Decision-making can occur under different conditions, including certainty, uncertainty, and risk. Understanding these conditions is crucial in applying Decision Theory principles effectively. The scope of Decision Theory is broad, encompassing various fields such as economics, finance, business, healthcare, and engineering.
- This can be problematic in fields like healthcare or finance, where understanding the rationale for decisions is crucial.
- These will be discussed in turn; it willbe suggested that the disputes may not be substantial but ratherindicate subtle differences in the interpretation of sequentialdecision models.
- Recall that the domain of the preferenceordering in Savage’s theory amounts to every functionfrom the set of states to the set of outcomes (what Broome 1991arefers to as the Rectangular Field Assumption).
- Defenders of resolute choice may have in mind a differentinterpretation of sequential decision models, whereby future“choice points” are not really points at which an agent isfree to choose according to her preferences at the time.
- The vNM theorem is a very important result for measuring the strengthof a rational agent’s preferences over sure options (thelotteries effectively facilitate a cardinal measure over sureoptions).
Axiom 2
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. 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. 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.
Decisions in stages, decision trees:
- Although Tversky’s results were laterreplicated, it should be noted that there is ongoing controversysurrounding the level of empirical support for intransitive preference(see Regenwetter et al. 2011 for a recent literaturereview).
- The future of Decision Theory is likely to be shaped by advancements in technology and data analytics.
- 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.
- Interpreting qualitative factors is an aspect that has little to do with rational approach of decision-making and in this way there are no static decision-models.
- Within both these areas one may distinguish individual decision theory, which concerns the choices of a single agent with specific goals and knowledge, and game theory, which deals with interactions among individuals.
Savage suggests that this definition ofcomparative belief is plausible in light of his axiom P4, which willbe stated below. When the above holds, we say that there is an expected utilityfunction that represents the agent’s preferences; in otherwords, the agent can be represented as maximising expectedutility. The last section provided an interval-valued utility representation ofa person’s preferences over lotteries, on the assumption thatlotteries are evaluated in terms of expected utility.
Those principles with respect to which offendingpreferences were later corrected included most notably Transitivityand Stochastic Dominance. Allais- or Ellsberg-style preferences weresubstantially more resilient, however, a fact confirmed in a laterstudy by Slovic & Tversky (1974). Another type of resilience ofpreferences, not considered by Savage, was more recently investigatedby van de Kuilen & Wakker (2006). They studied the effects ofproviding feedback on decision outcomes on the prevalence of commonconsequence effects in sequences of choices, finding, however, asignificant reduction in SEU violations. Normative decision theory is a branch of decision theory that focuses on identifying the rational principles and criteria that should guide individuals and organizations when making decisions. It provides a framework for evaluating and selecting the best course of action in situations with uncertainty and multiple possible choices.
There are various causes for making poor decisions, the two main theories regarding these poor decisions are Bounded Rationality and Sub optimization. In contrast, awareness of unawareness would seem to be of greatinterest from the perspective of decision-making. Less formally (and stated in terms of strict preference), the idea isthat if you prefer to stake the prize \(X\) on \(f\) rather than\(f’\), you must consider \(E\) more probable than \(F\). Therefore,you should prefer to stake the prize \(Y\) on \(g\) rather than \(g’\)since the prize itself does not affect the probability of theevents.
The same goes for preferences thatseem to violate Separability or Independence (of the contribution ofeach outcome to the overall value of an option), discussed further in Section 5.1 below. After all, an apt model of preference issupposedly one that captures, in the description of final outcomes andoptions, everything that matters to an agent. In that case, however,EU theory is effectively vacuous or impotent as a standard ofrationality to which agents can aspire. Moreover, it stretches thenotion of what are genuine properties of outcomes that can reasonablyconfer value or be desirable for an agent.
Shafir (1995) show that physicians are less likely to prescribe ibuprofen to patients in pain when they have the option of prescribing the inferior drug piroxicam than when piroxicam is unavailable. While this sort decision theory is concerned with of behavior does not discredit SEU2 as a normative principle, it does show that it is inaccurate as a description of human behavior. The second principle requires each act to have a value that depends only on the values and probabilities of the outcomes it might cause. You can change your settings at any time, including withdrawing your consent, by using the toggles on the Cookie Policy, or by clicking on the manage consent button at the bottom of the screen. Quickonomics provides free access to education on economic topics to everyone around the world. Our mission is to empower people to make better decisions for their personal success and the benefit of society.
It’s time to build
Mathematical and statistical models can be employed in assessing what should be the optimal decision, psychology and philosophy on the other hand, suggest the likely outcome using human factors and behaviours. In summary, descriptive decision theory is concerned with how people make decisions in the real world, acknowledging that cognitive limitations, emotional factors, and biases often influence decision processes. It provides valuable insights into the behaviors and deviations from rationality commonly observed in decision-making situations. For chance event nodes managers calculate certainty equivalents related to the events emanating from these nodes. Under the assumption that the decision maker has a neutral attitude toward risk, certainty equivalent of uncertain outcomes can be replaced by their expected value.
The Standard Model: Subjective Expected Utility
Similarly a bad decision, betting tails, can lead to the possibility of a $1.00 gain. He puts forward the canons of “old time religion” as principles for the practice of normative decision analysis. These are summarized by Wu and Eriksen (2013) as shown in Table 2.7 as direct quotes.
Comparative Probability
The orthodox normative decision theory, expectedutility (EU) theory, essentially says that, in situations ofuncertainty, one should prefer the option with greatestexpected desirability or value. (Note that in this context,“desirability” and “value” should beunderstood as desirability/value according to the agent inquestion.) This simple maxim will be the focus of much of ourdiscussion. 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. Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses the tools of expected utility and probability to model how individuals would behave rationally under uncertainty. It differs from the cognitive and behavioral sciences in that it is mainly prescriptive and concerned with identifying optimal decisions for a rational agent, rather than describing how people actually make decisions.
By the late 20th century, scholars like Daniel Kahneman and Amos Tversky challenged the assumptions of rational decision-making. Their work in behavioral economics highlighted cognitive biases and heuristics that influence real-world decisions, leading to the development of prospect theory, which modified expected utility theory by accounting for psychological factors. 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. Decisions are also affected by whether options are framed together or separately; this is known as the distinction bias. Intertemporal choice is concerned with the kind of choice where different actions lead to outcomes that are realised at different stages over time.
In any case, it turns out that when a person’spreferences satisfy Savage’s axioms, we can read off herpreferences a comparative belief relation that can be represented by a(unique) probability function. Decision theory is a study of an agent’s rational choices that supports progress in technology such as work on machine learning and artificial intelligence. It looks at how decisions are made, how multiple decisions influence one another, and how decision-making parties deal with uncertainty. A number of studies set out to test the normative adequacy of SEUalong the proposed lines. MacCrimmon (1968) reported violations, in asample of experienced business executives, of a wide range ofconsequences of SEU, a number of which persisted after subjects werenotably provided with considerations both supporting and underminingthese principles.
LaraBuchak (2013) develops a decision theory on which the explanation forAllais’ preferences is not the different value that theoutcome $0 has depending on what lottery it is part of. However, the contribution that $0makes towards the overall value of an option partly depends on whatother outcomes are possible. Buchak introduces a riskfunction that represents people’s willingness to tradechances of something good for risks of something bad. And she showsthat if an agent satisfies a particular set of axioms, which isessentially Savage’s except that the Sure Thing Principle isreplaced with a strictly weaker one, then the agent’spreferences can be represented as maximising risk weightedexpected utility.
Grant and Quiggin (2013a, 2013b), for instance,suggest that these judgments are made based on induction from pastsituations where one experienced awareness growth. From the perspective of decision-making, unawareness of unawareness isnot of much interest. After all, if one is not even aware of thepossibility that one is unaware of some state or outcome, then thatunawareness cannot play any role in one’s reasoning about whatto do. However, decision-theoretic models have been proposed for how arational person responds to growth in awareness (that ismeant to apply even to people who previously were unaware of theirunawareness). In particular, economists Karni and Vierø (2013,2015) have recently extended standard Bayesian conditionalisation tosuch learning events. Their theory, Reverse Bayesianism,informally says that awareness growth should not affect the ratios ofprobabilities of the states/outcomes that the agent was aware ofbefore the growth.
Decision Science (Part : The Interdisciplinary Nature of Decision Science
As noted, a special case is when the content of \(p\) is suchthat it is recognisably something the agent can choose to make true,i.e., an act. Savagewent one step further than this, and defined comparativebelief in terms of preferences. The proponents of fuzzy logic, possibility theory, 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 can sometimes be sensitive to assumptions about the probabilities of various events, whereas non-probabilistic rules, such as minimax, are robust in that they do not make such assumptions. A highly controversial issue is whether one can replace the use of probability in decision theory with something else.
For a domainof options we speak of an agent’s preference ordering,this being the ordering of options that is generated by theagent’s preference between any two options in that domain. After World War II, decision theory expanded into economics, particularly with the work of economists like Milton Friedman and others, who applied it to market behavior and consumer choice theory. This era also saw the development of Bayesian decision theory, which incorporates Bayesian probability into decision-making models. 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.
Utility measures of preference
The two main types of utility function that will playa role are the ordinal utility function and the moreinformation-rich interval-valued (or cardinal)utility function. The above can be taken as a preliminary characterisation of rationalpreference over options. Even this limited characterisation iscontentious, however, and points to divergent interpretations of“preferences over prospects/options”. We proceed by first introducing basic candidate properties of(rational) preference over options and only afterwards turning toquestions of interpretation. As noted above, preference concerns thecomparison of options; it is a relation between options.