
).
8.
Stevens
S.S.
:
To Honor Fechner and Repeal His Law
,
Science, New Series
, Vol.
133
, No.
3446
, pp
80
86
, (
1961
).
9.
Knuth
K.H
and
Walsh
J.L.
:
Personal Communication
, (
2016
).
10.
Aczel
J.
:
Lectures on Functional Equations and Their Applications
,
Dover Publications, Inc.
,
New York
, (
1966
).
11.
Fancher
R.E.
:
Pioneers of Psychology
,
W. W. Norton and Company
,
London
, (
1990
).
12.
Jaynes
E.T.
:
Probability Theory: The Logic of Science
.
Cambridge University Press
, (
2003
).
13.
Jorion
P.
:
Value at Risk: The New Benchmark for Managing Financial Risk
,
McGraw-Hill
, (
2006
).
14.
Lindgren
B.W.
:
Statistical Theory
,
Chapman & Hall, Inc.
,
New York
, (
1993
).
15.
Hurwicz
L.
:
What Has Happened to the Theory of Games
,
Cowles Foundation Paper 75b, reprinted from American Economic Review
,
43
(
2
), May (
1953
).
16.
van Erp
H.R.N.
,
Linger
R.O.
, and
van Gelder
P.H.A.J.M.
:
Bayesian Decision Theory: A Simple Toy Problem
,
Bayesian Inference and Maximum Entropy Methods in Science and Engineering-35ᵗʰ International Workshop
,
Potsdam, New York
, (
2016
).