Titel_SS06

this may in turn lead to decisions biased towards not to engage in activities which actually
could be profitable for society. From the societal perspective and under the assumption that all
relevant outcomes and all uncertainties have been included into the formulation of the utility
function this behaviour is fundamentally irrational and also inappropriate if life saving
decision making is considered. What is extremely important, however, is that the perception
of the public and the corresponding societal consequences in case of adverse events is
explicitly accounted for as a “follow up” consequence in the formulation of the utility
function, see also Figure 4.5.

Ideally the public would be informed about risk based decision making to a degree where all
individuals would behave as rational decision makers, i.e. not overreact in case of adverse
events - in which case the risk averse behaviour would be eliminated. This ideal situation may
not realistically be achievable but should be considered as one possible means of risk
treatment in risk based decision making.

It is a political responsibility that societal decisions take basis in a thorough assessment of the
risks and benefits including all uncertainties affecting the decision problem. In some cases,
however, due to different modelling assumptions, different experts in decision making may
identify differing optimal decisions for the same decision problem. The problem then remains
to use such information as a support for societal decision making.

Comparison of decision alternatives

The basis for preference ordering of different decision alternatives is the corresponding risk or
more generally the corresponding expected utilities EUa(), 1,2,..jdj n:

1

() ( )(, )

nOj

jij

i

EUa pOa ua O



 ji (4.4)

where E is the expectation operator, is the number of possible outcomes associated

with alternative ,

noj Oi

aj p(Oaij) is the probability that each of these outcomes will take place

(given ) and is the utility associated with the set (,. This presentation

assumes a discrete set of outcomes but can straightforwardly be generalized to continuous
sample spaces. Considering the consequence modelling including specific consideration of
indirect consequences Equation

aj ua(, )jiO aOji)

(4.5) can be rewritten as:

111

()

( ,)(,)( ,) ( ,) (, (),)( ,)

EXP EXP STA

j

nnn

ij kjDijj kj l kjIDlD j kj

kkl

EUa

pCEXacCapEXa pSEXac Sc apEXa





^ C

(4.5)

In principle this formulation of the expected benefit may now readily be utilized in a decision
analytical framework for the identification of optimal decision alternatives. In the previous
lecture the prior, posterior and pre-posterior decision analyses were introduced for the
purpose of decision support in engineering.