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.

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.

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.

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• Forex Trading

March 4, 2021

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