Civil Engineering Reference
In-Depth Information
Laplace criterion
Laplace criterion is based on the 'principle of insuffi cient reason,' proposed
by Jacob Bernoulli. The criterion states that 'if we are ignorant of the ways
an event can occur (and therefore have no reason to believe that one way
will occur preferentially compared to another),' then they should all be
treated as equally likely, being assigned the probability 1/
n
, where
n
is the
number of states. Thus, accordingly, the ranking for the fi ve alternatives are:
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>
(
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>
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>
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(
)
A
072
.
A
070
.
A
059
.
A
058
.
A
056
.
3
5
1
4
2
Maximin criterion
Under the Maximin criterion, the decision maker takes a pessimistic view-
point. The decision makers assume that the worst that can happen will, and
then they take the action with the best (
maximum
) worst case (
minimum
)
scenario. Under this assumption, it would be best to choose that action
which maximizes the minimum payoff among all possible actions.
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>
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>
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>
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>
(
)
A
041
.
A
038
.
A
026
.
A
015
.
A
006
.
3
5
4
1
2
Maximax criterion
Under the Maximax criterion, the decision maker takes an optimistic view-
point. The decision makers take the action with the best (
maximum
) of the
best (
maximum
) case scenario. Under this assumption, it would be best to
choose the action which maximizes the maximum payoff among all possible
actions.
(
)
>
(
)
>
(
)
>
(
)
>
(
)
A
100
.
A
100
.
A
092
.
A
089
.
A
086
.
4
2
3
5
1
Minimax regret criterion
Minimax decision making is based on opportunistic loss. Often, decision
makers have taken a certain action only to regret it later when the true
state of nature is known; e.g. the payoff was not as great as it could have
been if a different action had been taken. The difference between what
could have been obtained and what was actually obtained has been defi ned
as 'regret.' For example, Scawthorn (2003) expounded this as:
. . . a plant manager chooses to delay seismic retrofi t due to its high cost
and judgment that there is an extremely small chance of a major
earthquake in the next 5 years. An earthquake occurs soon after this
decision, which causes a 30-day interruption of operations. Even though
the decision was in fact a wise one, given the decision maker's
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