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.
It’s time to build
- Now, Savage’s theory is neutral about how to interpret thestates in \(\bS\) and the outcomes in \(\bO\).
- Bradley and Stefánsson (2017) also develop a new decisiontheory partly in response to the Allais paradox.
- 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.
Economists have traditionally been skepticalof any talk of a person’s desires and beliefs that goes beyondwhat can be established by 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.
Human vs. AI Decision-Making
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.
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. The above result may seem remarkable; in particular, the fact that aperson’s preferences can determine a unique probability functionthat represents her beliefs. On a closer look, however, it is evidentthat some of our beliefs can be determined by examining ourpreferences. Suppose you are offered a choice between two lotteries,one that results in you winning a nice prize if a coin comes up headsbut getting nothing if the coin comes up tails, another that resultsin you winning the same prize if the coin comes up tails but gettingnothing if the coin comes up heads.
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.
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 theory is concerned with 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.
Employment and Human Skills
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.
Is there anyprobability \(p\) such that you would be willing to accept a gamblethat has that probability of you losing your life and probability\((1-p)\) of you gaining $10? However,the very same people would presumably cross the street to pick up a$10 bill they had dropped. But that is just taking a gamble that has avery small probability of being killed by a car but a much higherprobability of gaining $10! More generally, although people rarelythink of it this way, they constantly take gambles that have minusculechances of leading to imminent death, and correspondingly very highchances of some modest reward. 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. Peterson also provides some helpful sections on the influence of game theory on evolutionary theory and ethical theory.
2 On rational desire
Companies use the decision theory in operation research because it considers several outcomes, rational reasoning, and influencing factors to understand how a person thinks logically rather than idealistically. Decision theory refers to a range of econometric and statistical tools for analyzing an individual’s choices. In other words, it lets the entity make the best logical decision possible when dealing with uncertain and unknown circumstances. It can actually be seen as a weak version ofIndependence and the Sure Thing Principle, and it plays a similar rolein Jeffrey’s theory.
Types of Decision-Making: Under Certainty, Risk, and Uncertainty
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 theory provides a number of suggestions for how to estimate complex probabilities under uncertainty, most of which are derived from Bayesian inference. AI technologies such as machine learning, natural language processing, and computer vision are trusted aspects of business today, used to increase profits and reach set goals. Decision automation relies on prescriptive or predictive analytics, benefiting from its scalability, speed, and consistency in decision-making.
- Moreover, he complements his technical expertise with broad philosophical perspective, frequently commenting on the philosophical meanings, bases, and objections that are pertinent to the various models and principles of decision theory.
- It would have beenbetter were he able to sail unconstrained and continue on home toIthaca.
- In effect, Non-Atomicityimplies that \(\bS\) contains events of arbitrarily small probability.It is not too difficult to imagine how that could be satisfied.
Frequently Asked Questions (FAQs)
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. Perhaps there is always a way to contrive decision models such thatacts are intuitively probabilistically independent of states. Recall that Savage was tryingto formulate a way of determining a rational agent’s beliefsfrom her preferences over acts, such that the beliefs can ultimatelybe represented by a probability function. If we are interested inreal-world decisions, then the acts in question ought to berecognisable options for the agent (which we have seen isquestionable). Moreover, now we see that one of Savage’srationality constraints on preference—the Sure ThingPrinciple—is plausible only if the modelled acts areprobabilistically independent of the states.
Intertemporal choice
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.