# Decision Theories Definition & Meaning

But on an

optimistic reading of these results, they assure us that we can

meaningfully talk about what goes on in other people’s minds

without much evidence beyond information about their dispositions to

choose. According to Yudkowsky and Soares, standard decision theories are based on general arguments and brute intuitions. Moreover, they say, representation theorems reveal that the maximising of expected utility is derived from the basic constraints on rational preference and belief. Therefore, they reject the preference norms of the CDT and offer decision theory is concerned with a representation theorem for FDT. Arguably, defenders of resolute choice actually have in mind a

different interpretation of sequential decision models, whereby future

“choice points” are not really points at which an agent is

free to choose according to her preferences at the time. In what follows, thes standard interpretation of sequential decision models will be assumed, and moreover, it will be assumed that rational agents reason about

such decisions in a sophisticated manner (as per Levi 1991, Maher

1992, Seidenfeld 1994, amongst others).

We want to show its punctuated continuity with, and its debt to, the achievements of the past. Our debt, notwithstanding, we also draw contrasts between our engineering decision-design methods and other traditional methods. A number of experimental studies in the 1960s and 1970s subsequently

confirmed the robustness of the effects uncovered by Allais.

## 1 Was Ulysses rational?

In addition, it is an interdisciplinary field, encompassing economists, philosophers, computer scientists, and biologists. Probability theory is a fundamental mathematical concept that is used by statisticians and business analysts to understand the relationships between two simultaneous events. There are numerous applications of probability theory, from the study of the probability of a person winning the lottery to how the stock market works.

The Allais paradox, discussed in Section

2.3 above, is a classic example where the aforementioned

separability fails. For ease of reference, the options that generate

the paradox are reproduced as Table 3. Recall

from Section 2.3 that people tend to

prefer \(L_2\) over \(L_1\) and \(L_3\)

over \(L_4\)—an attitude that

has been called Allais’ preferences—in violation

of expected utility theory.

## Personal account

This analysis was popularized by Barry Schwartz in his 2004 book, The Paradox of Choice. In recent decades, there has been increasing interest in what is sometimes called ‘behavioral decision theory’ and this has contributed to a re-evaluation of what rational decision-making requires (see for instance Anand, 1993). When analyzing decision theory, the analysis often consists of what makes an optimal decision, who that optimal decision-maker may be, and how they can come to that decision. Discussing how people “ought” to make decisions in certain scenarios is part of this study as well.

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The vNM theorem effectively

shores up the gaps in reasoning by shifting attention back to the

preference relation. In addition to Transitivity and Completeness, vNM

introduce further principles governing rational preferences over

lotteries, and show that an agent’s preferences can be

represented as maximising expected utility whenever her preferences

satisfy these principles. The last section provided an interval-valued utility representation of

a person’s preferences over lotteries, on the assumption that

lotteries are evaluated in terms of expected utility. Why should we assume that people evaluate lotteries

in terms of their expected utilities? Theorem 2 (von Neumann-Morgenstern)

Let \(\bO\) be a finite set of outcomes, \(\bL\)

a set of corresponding lotteries that is closed under probability

mixture and \(\preceq\) a weak preference relation

on \(\bL\). Then \(\preceq\) satisfies axioms 1–4 if

and only if there exists a function \(u\), from

\(\bO\) into the set of real numbers, that is unique up to

positive linear transformation, and relative to which \(\preceq\) can

be represented as maximising expected utility.

## Normative Decision Theory

The sequential decision model, on the

other hand, has tree or extensive form (such as

in Figure 1). It depicts a series of anticipated

choice points, where the branches extending from a choice point

represent the options at that choice point. Some of these branches

lead to further choice points, often after the resolution of some

uncertainty due to new evidence. As noted in Section 4, criticisms of the

EU requirement of a complete preference ordering are motivated by both

epistemic and desire/value considerations. On the values side, many

contend that a rational agent may simply find two

options incomparable due to their incommensurable

qualities. Likewise, on the belief side, some contend (notably,

Joyce 2010) that the evidence may be such that it does not commit a

rational agent to precise beliefs measurable by a unique probability

function.

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Then it seems perfectly reasonable to prefer \(g\) over \(f\)

but \(f’\) over \(g’\). We

say that alternative \(f\)

“agrees with” \(g\) in

event \(E\) if, for any state in

event \(E\), \(f\) and \(g\) yield

the same outcome. Suppose, however, that there is probabilistic

dependency between the states of the world and the alternatives we are

considering, and that we find \(Z\) to be better than both \(X\) and

\(Y\), and we also find \(W\) to be better than both \(X\) and \(Y\). Moreover, suppose that \(g\) makes \(\neg E\) more likely than \(f\)

does, and \(f’\) makes \(\neg E\) more likely than \(g’\) does.

## Complex decisions

If the probability of retrieval is proportional to the similarity between cases, then the averaged case-based assessment constitutes the expectation of retrieved value. A good decision is a good choice given the alternatives at the time when a commitment and resources are pledged. The chronological separation, between commitment and outcomes, permits uncertainty to intervene, aleatory unpredictable conditions that can generate an unintended outcome. Normative decision theory is concerned with optimal decisions, where optimality is determined by the ideal, rational decision maker. In contrast, prescriptive decision theory focuses on explaining observed behaviors with conceptual models, while descriptive theory aims to analyze how individuals make decisions.

- Bayesian decision theory and traditional Game Theory share a common decision rule—maximizing expected utility—in decisions under risk—where the problem includes a well defined probability for all states of affairs.
- If she is lucky, she may have access to comprehensive weather

statistics for the region. - But unlike Buchak, they

suggest that what explains Allais’ preferences is that the value

of wining nothing from a chosen lottery partly depends on what would

have happened had one chosen differently. - Note that some of

these challenges to EU theory are discussed in more depth in

Section 5

below.

March 4, 2021