The body of knowledge concerned with making selection from a range of alternative possible actions.

Decision theory is in practice an extremely confusing term to managers because
there are many different views about the subject-matter included. Some say
that decision theory can be equated with statistics since they say statistics
is the science of decision-making under uncertainty. There is, therefore,
a number of textbooks with decision theory or sometimes statistical decision
theory in their titles and these books are straightforward statistics textbooks.
Others regard decision theory as both science and art and there are several
textbooks on *The Art of Judgement* that rarely mention statistics or statistical
concepts. Notable are the writings of Sir Geoffrey Vickers and H A Simon.
Other writers treat the subject as a part of operations research and draw
on different branches of pure and applied mathematics and statistics for
their material. Typically, these books include utility theory, decision rules
(minimax etc), the Bayes theorem, some probability theory, some game theory,
some set theory (Boolean algebra, symbolic logic) and truth tables. Yet others
equate the subject with management techniques and include industrial democracy
and network analysis in their belief.

Decision theory practitioners, in order to improve the quality of their decisions, endeavour to find out the processes that take place when decisions are made, and always seek to find ways of teaching people to make decisions. There are two kinds of decision: programmed and unprogrammed.

Programmed decisions are those taken according to rules in highly structured organisations, for example, the fighting and civil services and, in industry, production areas. These decisions can be taken by relatively junior staff, and some can be executed by computers or even by servo-mechanisms – the speed-control mechanism on a clockwork motor, for instance.

Unprogrammed, or free-ranging decisions, deal with new areas and new problems, and are the main pre-occupation of senior managers – or at least they should be!

By classifying decisions managers can free themselves more for creative work, for planning and for innovation. Application of decision theory can indicate the level at which decisions should be made, can indicate the technique appropriate to the solution of the problem on which decisions have to be made, and can provide a valuable lead as to which sectors in a business can be computerised.

A common textbook example of heuristic (trial and error) decision making
is as follows. Given a balance (which does not measure weights but shows
only which side is heavy and light) and 12 balls, 11 of which are the same
weight and one is light or heavy, find the odd ball in three weighings only.
This *can* be done.

A visual aid device for illustrating some or all of the choices available at various stages in a multi-stage decision process, and the consequences of each choice.

*Decision trees* are pictorial networks of alternative courses of action showing
the possible outcomes of different choices, taking into account probabilities,
costs and returns. Decision trees enable a manager to set out the consequences
of choices, ensuring that he has considered all possibilities and to assess
the likelihood of each different possibility and to assess the result of
each possibility in terms of cost and profit.

The figure illustrates a simple decision tree for investment analysis.
In the example 500,000 monetary units are to be invested and the decision
is to invest either in shares or savings. The values, of course are
hypothetical because the diagram represents **risk** and not actual returns.
(Furthermore, interest, dividends, share values and other anticipated gains/losses
can be added to enhance the value of the analyses but have been omitted here
for simplicity to illustrate the principles involved).

The starting point in a multi-stage decision process is conventionally shown by means of a circle with lines radiating outwards towards the right, each representing a possible choice and each terminated by a circle node, representing the state after the particular choice has been made. Stage 1 has only one state, the present or starting position. Subsequent decision choices after the first are shown similarly by radiating lines from the relevant node of stage 2. If the outcome of each choice or the probability of the particular outcome arising can be calculated, it is usual to show the relevant quantities on the decision arrows.

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