Decision theory

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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 that they do.

Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. The basic premise of rational choice theory is that aggregate social behavior results from the behavior of individual actors, each of whom is making their individual decisions. The theory also focuses on the determinants of the individual choices.

In economics, an agent is an actor and more specifically a decision maker in a model of some aspect of the economy. Typically, every agent makes decisions by solving a well- or ill-defined optimization or choice problem.

Norms are concepts (sentences) of practical import, oriented to effecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply "ought-to" types of statements and assertions, in distinction to sentences that provide "is" types of statements and assertions. Common normative sentences include commands, permissions, and prohibitions; common normative abstract concepts include sincerity, justification, and honesty. A popular account of norms describes them as reasons to take action, to believe, and to feel.

Contents

Decision theory is closely related to the field of game theory [2] and is an interdisciplinary topic, studied by economists, statisticians, psychologists, biologists, [3] political and other social scientists, philosophers, [4] and computer scientists.

Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Empirical applications of this rich theory are usually done with the help of statistical and econometric methods.

Statistics study of the collection, organization, analysis, interpretation, and presentation of data

Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. See glossary of probability and statistics.

Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". The first known use of the term "econometrics" was by Polish economist Paweł Ciompa in 1910. Jan Tinbergen is considered by many to be one of the founding fathers of econometrics. Ragnar Frisch is credited with coining the term in the sense in which it is used today.

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 compute 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]

Normative generally means relating to an evaluative standard. Normativity is the phenomenon in human societies of designating some actions or outcomes as good or desirable or permissible and others as bad or undesirable or impermissible. A norm in this normative sense means a standard for evaluating or making judgments about behavior or outcomes. Normative is sometimes also used, somewhat confusingly, to mean relating to a descriptive standard: doing what is normally done or what most others are expected to do in practice. In this sense a norm is not evaluative, a basis for judging behavior or outcomes; it is simply a fact or observation about behavior or outcomes, without judgment. Many researchers in this field try to restrict the use of the term normative to the evaluative sense and refer to the description of behavior and outcomes as positive, descriptive, predictive, or empirical.

Rationality is the quality or state of being rational – that is, being based on or agreeable to reason. Rationality implies the conformity of one's beliefs with one's reasons to believe, and of one's actions with one's reasons for action. "Rationality" has different specialized meanings in philosophy, economics, sociology, psychology, evolutionary biology, game theory and political science.

Decision analysis (DA) is the discipline comprising the philosophy, methodology, and professional practice necessary to address important decisions in a formal manner. Decision analysis includes many procedures, methods, and tools for identifying, clearly representing, and formally assessing important aspects of a decision, for prescribing a recommended course of action by applying the maximum expected utility action axiom to a well-formed representation of the decision, and for translating the formal representation of a decision and its corresponding recommendation into insight for the decision maker and other stakeholders.

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, 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]

In the social sciences and philosophy, a positive or descriptive statement concerns what "is", "was", or "will be", and contains no indication of approval or disapproval. Positive statements are thus the opposite of normative statements. Positive statement is based on empirical evidence. For examples, "An increase in taxation will result in less consumption" and "A fall in supply of petrol will lead to an increase in its price". However, positive statement can be factually incorrect: "The moon is made of green cheese" is empirically false, but is still a positive statement, as it is a statement about what is, not what should be.

Amos Tversky Israeli psychologist

Amos Nathan Tversky was a cognitive and mathematical psychologist, a student of cognitive science, a collaborator of Daniel Kahneman, and a figure in the discovery of systematic human cognitive bias and handling of risk.

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'

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 what is sometimes called "behavioral decision theory" and contributing to a re-evaluation of what useful decision-making requires. [7] [8]

Types of decisions

Choice under uncertainty

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 (see [9] for a review).

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. The prospect theory of Daniel Kahneman and Amos Tversky renewed the empirical study of economic behavior with less emphasis on rationality presuppositions. 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

Intertemporal choice is concerned with the kind of choice where different actions lead to outcomes that are realised at different points in time. 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. [13]

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 may be limited in resources or are boundedly rational (have finite time or intelligence); in such cases the issue, more than the deviation between real and optimal behaviour, is 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[ citation needed ]. Decisions are also affected by whether options are framed together or separately; this is known as the distinction bias. In 2011, Dwayne Rosenburgh explored and showed how decision theory can be applied to complex decisions that arise in areas such as wireless communications. [14]

Heuristics

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. [15] 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. [16] 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. [17] 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. [18] 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. [19]

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:

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

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.

See also

Related Research Articles

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or satisfaction within the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. But the term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a consumer's preference ordering over a choice set. As such, it is devoid of its original interpretation as a measurement of the pleasure or satisfaction obtained by the consumer from that choice.

Bounded rationality is the idea that rationality is limited when individuals make decisions: by the tractability of the decision problem, the cognitive limitations of the mind, and the time available to make the decision. Decision-makers, in this view, act as satisficers, seeking a satisfactory solution rather than an optimal one.

Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the economic decisions of individuals and institutions and how those decisions vary from those implied by classical theory.

Prospect theory

Prospect theory is a theory in cognitive psychology that describes the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are uncertain. The theory states that people make decisions based on the potential value of losses and gains rather than the final outcome, and that people evaluate these losses and gains using some heuristics. The model is descriptive: it tries to model real-life choices, rather than optimal decisions, as normative models do.

In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its negative, in which case it is to be maximized.

In economics, game theory, and decision theory, the expected utility hypothesis, concerning people's preferences with regard to choices that have uncertain outcomes (gambles), states that the subjective value associated with an individual's gamble is the statistical expectation of that individual's valuations of the outcomes of that gamble, where these valuations may differ from the dollar value of those outcomes.

In decision theory, subjective expected utility is the attractiveness of an economic opportunity as perceived by a decision-maker in the presence of risk. Characterizing the behavior of decision-makers as using subjective expected utility was promoted and axiomatized by L. J. Savage in 1954 following previous work by Ramsey and von Neumann. The theory of subjective expected utility combines two subjective concepts: first, a personal utility function, and second a personal probability distribution.

Gerd Gigerenzer German psychologist

Gerd Gigerenzer is a German psychologist who has studied the use of bounded rationality and heuristics in decision making. Gigerenzer is director emeritus of the Center for Adaptive Behavior and Cognition (ABC) at the Max Planck Institute for Human Development and director of the Harding Center for Risk Literacy, both in Berlin, Germany.

The Ellsberg paradox is a paradox in decision theory in which people's choices violate the postulates of subjective expected utility. It is generally taken to be evidence for ambiguity aversion. The paradox was popularized by Daniel Ellsberg, although a version of it was noted considerably earlier by John Maynard Keynes.

In decision theory and economics, ambiguity aversion is a preference for known risks over unknown risks. An ambiguity-averse individual would rather choose an alternative where the probability distribution of the outcomes is known over one where the probabilities are unknown. This behavior was first introduced through the Ellsberg paradox.

Bayes linear statistics is a subjectivist statistical methodology and framework. Traditional subjective Bayesian analysis is based upon fully specified probability distributions, which are very difficult to specify at the necessary level of detail. Bayes linear analysis attempts to solve this problem by developing theory and practise for using partially specified probability models. Bayes linear in its current form has been primarily developed by Michael Goldstein. Mathematically and philosophically it extends Bruno de Finetti's Operational Subjective approach to probability and statistics.

An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare the different decision outcomes, one commonly assigns a utility value to each of them. If there is uncertainty as to what the outcome will be, then under the von Neumann–Morgenstern axioms the optimal decision maximizes the expected utility.

In decision theory, the von Neumann-Morgenstern utility theorem shows that, under certain axioms of rational behavior, a decision-maker faced with risky (probabilistic) outcomes of different choices will behave as if he or she is maximizing the expected value of some function defined over the potential outcomes at some specified point in the future. This function is known as the von Neumann-Morgenstern utility function. The theorem is the basis for expected utility theory.

In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature. The elements of a lottery correspond to the probabilities that each of the states of nature will occur. Much of the theoretical analysis of choice under uncertainty involves characterizing the available choices in terms of lotteries.

Trade-off talking rational economic person (TOTREP) is one term, among others, used to denote, in the field of choice analysis, the rational, human agent of economic decisions.

Bayesian inference in marketing

In marketing, Bayesian inference allows for decision making and market research evaluation under uncertainty and with limited data.

Ecological rationality is a particular account of practical rationality, which specifies the norms of rational action – what one ought to do in order to be rational. The presently dominant account of practical rationality, rational choice theory, maintains that practical rationality consists in making decisions in accordance with certain rules, irrespective of context. Ecological rationality, in contrast, claims that the rationality of a particular decision depends on the circumstances in which it takes place. What is considered rational under the rational choice account thus might not be considered rational under the 'ecological rationality' account, and vice versa.

References

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  16. Bobadilla-Suarez, Sebastian et al. “Fast or Frugal, but Not Both: Decision Heuristics Under Time Pressure.” Journal of Experimental Psychology: Learning, Memory, and Cognition 44.1 (2018): 24–33. Web.
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Further reading

de Finetti, Bruno. "Foresight: its Logical Laws, Its Subjective Sources," (translation of the 1937 article in French) in H. E. Kyburg and H. E. Smokler (eds), Studies in Subjective Probability, New York: Wiley, 1964.