Decision Theory Stanford Encyclopedia of Philosophy

This brings us to the Transitivity axiom, which says that if an option \(B\) is weakly preferred to \(A\), and\(C\) weakly preferred to \(B\), then \(C\) is weakly preferred to\(A\). A recent challenge to Transitivity turns on heterogeneous setsof options, as per the discussion of Completeness above. But here adifferent interpretation of preference is brought to bear on thecomparison of options. The idea is that preferences, or judgments ofdesirability, may be responsive to a salience condition. For example,suppose that the most salient feature when comparing cars \(A\) and\(B\) is how fast they can be driven, and \(B\) is no worse than \(A\)in this regard, yet the most salient feature when comparing cars \(B\)and \(C\) is how safe they are, and that \(C\) is no worse than \(B\)in this regard.

Basic Concepts: Preference, Utility, and Probability

But of course, in mathematical and logical contexts, even such brief errors can be substantive and, to novices, confusing. It should be noted that probably no individual student will be confused by all of the potentially confusing errors I just mentioned. But, like the technically difficult passages mentioned above, the potentially confusing errors will require instructors to give some additional thought to the question of what sort of guidance they want to provide for their students as they work through this text. Obviously, such quantitative precision is only possible in problems in which all the numbers and probabilities are known ahead of time.

What is the best way to make decisions in uncertain situations?

• 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.
• Perhaps no such people exist (and Savage’s axiom P5 indeed makes clear that his result does not pertain to such people).Nevertheless, it seems a definition of comparative beliefs should notpreclude that such people, if existent, have strictcomparative beliefs.
• When a person makes a decision, their belief system, morals, values, social background, and even fears and uncertainty play a crucial role.
• Decision theory is an interdisciplinary area of study that concerns mathematicians, statisticians, economists, philosophers, managers, politicians, psychologists and anyone else interested in analyses of decisions and their consequences.
• Indeed, some of the most compelling counterexamples to EU axioms ofpreference rest on ethical considerations.

Economists have traditionally been skepticalof any talk of a person’s desires and beliefs that goes beyondwhat can be established by decision theory is concerned with examining the person’s preferences,which they take to be the only attitude that is directly revealed by aperson’s behaviour. For these economists, it is thereforeunwelcome news if we cannot even in principle determine thecomparative beliefs of a rational person by looking at herpreferences. Let us nonetheless proceed by first introducing basic candidateproperties of (rational) preference over options and only afterwardsturning to questions of interpretation.

In summary, decision theory offers a valuable framework for making informed decisions by considering the outcomes, probabilities, and utilities. While it has limitations, especially related to human behavior and data uncertainty, its principles can be applied across a range of contexts to improve both strategic planning and everyday decision-making. To apply decision theory, the business would first identify the possible outcomes and then estimate the likelihood (probability) of each. The next step would involve assessing the value (or utility) of the outcomes, taking into account both the expected benefits (like increased sales) and costs (such as investment and operational costs).

AI-Driven Decision-Making Models

• Then there is a desirability measure on \(\Omega\setminus \bot \) and a probability measure on \(\Omega\) relative towhich \(\preceq\) can be represented as maximising desirability.
• Forinstance, any event \(F\) can be partitioned into two equiprobablesub-events according to whether some coin would come up heads or tailsif it were tossed.
• But as we will see, Jeffrey’s theory haswell-known problems of its own, albeit problems that are notinsurmountable.
• For instance, it may be that Bangkok isconsidered almost as desirable as Cardiff, but Amsterdam is a long waybehind Bangkok, relatively speaking.
• For personal decisions, simple weighted lists of pros and cons, considering different outcomes and their likelihoods, can help individuals make more considered and rational choices.

Then assuming that thedesirability of the prize (and similarly the desirability of no prize)is independent of how the coin lands, your preference between the twolotteries should be entirely determined by your comparative beliefsfor the two ways in which the coin can land. For instance, if youstrictly prefer the first lottery to the second, then that suggestsyou consider heads more likely than tails. Decision theory is concerned with the reasoning underlying anagent’s choices, whether this is a mundane choice between takingthe bus or getting a taxi, or a more far-reaching choice about whetherto pursue a demanding political career. (Note that “agent”here stands for an entity, usually an individual person, that iscapable of deliberation and action.) Standard thinking is that what anagent chooses to do on any given occasion is completely determined byher beliefs and desires or values, but this is not uncontroversial, aswill be noted below. In any case, decision theory is as much a theoryof beliefs, desires and other relevant attitudes as it is a theory ofchoice; what matters is how these various attitudes (call them“preference attitudes”) cohere together. From the perspective of decision-making, unawareness of unawareness isnot of much interest.

Future Directions in Decision Theory

This kind of information about therelative distance between options, in terms of strength of preferenceor desirability, is precisely what is given by an interval-valuedutility function. There are several tools and platforms available that can assist in automating decision-making processes. For instance, GiniMachine is an AI-powered decision management platform that can process terabytes of historical data, building, validating, and deploying predictive models in minutes. Other tools like Rationale AI assist in making tough decisions by providing pros and cons, SWOT analysis, multi-criteria analysis, or causal analysis.

Using this information, decision theory models—such as decision trees or utility theory—can help the business evaluate the expected utility of investing versus not investing, guiding them toward the decision expected to offer the greatest overall benefit. As noted in Section 4, criticisms of the EU requirement of a complete preference orderingare motivated by both epistemic and desire/value considerations. Onthe value side, many contend that a rational agent may simply find twooptions incomparable due to their incommensurablequalities. (Here a prominent usage of these terms will be followed,whereby particular options may be described as incomparable in value,while general properties or dimensions of value may be described asincommensurable.) As in, the agent’s evaluations of thedesirability of sure options may not be representable by any preciseutility function. Likewise, on the belief side, some contend (notably,Joyce 2010 and Bradley 2017) that the evidence may be such that itdoes not commit a rational agent to precise degrees of beliefmeasurable by a unique probability function.

Individuals can use decision-making models to weigh the pros and cons of different alternatives and make informed decisions. This decision analysis theory analyzes the repercussions of ideal logical decisions based on a set of values. Instead, it deals with expected behavior, decision-making processes, and the best potential outcome. This theory employs tools, procedures, and computer applications to arrive at an optimal decision. The static model has familiar tabular or normalform, with each row representing an available act/option, and columnsrepresenting the different possible states of the world that yield agiven outcome for each act. The sequential decision model, on theother hand, has tree or extensive form (such as in Figure 1).

Decision trees are a supervised learning algorithm used for classification and regression modeling. They enable developers to analyze the possible consequences of a decision, and as an algorithm accesses more data, it can predict outcomes for future data. Decision theory is a multidisciplinary field that combines insights from economics, philosophy, psychology, and statistics to understand how individuals make decisions. Counterfactuals play a crucial role in decision theory, as they enable individuals to evaluate the potential consequences of different alternatives.

Bradley and Stefánsson (2017) also develop a new decisiontheory partly in response to the Allais paradox. But unlike Buchak,they suggest that what explains Allais’ preferences is that thevalue of wining nothing from a chosen lottery partly depends on whatwould have happened had one chosen differently. To accommodate this,they extend the Boolean algebra in Jeffrey’s decision theory tocounterfactual propositions, and show that Jeffrey’sextended theory can represent the value-dependencies one often findsbetween counterfactual and actual outcomes.

2 On rational desire

For instance, theaforementioned authors considered and characterised preferences thatexhibit exponential time discounting. This disanalogy is due to the fact that there is nosense in which the \(p_i\)s that \(p\) is evaluated in terms of needto be ultimate outcomes; they can themselves be thought of asuncertain prospects that are evaluated in terms of their differentpossible realisations. In most ordinary choice situations, the objects of choice, over whichwe must have or form preferences, are not like this.

When a person makes a decision, their belief system, morals, values, social background, and even fears and uncertainty play a crucial role. Uncertainties such as states, repercussions, and behaviors cause people to choose one option. As the reader will recall, Savage takes for granted a set of possibleoutcomes \(\bO\), and another set of possible states of the world\(\bS\), and defines the set of acts, \(\bF\), as the set of allfunctions from \(\bS\) to \(\bO\).

When the set of outcomes corresponding to any given decision is not known, we refer to this situation as decision under uncertainty, the field of study which dominates decision theory. Decision theory is not only a theory of choice but also a theory of beliefs, desires, and other relevant attitudes. The theory has practical implications for actions, inferences, and valuing, and it addresses challenges to traditional expected utility (EU) theory. Decision theory can also be applied to personal decision-making, such as career choices and life planning.

It is a branch of applied probability theory and analytic philosophy that involves assigning probabilities to various factors and numerical consequences to outcomes. The theory is concerned with identifying optimal decisions, where optimality is defined in terms of the goals and preferences of the decision-maker. Finally, decision theory should be of great interest to philosophersof mind and psychology, and others who are interested in how peoplecan understand the behaviour and intentions of others; and, moregenerally, how we can interpret what goes on in other people’sminds. But on an optimisticreading of these results, they assure us that we can meaningfully talkabout what goes on in other people’s minds without much evidencebeyond information about their dispositions to choose. Richard Jeffrey’s expected utility theory differs fromSavage’s in terms of both the prospects (i.e., options)under consideration and the rationality constraints onpreferences over these prospects. The distinct advantage ofJeffrey’s theory is that real-world decision problems can bemodelled just as the agent perceives them; the plausibility of therationality constraints on preference do not depend on decisionproblems being modelled in a particular way.