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Decision theory (or the theory of choice not to be confused with choice
theory) is the study of an agent's choices.[1]
Decision theory can be broken into two branches: normative decision theory,
which analyzes the outcomes of decisions or determines the optimal decisions
given constraints and assumptions, and descriptive decision theory, which
analyzes how agents actually make the decisions they do. Decision theory is
closely related to the field of game theory[2] and is an interdisciplinary
topic, studied by economists, statisticians, data scientists, psychologists,
biologists,[3] political and other social scientists, philosophers[4] and
computer scientists. Empirical applications of this rich theory are usually
done with the help of statistical and econometric methods.
Normative and descriptive:
Normative decision theory is concerned with identification of optimal decisions
where optimality is often determined by considering an ideal decision maker who
is able to calculate with perfect accuracy and is in some sense fully rational.
The practical application of this prescriptive approach (how people ought to
make decisions) is called decision analysis and is aimed at finding tools,
methodologies, and software (decision support systems) to help people make
better decisions.[5][6] In contrast, positive or descriptive decision theory is
concerned with describing observed behaviors often under the assumption that
the decision-making agents are behaving under some consistent rules. These
rules may, for instance, have a procedural framework (e.g. Amos Tversky's
elimination by aspects model) or an axiomatic framework (e.g. stochastic
transitivity axioms), reconciling the Von Neumann-Morgenstern axioms with
behavioral violations of the expected utility hypothesis, or they may
explicitly give a functional form for time-inconsistent utility functions (e.g.
Laibson's quasi-hyperbolic discounting).[5][6] The prescriptions or predictions
about behavior that positive decision theory produces allow for further tests
of the kind of decision-making that occurs in practice. In recent decades,
there has also been increasing interest in "behavioral decision
theory", contributing to a re-evaluation of what useful decision-making
requires.[7][8]
Types of decisions:
Choice under uncertainty:
Further information: Expected utility hypothesis The area of choice under
uncertainty represents the heart of decision theory. Known from the 17th
century (Blaise Pascal invoked it in his famous wager, which is contained in
his Pensées, published in 1670), the idea of expected value is that,
when faced with a number of actions, each of which could give rise to more than
one possible outcome with different probabilities, the rational procedure is to
identify all possible outcomes, determine their values (positive or negative)
and the probabilities that will result from each course of action, and multiply
the two to give an "expected value", or the average expectation for
an outcome; the action to be chosen should be the one that gives rise to the
highest total expected value. In 1738, Daniel Bernoulli published an
influential paper entitled Exposition of a New Theory on the Measurement of
Risk, in which he uses the St. Petersburg paradox to show that expected value
theory must be normatively wrong. He gives an example in which a Dutch merchant
is trying to decide whether to insure a cargo being sent from Amsterdam to St
Petersburg in winter. In his solution, he defines a utility function and
computes expected utility rather than expected financial value.[9] In the 20th
century, interest was reignited by Abraham Wald's 1939 paper[10] pointing out
that the two central procedures of sampling-distribution-based
statistical-theory, namely hypothesis testing and parameter estimation, are
special cases of the general decision problem. Wald's paper renewed and
synthesized many concepts of statistical theory, including loss functions, risk
functions, admissible decision rules, antecedent distributions, Bayesian
procedures, and minimax procedures. The phrase "decision theory"
itself was used in 1950 by E. L. Lehmann.[11]
The revival of subjective probability theory, from the work of Frank Ramsey,
Bruno de Finetti, Leonard Savage and others, extended the scope of expected
utility theory to situations where subjective probabilities can be used. At the
time, von Neumann and Morgenstern's theory of expected utility[12] proved that
expected utility maximization followed from basic postulates about rational
behavior.
The work of Maurice Allais and Daniel Ellsberg showed that human behavior has
systematic and sometimes important departures from expected-utility
maximization.[13] The prospect theory of Daniel Kahneman and Amos Tversky
renewed the empirical study of economic behavior with less emphasis on
rationality presuppositions. It describes a way by which people make decisions
when all of the outcomes carry a risk.[14] Kahneman and Tversky found three
regularities – in actual human decision-making, "losses loom larger
than gains"; persons focus more on changes in their utility-states than
they focus on absolute utilities; and the estimation of subjective
probabilities is severely biased by anchoring.
Intertemporal choice:
Main article: Intertemporal choice:
Intertemporal choice is concerned with the kind of choice where different
actions lead to outcomes that are realised at different stages over time.[15]
It is also described as cost-benefit decision making since it involves the
choices between rewards that vary according to magnitude and time of
arrival.[16] If someone received a windfall of several thousand dollars, they
could spend it on an expensive holiday, giving them immediate pleasure, or they
could invest it in a pension scheme, giving them an income at some time in the
future. What is the optimal thing to do? The answer depends partly on factors
such as the expected rates of interest and inflation, the person's life
expectancy, and their confidence in the pensions industry. However even with
all those factors taken into account, human behavior again deviates greatly
from the predictions of prescriptive decision theory, leading to alternative
models in which, for example, objective interest rates are replaced by
subjective discount rates. Interaction of decision makers Some decisions are
difficult because of the need to take into account how other people in the
situation will respond to the decision that is taken. The analysis of such
social decisions is more often treated under the label of game theory, rather
than decision theory, though it involves the same mathematical methods. From
the standpoint of game theory, most of the problems treated in decision theory
are one-player games (or the one player is viewed as playing against an
impersonal background situation). In the emerging field of socio-cognitive
engineering, the research is especially focused on the different types of
distributed decision-making in human organizations, in normal and
abnormal/emergency/crisis situations.[17]
Complex decisions:
Other areas of decision theory are concerned with decisions that are difficult
simply because of their complexity, or the complexity of the organization that
has to make them. Individuals making decisions are limited in resources (i.e.
time and intelligence) and are therefore boundedly rational; the issue is thus,
more than the deviation between real and optimal behaviour, the difficulty of
determining the optimal behaviour in the first place. One example is the model
of economic growth and resource usage developed by the Club of Rome to help
politicians make real-life decisions in complex situations.
Decisions are also affected by whether options are framed together or
separately; this is known as the distinction bias.
Heuristics:
Main article: Heuristics in judgment and decision-making:
Heuristics in decision-making is the ability of making decisions based on
unjustified or routine thinking. While quicker than step-by-step processing,
heuristic thinking is also more likely to involve fallacies or
inaccuracies.[18] The main use for heuristics in our daily routines is to
decrease the amount of evaluative thinking we perform when making simple
decisions, making them instead based on unconscious rules and focusing on some
aspects of the decision, while ignoring others.[19] One example of a common and
erroneous thought process that arises through heuristic thinking is the
Gambler's Fallacy — believing that an isolated random event is affected by
previous isolated random events. For example, if a coin is flipped to tails for
a couple of turns, it still has the same probability of doing so; however it
seems more likely, intuitively, for it to roll heads soon.[20] This happens
because, due to routine thinking, one disregards the probability and
concentrates on the ratio of the outcomes, meaning that one expects that in the
long run the ratio of flips should be half for each outcome.[21]
Another example is that decision-makers may be biased towards preferring
moderate alternatives to extreme ones; the Compromise Effect operates under a
mindset that the most moderate option carries the most benefit. In an
incomplete information scenario, as in most daily decisions, the moderate
option will look more appealing than either extreme, independent of the
context, based only on the fact that it has characteristics that can be found
at either extreme.[22]
Alternatives A highly controversial issue is whether one can replace the use of
probability in decision theory by other alternatives.
Probability theory:
Advocates for the use of probability theory point to: the work of Richard
Threlkeld Cox for justification of the probability axioms, the Dutch book
paradoxes of Bruno de Finetti as illustrative of the theoretical difficulties
that can arise from departures from the probability axioms, and the complete
class theorems, which show that all admissible decision rules are equivalent to
the Bayesian decision rule for some utility function and some prior
distribution (or for the limit of a sequence of prior distributions). Thus, for
every decision rule, either the rule may be reformulated as a Bayesian
procedure (or a limit of a sequence of such), or there is a rule that is
sometimes better and never worse.
Alternatives to probability theory:
The proponents of fuzzy logic, possibility theory, quantum cognition,
Dempster–Shafer theory, and info-gap decision theory maintain that
probability is only one of many alternatives and point to many examples where
non-standard alternatives have been implemented with apparent success; notably,
probabilistic decision theory is sensitive to assumptions about the
probabilities of various events, while non-probabilistic rules such as minimax
are robust, in that they do not make such assumptions.
Ludic fallacy:
Main article: Ludic fallacy:
A general criticism of decision theory based on a fixed universe of
possibilities is that it considers the "known unknowns", not the
"unknown unknowns"[citation needed]: it focuses on expected
variations, not on unforeseen events, which some argue have outsized impact and
must be considered – significant events may be "outside model".
This line of argument, called the ludic fallacy, is that there are inevitable
imperfections in modeling the real world by particular models, and that
unquestioning reliance on models blinds one to their limits.
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