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 191

2. Decision-making perspective. The relationship between design and external
environment has long been studied in a completely different stream of research,
namely decision-making (Savage 1972 ; Friedman and Savage 1948 ; Ra ¨ ffa
1968 ; Wald 1950 ) . In decision-making, the question is to find a choice function
that helps to identify the design alternative that best fits a set of probable states
of nature. Contrary to the design- approaches, the set of states of nature can
follow very general structures—it is only supposed to be a probability space-,
just like the set of alternatives (which can be a simple list). Note that, even if
this approach is not “design-oriented”, decision-making largely used in R&D
and engineering department to decide on the portfolio of projects to be
launched. The “probable states of nature” are the markets and the decision
alternatives are the products (or the technologies) to be developed. Another
very useful case of application that uses the same framework are Taguchi
methods, which actually help to analyse what is the best alternative to meet
with varied external contexts.
Let's analyse the Wald statistical decision-making model (derived from
decision theory), one of the most general models of decision-making under
uncertainty. The models unfolds as follows:
- There are states of nature θ in Θ and random variables X i within R n with
L(X 1 ,X 2 , ... X n , θ) the likelihood function for (X 1 ,X 2 ... X n ) and μ(θ), a priori
density on θ. This is a representation of the states of nature, the probability of
states is subjective and there is model associated to the subjective probability:
the random variables model knowledge creation on these same states of
nature—the a priori probability density on θ depends on X i .
- There is a set D of decisions δ (These are the known alternatives: known
technologies, known products ... )
- The relationship between the states of nature and the set of known decisions is
modeled as follows: these is a cost function C(θ,δ) that associates a certain
cost to every pair (state of nature; decision) [this cost function can also be a
utility function, see (Savage 1972 ) ]; the action consists in deciding for a
certain δ ι , depending on θ, μ(θ) and x i (the results of the sampling operation).
Ie one looks for a decision function ψ,

ψ

x ∈ R n ! λ x ðÞ

that leads to decide for a certain δ ι . According to the decision-making theory,
the best decision function, the function that minimizes the expected cost
function:

ð

μðÞdδd x dθ

EðÞ¼ρμ; ψ ð Þ¼ C θ; ð λ x ðÞL x ; θ ð13:1Þ

R n DΘ

Hence decision-making models helps to select the design alternative that has
the best fit with a set of (subjectively) probable states of nature θ, μ(θ) according