A New Perspective for Risk Management: A Study of the Design of Generic Technology with a Matroid Model in C-K Theory - Principia Designae: Pre-Design, Design, and Post-Design - page 193

ð ð

M δ nþ1 ð Þ¼μ= C θ, δ nþ1 ð ÞμðÞdθ < min

i¼1 ... n

C θ, δ i ð ÞμðÞdθ

Θ Θ

An even more robust solution would be independent of μ. It means that whatever
the belief on the states of nature—ie even for states of nature considered extremely
low-, the alternative δ n+1 is the better. This can be written as:

ð ð

8i ¼ 1 ... n, 8μ, C θ, δ nþ1 ð ÞμðÞdθ < C θ, δ i ð ÞμðÞdθ ð13:3Þ

Θ Θ

Example: Raincoat Cap
Let's illustrate what it means on a simple example of decision making situation
(see Fig. 13.1 ). Suppose that the decision maker wants to have a walk and his
decision space is D¼ {d 1 : take a cap to protect against the sun; d 1 , take a raincoat to
protect against the rain}; the states of natures are Θ¼ {θ 1 , sunny weather; θ 2 , rainy
weather}; and subjective probability are, for instance {μ(θ 1 ) ¼0,51; μ(θ 2 ) ¼1-
μ(θ 1 ) ¼0,49}. The utility function is U N 2 !R, for instance : U(θ 1 ; d 1 ) ¼100;
U(θ 2 ; d 2 ) ¼10; U(θ 1 , d 2 ) ¼100; U(θ 2 ; d 1 ) ¼10. This situation is usually
represented by a decision-hazard tree (see Fig. 13.1 ). One computes the expected
utility associated to each decision. With these data, the decision-maker should
choose d 1 —and one also understands the fragility of this choice, due to the
proximity between μ(θ 1 ) and μ(θ 2 ). This remark usually leads to increase knowl-
edge (e.g. look at weather forecast even if it reduces the walk time).
If we add the hypothesis that the actor can design a new solution, then the dominat-
ing solution can be designed as d 3 such that U(θ 1 ; d 3 ) ¼100; U(θ 2 ; d 3 ) ¼100.
The design of d 3 might lead to a kind of “raincoat-cap”.
Note that industrial history is actually full of such design. The graph in Fig. 13.2
illustrates the fact

that some technologies are for instance independent of

q 1

U = 100
µ = 0,51

q 1

U = 100
µ = 0,51

E 1 = 56

E 1 = 56

U = 10
µ = 0,49

U = 10
µ = 0,49

q 2 q 2

d 1

d 1

U = 10
µ = 0,51

U = 10
µ = 0,51

q 1

q 1

d 2

d 2

E 2 = 54

E 2 = 54

U = 100
µ = 0,49

U = 100
µ = 0,49

q 2

q 2

d 3

U = 100
µ = 0,51

q 1

E 1 = 100

U = 100
µ = 0,49

q 2

Fig. 13.1 Raincoat-cap example. (a) Selection of the solution with the best expected utility;