Automating decision-making processes can be achieved through the use of artificial intelligence (AI). AI can handle tasks such as anomaly detection, data crunching, complex analysis, and spotting trends, which can help businesses make faster, accurate, and consistent decisions. AI excels in consistency, focus, and attention to detail, which can outperform humans in specific decision-making tasks. However, humans are better at understanding context, exercising judgment, and critical thinking, particularly in nuanced situations. AI systems can help eliminate human biases in decision-making, provided they are trained on unbiased data.

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 two central concepts in decision theory are preferencesand prospects (or equivalently, options). Roughlyspeaking, when we (in this entry) say that an agent“prefers” the “option” \(A\) over \(B\) wemean that the agent takes \(A\) to be more desirable or choice-worthythan \(B\). Beyond this, there is room for argument aboutwhat preferences over options actually amount to, or in other words,what it is about an agent (perhaps oneself) that concerns us when wetalk about his/her preferences over options.

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.

• AI decision-making raises ethical questions, such as the extent to which AI should be allowed to make decisions without human oversight, and social issues, such as the impact of AI on employment and societal structures.
• AI lacks the ability to use human wisdom and discernment, and the goal of AI in decision making is not complete automation, but to help humans make quicker and better decisions through streamlined processes.
• On this reading, sequentialdecision models introduce considerations of rationality-over-time.

Financial Planning and Analysis (FP&A)

Let us conclude by summarising the main reasons why decision theory,as described above, is of philosophical interest. The aim is to characterise the attitudes of agents whoare practically rational, and various (static and sequential)arguments are typically made to show that certain practicalcatastrophes 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. Therefore, decision theory has great implicationsfor debates in epistemology and philosophy of science; that is, fortheories of epistemic rationality. Either way, it may yet be argued that EU theory does not go far enoughin structuring an agent’s preference attitudes so that we mayunderstand the reasons for these preference attitudes.Dietrich and List (2013 & 2016a) have proposed a more generalframework that fills this lacuna. In their framework, preferencessatisfying some minimal constraints are representable as dependent onthe bundle of properties in terms of which each option is perceived bythe agent in a given context.

3 The von Neumann and Morgenstern (vNM) representation theorem

• Some of therequired conditions on preference should be familiar by now and willnot be discussed further.
• Game theory occupies about a sixth of the book, with the principal topics being zero-sum games, the prisoner’s dilemma, Nash equilibrium strategy sets, and the Nash solution to bargaining problems.
• She will never choose a strategy that is worse by her ownlights than another strategy that she might otherwise have chosen, ifonly her preferences were such that she would choose differently atone or more future decision nodes.
• For these economists, it is thereforeunwelcome news if we cannot even in principle determine thecomparative beliefs of a rational person by looking at herpreferences.
• 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.
• This information suffices to ordinally representyour judgement; recall that any assignment of utilities is thenacceptable as long as \(C\) gets a higher value than \(B\) which getsa higher value than \(A\).

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.

Challenges to EU theory

Determinism posits that the universe is governed by laws and principles that predetermine the course of events. As noted, a special case is when the content of\(p\) is such that it is recognisably something the agent can chooseto make true, i.e., an act. The above problems suggest there is a need for an alternative theoryof choice under uncertainty. Richard Jeffrey’s theory, whichwill be discuss next, avoids all of the problems that have beendiscussed so far. But as we will see, Jeffrey’s theory decision theory is concerned with haswell-known problems of its own, albeit problems that are notinsurmountable.

Frequently Asked Questions (FAQs)

David Lewis (1988, 1996) famously employed EU theory to argueagainst anti-Humeanism, the position that we are sometimesmoved entirely by our beliefs about what would be good, rather than byour desires as the Humean claims. For instance,Broome (1991c), Byrne and Hájek (1997) and Hájek andPettit (2004) suggest formulations of anti-Humeanism that are immuneto Lewis’ criticism, while Stefánsson (2014) and Bradleyand Stefánsson (2016) argue that Lewis’ proof relies on afalse assumption. Nevertheless, Lewis’ argument no doubtprovoked an interesting debate about the sorts of connections betweenbelief and desire that EU theory permits. There are, moreover, furtherquestions of meta-ethical relevance that one might investigateregarding the role and structure of desire in EU theory.

Potential Applications in AI and Machine Learning

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 \(\bO\).

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.

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.

Now, Savage’s theory is neutral about how to interpret thestates in \(\bS\) and the outcomes in \(\bO\). 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. 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. Nevertheless, it does seem that an argument can be made that anyreasonable person will satisfy this axiom. Suppose you are indifferentbetween two propositions, \(p\) and \(q\), that cannot besimultaneously true. And suppose now we find a proposition \(r\), thatis pairwise incompatible with both \(p\) and \(q\), and which you findmore desirable than both \(p\) and \(q\).

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).