Info-gap decision theory is based on three elements. The first
element is an *info-gap model of uncertainty,* which is a
non-probabilistic quantification of uncertainty. The uncertainty
may
be in the value of a parameter, such as a drag coefficient or turn
radius, or in a vector such as probabilities that a target is
present in each of several geographical cells. An info-gap may in the
shape of a utility function or the shape of the tail of the
probability distribution
function (pdf) of extreme events. An info-gap may be in the size
and shape of a set of such entities, such as the set of possible
pdf's or the set of possible utility functions. In all cases an
info-gap model is an
unbounded family of nested sets of possible realizations. For
instance, if the uncertain entity is a function then the info-gap model is an unbounded family of nested sets of realizations of this function.
An info-gap model does not posit a worst case or most extreme
uncertainty. (Sometimes the family of sets is bounded by
virtue of the definition of the uncertain entity. For instance, a
probability must be between zero and one, so the family of nested
sets of possible probability values is bounded. However, this bound
does not derive from knowledge about the event whose probability is
uncertain, but only from the mathematical definition of
probability.
Such an info-gap model is unbounded in the universe of probability values.)

The second element of an info-gap analysis is a *model of the
system,* such as a the overall benefit of target detection. The
model expresses our knowledge about the system, and may
also depend on uncertain elements whose uncertainty is represented
by an info-gap model of uncertainty. The system model also depends on the
decisions to be made, and quantifies the outcomes of those
decisions
given specific realizations of the uncertainties. For instance, the
model may express the expected number of targets detected, the
decrease in enemy capabilities, and so on.

The third element of an info-gap analysis is a set of *performance
requirements.* These specify values of the outcomes which the decision maker
requires or aspires to achieve. These values may constitute success
of the decision, or at least minimally acceptable values. For
instance, one may require that the average number of targets which
are detected be no less than a specified value. Performance
requirements can
embody the concept of satisficing: doing good enough or meeting
critical requirements. Alternatively, the performance requirements
can express windfall aspirations for better-than-anticipated
outcomes. Both satisficing and
windfalling requirements arise in practice, though satisficing
requirements are the most common.

These three components - uncertainty model, system model, and
performance requirements - are combined in formulating two
*decision functions* which support the choice of a course of
action.

The *robustness function* assesses the greatest tolerable horizon of uncertainty. The
robustness function is a quantitative answer to the question: how wrong
can we be in our data, models and understanding, and the action we
are considering will still lead to an acceptable outcome. The robustness
function is based on a satisficing performance requirement. When
operating under severe uncertainty, a decision which achieves an
acceptable outcome over a large range of uncertain realizations is
preferable to a decision which fails to achieve an acceptable
outcome even under small error. In this way the robustness function
generates preferences on available decisions.

The *opportuneness function* assesses the lowest horizon of uncertainty which is
necessary for better-than-anticipated outcomes to be possible
(though not guaranteed). The windfalling decision maker asks: how wrong must
we be in order for quite attractive outcomes to be possible? The
opportuneness function is based on windfalling rather than satisficing.
When
operating under severe uncertainty it is possible that best-model
anticipations are overly pessimistic; the windfaller seeks to
exploit the ambient uncertainty. A decision which would result in a
really wonderful outcome if we err only slightly is preferred (by
the windfaller) over a decision which requires great deviation in
order to enable the same outcome. The opportuneness function thus generates
preferences over the available decisions. These preferences may not
agree with the preferences generated by the robustness function.

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