It requires significant investment and expertise to develop, implement, and maintain, and poses technical and operational risks. AI systems can help eliminate human biases in decision-making, provided they are trained on unbiased data. However, if the training data contains biases, the AI system can perpetuate or even amplify these biases, leading to unfair decisions. AI systems that have access to more data can perform better, especially if the data is personal, as it allows for more personalized predictions.
- 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.
- However, the ingredients and structure of his theoremwill be laid out, highlighting its strengths and weaknesses.
- Brown (2011) and Dietrich andList (2017) demonstrate that in fact the choice-theoreticrepresentation of ethical theories better facilitates distinctionsbetween them; terms like “(non)consequentialism” can beprecisely defined, albeit in debatable ways.
- The orthodox normative decisiontheory, expected utility (EU) theory, essentially says that,in situations of uncertainty, one should prefer the option withgreatest expected desirability or value.
- The central goal of rational choice theory is to identify the conditions under which a decision maker’s beliefs and desires rationalize the choice of an action.
That seems veryreasonable if we can assume separability between outcomes indifferent states of the world; i.e., if the contribution that anoutcome in one state of the world makes towards the overall value ofan option is independent of what other outcomes the option mightresult in. For then identical outcomes (with equal probabilities)should cancel each other out in a comparison of two options, whichwould entail that if two options share an outcome in some state of theworld, then when comparing the options, it does not matter what thatshared outcome is. Even if we suspend doubts about the basic commitments of prominentversions of EU theory (which will be taken upin Section 5), there is a large question as towhat the theory really establishes about how agents should reason inthe real world. This section begins with the negative perspective, byconsidering the gaps left open by EU theory regarding rationalpreference attitudes. The positive perspective will then be discussed, inparticular the substantial contribution that EU theory makes, not justto questions of choice or practical rationality, but also toepistemology and value theory. Theorem 4 (Bolker)Let \(\Omega\) be a complete and atomless Boolean algebra ofpropositions, and \(\preceq\) a continuous, transitive and completerelation on \(\Omega \setminus \bot \), that satisfies Averaging andImpartiality.
Multi-Criteria Decision Analysis (MCDA) is an extension of Decision Theory that considers multiple conflicting criteria when making decisions. This approach is particularly valuable in situations where trade-offs are necessary, such as environmental assessments or project evaluations. MCDA techniques help decision-makers systematically evaluate alternatives based on various criteria, enabling them to arrive at more balanced and informed conclusions. Decision Theory has a wide range of applications across various fields, including finance, healthcare, marketing, and artificial intelligence. Marketers utilize Decision Theory to optimize advertising strategies and consumer targeting.
- Expected utility theory has been criticised for not allowing forvalue interactions between outcomes in different, mutuallyincompatible states of the world.
- This brings us to the Transitivity axiom,which says that if an option \(B\) isat least as preferable as \(A\),and \(C\) is at least as preferableas \(B\), then \(A\) cannot be strictly preferred to \(C\).
- Is there anyprobability \(p\) such that you wouldbe willing to accept a gamble that has that probability of you losingyour life and probability \((1-p)\)of you winning $10?
- Nevertheless, it seems a definition of comparative beliefsshould not preclude that such people, if existent, have comparativebeliefs.
- Every time we go for a walk,drive our car, fly somewhere, and so on, there is some chance of ushaving a fatal accident.
Intertemporal choice
The aim is to characterise theattitudes of agents who are practically rational, and various (staticand sequential) arguments are typically made to show that certainpractical catastrophes befall agents who do not satisfy standarddecision-theoretic constraints. In particular, normativedecision theory requires that agents’ degrees of beliefs satisfythe probability axioms and that they respond to new information byconditionalisation. decision theory is concerned with Therefore, decision theory has great implicationsfor debates in epistemology and philosophy of science; that is, fortheories of epistemic rationality.
3 The von Neumann and Morgenstern (vNM) representation theorem
Nevertheless, Lewis’ argument nodoubt provoked an interesting debate about the sorts of connectionsbetween belief and desire that EU theory permits. There are, moreover,further questions of meta-ethical relevance that one might investigateregarding the role and structure of desire in EU theory. For instance,Jeffrey (1974) and Sen (1977) offer some preliminary investigations asto whether the theory can accommodate higher-orderdesires/preferences, and if so, how these relate to first-orderdesires.
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. 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 utility10 proved that expected utility maximization followed from basic postulates about rational behavior. 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. Bayesian Decision Theory incorporates Bayes’ theorem to update the probabilities of outcomes as new information becomes available.
Alternatives to probability theory
On a closer look, however, it is evidentthat some of our beliefs can be determined by examining ourpreferences. The only information contained in an ordinal utility representation ishow the agent whose preferences are being represented orders options,from least to most preferable. This means that if \(u\) is an ordinalutility function that represents the ordering \(\preceq\), then anyutility function \(u’\) that is an ordinal transformation of\(u\)—that is, any transformation of \(u\) that also satisfiesthe biconditional in (1)—represents \(\preceq\) just as well as\(u\) does. Hence, we say that an ordinal utility function isunique only up to ordinal transformations. Let us conclude by summarising the main reasons why decisiontheory, as described above, is of philosophical interest.
Formalizing and modeling different decision-making scenarios in AI involves a combination of decision theory, machine learning techniques, and AI-driven decision-making models. These models can be used to make more precise and valuable decisions, streamline processes, and enhance decision-making initiatives. Under the first description, where the status quo is $300, people see themselves as trying to secure an additional gain, and so opt for the safe alternative. Under the second description, where the status quo is $500, people see themselves avoiding losses, and so incline toward the risky choice.
What is the best way to make decisions in uncertain situations?
It alsoensures, as the name suggests, that a sufficiently rich preferenceordering over lotteries can be represented by a continuous cardinalfunction. When these conditions are met, the agent’s goals and values affect her decision only via her desires for consequences, and her beliefs influence her choice via her uncertainty about which state obtains. The agent will use her beliefs about states to select an act that provides the best means for securing a desirable consequence. A similar “dynamic consistency” argument can be used todefend EU preferences in addition to learning in accordance withconditionalisation (see Hammond 1976, 1977, 1988b,c). It is assumed,as before, that the agent takes a sophisticated approach to sequentialdecision problems.
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. 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. We first describe theprospects or decision set-up and the resultant expected utility rule,before turning to the pertinent rationality constraints on preferencesand the corresponding theorem.
It’s time to build
Instead of adding specific belief-postulates to Jeffrey’s theory,as Joyce suggests, one can get the same uniqueness result by enrichingthe set of prospects. In our continuing investigation of rational preferences overprospects, the numerical representation(or measurement) of preference orderings will becomeimportant. 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 sequential decision model, on theother hand, has tree or extensive form (such as in Figure 1). It depicts a series of anticipated choice points, where the branchesextending from a choice point represent the options at that choicepoint. Some of these branches lead to further choice points, oftenafter the resolution of some uncertainty due to new evidence.
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. Uncertainty is a key aspect of decision theory, and it can refer to unknown states of the world, probabilities, or the consequences of decisions in terms of payoffs or losses. Decision theory offers tools to handle uncertainty, such as probabilistic models and the assessment of objectives given specified decision criteria. For theoretical purposes, it is useful to idealize the decision setting by assuming that the repertoire of actions is rich.
This entry will focus on rational choice theory for the single agent, but some descriptive results will be mentioned in passing. 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).