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Summary

Megan, Joe and Nick have decided to spend the summer holiday together. Unfortunately, they disagree on where to go. The set of alternatives includes Acapulco (a), Belize (b) and Cape Cod (c). Everyone in the group agrees that it would be fair to make the decision by voting, and their preferences are as follows.

Megan prefers a to b, and b to c. (a ≻ b ≻ c)

Joe prefers b to c, and c to a. (b ≻ c ≻ a)

Nick prefers c to a, and a to b. (c ≻ a ≻ b)

It seems plausible to maintain that, conceived of as a group, the friends prefer a to b, because in a pairwise choice a will get two votes (from Megan and Nick) whereas b will get just one (from Joe). Furthermore, the group prefers b to c, because b will get two votes (from Megan and Joe) and c one (from Nick). Finally, the group also prefers c to a, because c will get two votes (from Joe and Nick) and a one (from Megan). However, by now the voting rule has produced a cyclic preference ordering: a is preferred to b, and b to c, and c to a. This holds true although none of the individual preference orderings is cyclic.

The observation that the majority rule can give rise to cyclic preference orderings is not a novel discovery. This point was extensively analyzed already by the French nobleman Marquis de Condorcet in the eighteenth century. Nowadays this result is known as the voting paradox. It serves as a classic illustration of the difficulties that arise if a group wishes to aggregate the preferences of its individual members into a joint preference ordering. Evidently, if group preferences are cyclic, they cannot be choice guiding. (But why not roll a die and let chance make the decision? Answer: This does not explain why one option is better than another. It can hardly be better to spend the summer in Acapulco because a die landed in a certain way on a particular occasion.)

Summary

The focus of this chapter is on the role of causal processes in decision making. In some decision problems, beliefs about causal processes play a significant role in determining what we intuitively think it is rational to do. However, it has turned out to be very difficult to give a convincing account of what role beliefs about causal process should be allowed to play. Much of the discussion has focused on a famous example known as Newcomb's problem. We shall begin by taking a look at this surprisingly deep problem.

Newcomb's Problem

Imagine a being who is very good at predicting other people's choices. Ninety-nine percent of all predictions made by the being so far have been correct. You are offered a choice between two boxes, B1 and B2. Box B1 contains $1,000 and you know this, because it is transparent and you can actually see the money inside. Box B2 contains either a million dollars or nothing. This box is not transparent, so you cannot see its content. You are now invited to make a choice between the following pair of alternatives: You either take what is in both boxes, or take only what is in the second box. You are told that the predictor will put $1 million in box B2 if and only if she predicts that you will take just box B2, and nothing in it otherwise. The predictor knows that you know this. Thus, in summary, the situation is as follows. First the being makes her prediction, then she puts either $1 million or nothing in the second box, according to her prediction, and then you make your choice. What should you do?

Alternative 1 Take box B1 ($1,000) and box B2 (either $0 or $1 m).

Alternative 2 Take only box B2 (either $0 or $1 m).

This decision problem was first proposed by the physicist William Newcomb in the 1960s. It has become known as Newcomb's problem, or the predictor's paradox. Philosopher Robert Nozick was the first author to discuss it in print. (According to legend, he learned about the problem from a mutual friend of his and Newcomb's at a dinner party.) Nozick identified two different, but contradictory, ways of reasoning about the problem.

Summary

The following decision problem appeared some years ago in Marilyn vos Savant's Ask Marilyn column in Parade Magazine.

You are a contestant in a game show hosted by Monty Hall. You have to choose one of three doors, and you win whatever is behind the door you pick. Behind one door is a brand new car. Behind the other two is a goat. Monty Hall, who knows what is behind the doors, now explains the rules of the game: “First you pick a door without opening it. Then I open one of the other doors. I will always pick a door to reveal a goat. After I have shown you the goat, I will give you the opportunity to make your final decision whether to stick with your initial door, or to switch to the remaining door.” Should you accept Monty Hall's offer to switch?

The Monty Hall problem has a simple and undisputable solution, which all decision theorists agree on. If you prefer to win a brand new car rather than a goat, then you ought to switch. It is irrational not to switch. Yet, a considerable number of Marilyn vos Savant's readers argued that it makes no difference whether you switch or not, because the probability of winning the car must be 1/3 no matter how you behave. Although intuitively plausible, this conclusion is false.

The point is that Monty Hall's behavior actually reveals some extra information that makes it easier for you to locate the car. To see this, it is helpful to distinguish between two cases. When you make your initial choice, the door you select either has a goat or the car behind it. In the first case, you pick a door with a goat behind it. This leaves two doors: one with a goat and the other with the car. Since only one of the remaining doors has a goat, Monty Hall must open that door.

Summary

“Daoism” has been used to denote a range of quite different areas of focus, ideas and debates across different periods of time. The English term “Daoism” has been used to identify different groups, practices or doctrines that incorporate at some level the notion of dao (way, path). However, the criteria for inclusion are sometimes obscure and arbitrary. We briefly consider the varied meanings of the term “Daoism” before discussing some key themes in one of its basic texts, the Daodejing (also referred to as the Laozi, bearing the name of its alleged author). We consider the terms dao, de (potency), ziran (nature, spontaneity) and wuwei (unconditioned action) as well as some distinctive features of Daoist thought. We will also draw on some of these insights to consider their relevance to issues in contemporary philosophical debates.

In traditional scholarship, Daoism has often been juxtaposed against Confucianism, sometimes as if it was a negative reaction to the latter. Differences between the traditions and their ideas were first expressed during the pre-Han period, for example, in the Lüshi Chunqiu, where Confucius is said to have learnt from a “Lao Dan,” believed to be Laozi (Graham 1998: 28). In the Shiji (Records of the Grand Historian), Confucius, overawed by Laozi, describes him as a dragon (Shiji 63). Similar stories are found in the Zhuangzi and the Record of Rites (Li Ji) (Graham 1998: 25, 26). In the Zhuangzi, Confucius is sometimes caricatured as lacking in deeper, Daoist wisdom which embraces flexible and skilful responsiveness. As we cover the ideas associated with Daoism below, we need to be mindful that many of the ideas had developed and evolved through time in the hands of different thinkers, and at times were entangled with political motivations. For example, the hostility between Daoism and Confucianism may have been due in part to the way they were brought together by Han historiographers to justify their ideologies and secure their positions (Loewe 1999; Lloyd 2002: 126–47).

The Philosophy and Practice of the Daojia

This section outlines Daoism, understood as the philosophy and practice of the Daojia (Daoist-group), with sections on Huang-Lao Daoism and Lao-Zhuang, or “philosophical Daoism” to follow.

Summary

Philosophers disagree about what probability is. Somewhat roughly put, there are three camps in this debate, objectivism, subjectivism and the epistemic approach. Objectivists maintain that probability statements refer to some facts in the external world. If you claim that the probability is fifty percent that the coin I hold in my hand will land heads up when tossed, then you are – according to the objectivist – referring to a property of the external world, such as the physical propensity of the coin to land heads up about every second time it is tossed. From an intuitive point of view, this seems to be a very plausible idea. However, subjectivists disagree with this picture. Subjectivists deny that probability statements can be understood as claims about the external world. What is, for instance, the probability that your suitor will ask you to marry him? It seems rather pointless to talk about some very complex propensity of that person, or count the number of marriage proposals that other people make, because this does not tell us anything about the probability that you will be faced with a marriage proposal. If it is true that the probability is, say, 1/2 then it is true because of someone's mental state.

According to the subjective view, probability statements refer to the degree to which the speaker believes something. When you say that the probability is 1/2 that your suitor will make a marriage proposal, this merely means that you believe to a certain degree that this proposal will be made, and the strength of your belief can be represented by the number 1/2; and if you were to start thinking that it was absolutely certain that you would get the offer, your subjective degree of belief would be 1. The scope of the subjective analysis can easily be extended to all kinds of examples, because virtually any probability statement can be interpreted as a claim about the speaker's subjective degree of belief. For instance, when you say that the probability is 1/2 that the coin will land heads up next time it is tossed, you are essentially referring to your subjective degree of belief that that event will occur.

Summary

During the fourth century B.C. it began to occur to the Chinese that words move in a world of their own, a region connected only in the most casual and precarious way with the world of reality … Now there were particular reasons, connected with the history and character not only of the Chinese language, but also of the script, which made this rift between language and actuality not merely a subject of detached philosophic enquiry … but a burning question of the day.

(Waley, The Way, 1958: 59–60)

Arthur Waley calls this phenomenon “The Language Crisis.” His description suggests it was as though a wave of consciousness had spread among the thinkers in China. The early thinkers questioned the nature of language and its connection with the world. Putting aside the concern about the accuracy of Waley's account of this phenomenon, we note that he rightly points out that there is a peculiarity in the Chinese language that complicates issues of language–world correspondence. It was important to many of the early thinkers to consider how each Chinese character (or name, ming) picked out entities or phenomena, or aspects of the world. The thinkers were also perplexed by the question of how, when two characters were combined to form a compound name, it was possible systematically to pick out the correct referents of the compound names. For example, what do “狗” (gou, dog) and “小” (xiao, small) pick out, and what does “小狗” (xiaogou) pick out? Were there regularities or patterns to these changes? Both the Confucian theory of correcting names (zhengming) and the Mohist preoccupation with standards (fa) involved some thought about how correct application of names might help to establish norms and thus bring order to society. In contrast, thinkers associated with the Daodejing advocated caution about the conventionality of language and its potentially manipulative power. The debates about names extended over a range of philosophical areas that we may think of as being loosely aligned with metaphysics, epistemology and philosophy of language. The discussions of the Mingjia (Disputers concerned with names) and the Later Mohist thinkers were not fully appreciated by thinkers of the Warring States period and long after.

Summary

Over the last two decades, interest in Chinese philosophy has grown significantly among Anglophone scholars, students and interested lay public: more excellent translations of original texts have been produced; scholarly journals highlighting the field established; successful international conferences organised; and monographs and anthologies published. The field has broadened in its engagement across disciplinary boundaries, in studies that bring together philosophical perspectives with historical, archaeological, religious or anthropological approaches. Just as important, dialogue across Western and Chinese philosophical traditions is burgeoning, fuelled in part by the conviction that Chinese philosophy can make significant and insightful contributions to contemporary debates.

An Introduction to Chinese Philosophy examines major philosophical concepts, themes and texts in early Chinese philosophy, paying special attention to the period between the fifth and the second centuries BCE, the earliest time from which we have a substantial collection of texts expressing a plethora of views. We may think of this period as one where we begin to see the origins of Chinese philosophy. The extant texts from this period incorporate key elements of philosophy: presentation of and reflection on worldviews, unmasking of assumptions, argumentation and justification of ideas and debates on values and ideals. The primary aim of this book is to introduce a representative overview of key philosophical ideas and debates proposed by thinkers of the time and which continue to be relevant today. Some attempt is made to compare the features of Chinese philosophy with parallel aspects of Western philosophy. However, the aim of such comparisons is to elucidate the characteristics of Chinese philosophy rather than to present and account for differences in the two fields.

This book is introductory in a few ways. First, it covers representative ideas, themes and debates so that these fundamental aspects of Chinese philosophy may inform further investigations into more complex and lesser-known areas. Second, it seeks to capture the spirit of the classical Chinese texts, but it cannot replace close reading of these texts. Good translations are available of many texts and recommendations are included in the list of suggested readings at the end of each chapter. If it is not possible to read more complete translations of the texts, readers should at least obtain a reliable compendium of primary sources such as William Theodore de Bary and Irene Bloom's Sources of Chinese Tradition (vol. 1: 1999).

Summary

The Yijing (The Book of Changes) incorporates sections that date from around the ninth century BCE. The older layer of the text, known as the “Basic Text” (Ben Jing), has traditionally been associated with divination. This older layer comprises:

Summary

Jane is having a romantic dinner with her fiancé in a newly opened French bistro in Santa Barbara, California. After enjoying a vegetarian starter, Jane has to choose a main course. There are only two options on the menu, Hamburger and Lotte de mer. Jane recalls that Lotte de mer means monkfish, and she feels that this would be a nice option so long as it is cooked by a first-class chef. However, she has some vague suspicions that this may not be the case at this particular restaurant. The starter was rather poor and cooking monkfish is difficult. She knows that almost every chef can make a decent hamburger.

Jane feels that she cannot assign any probability to the prospect of getting good monkfish. She simply knows too little about this newly opened restaurant. Because of this, she is in effect facing a decision under ignorance. In decision theory ignorance is a technical term with a very precise meaning. It refers to cases in which the decision maker (i) knows what her alternatives are and what outcomes they may result in, but (ii) is unable to assign any probabilities to the states corresponding to the outcomes (see Table 3.1). Sometimes the term “decision under uncertainty” is used synonymously.

Jane feels that ordering a hamburger would be a safe option, and a hamburger would also be better than having no main course at all. Furthermore, she feels that good monkfish is better than an edible hamburger, but terrible monkfish is worse than having no main course. This ranking can be represented on an ordinal scale, as explained in Chapter 2. Since ordinal scales only preserve the order between objects, any set of numbers will do as long as better outcomes are represented by higher numbers. An example is given in Table 3.2.

Which alternative should Jane choose? To answer this question the decision maker has either to apply some decision rule or provide some other kind of structured reasoning for choosing one alternative over another. This chapter surveys some of the most influential rules for making decisions under ignorance.

Summary

The primary themes and argumentative strategies in Zhuangzi's (c. 399 BCE–c.295 BCE) philosophy bear some resemblance to those in the Daodejing. The Zhuangzi bears the name of its alleged author but, like the Daodejing, its sections were most probably composed by different authors, and the extant text contains writings collected over a period of time. Although some of its subject matter overlaps with that in the Daodejing, its style is quite different. It is inquisitive, being playful and critical at the same time, using many examples from the natural world – monkeys, fish, cicadas, frogs and summer insects, to name a few – to illustrate its questions. Because it often leaves its questions unresolved, it seems as if it is inviting readers to come to their own conclusions. Some of these characteristics of the text are reflected in its chapter titles, for example, chapter 1 is entitled “Going Rambling without a Destination” (“Xiaoyao You”) and chapter 4, “Worldly Business among Men” (“Renjian Shi”) (trans. Graham, Chuang-Tzu, 2001). Yet in spite of the seemingly light-hearted way in which the text brings up questions, the reader is always aware that it treats its questions with utmost seriousness.

The Zhuangzi dates from between the fourth to the second centuries BCE, and debate persists concerning when particular sections might have been written and by whom (Graham 2003a: 58). Traditionally, the two texts, the Daodejing and Zhuangzi, had been grouped as belonging to one tradition, the Lao-Zhuang tradition. There was also some consensus that the Daodejing was composed earlier than the Zhuangzi, and, as they stand in that relation, that the Daodejing is a less sophisticated text while the Zhuangzi represents a mature, developed Daoism. For example, Wing-tsit Chan notes:

The Dao in Laozi is still wordly, whereas in Zhuangzi it becomes transcendental. While Laozi emphasizes the difference between glory and disgrace, strength and weakness, and so forth, and advocates the tender values, Zhuangzi identifies them all. Laozi aims at reform, but Zhuangzi prefers to “Travel beyond the mundane world” … It is not wrong, after all, to link Laozi and Zhuangzi together, although it must be borne in mind that [Zhuangzi] certainly carried Daoism to new heights.

(Chan, Source Book, 1963a: 178; annotations by author)

Summary

This book is an introduction to decision theory. My ambition is to present the subject in a way that is accessible to readers with a background in a wide range of disciplines, such as philosophy, economics, psychology, political science and computer science. That said, I am myself a philosopher, so it is hardly surprising that I have chosen to discuss philosophical and foundational aspects of decision theory in some detail. In my experience, readers interested in specific applications of the subject may find it helpful to start with a thorough discussion of the basic principles before moving on to their chosen field of specialization.

My ambition is to explain everything in a way that is accessible to everyone, including readers with limited knowledge of mathematics. I therefore do my best to emphasize the intuitive ideas underlying the technical concepts and results before I state them in a more formal vocabulary. This means that some points are made twice, first in a nontechnical manner and thereafter in more rigorous ways. I think it is important that students of decision theory learn quite a bit about the technical results of the subject, but most of those results can no doubt be explained much better than what is usually offered in textbooks. I have tried to include only theorems and proofs that are absolutely essential, and I have made an effort to prove the theorems in ways I believe are accessible for beginners. In my experience, this sometimes comes into conflict with the ambition to present technical material in the minimalist style usually preferred by experts.

Most of the technical results are presented in twenty “boxes” clearly separated from the main body of the text. In principle, it should be possible to read the book without reading the boxes, although they hopefully deepen the student's understanding of the subject. I have also included over 100 exercises (and solutions), most of which should be fairly straightforward. Unlike other textbooks, no exercise asks the reader to prove some theorem I did not bother to prove myself. Finally, the Appendix contains a glossary in which I try to briefly explain some of the key terms and concepts. I believe the glossary might be particularly useful for readers wishing to study only a selected number of the chapters.

Summary

This chapter gives an overview of how people actually do make decisions. The headline news is that people frequently act in ways deemed to be irrational by decision theorists. This shows either that people should behave differently, or that there is something wrong with the normative theories discussed in the preceding chapters of this book. After reviewing the empirical findings, both conclusions will be considered.

The interest in descriptive decision theory arose alongside the development of normative theories. Given the enormous influence axiomatic theories had in the academic community in the latter half of the twentieth century, it became natural to test the axioms in empirical studies. Since many decision theorists advocate (some version of) the expected utility principle, it is hardly surprising that the axioms of expected utility theory are the ones most researched. Early studies cast substantial doubt on the expected utility principle as an accurate description of how people actually choose. However, it was not until 1979 and the publication of a famous paper by Kahneman and Tversky that it finally became widely accepted that expected utility theory is a false descriptive hypothesis. Kahneman and Tversky's paper has become one of the most frequently quoted academic publications of all time. (Kahneman was awarded the Nobel Prize in Economics in 2002, but Tversky had died a few years earlier.) In what follows, we will summarize their findings, as well as some later observations.

Observed Violations of the Expected Utility Principle

Kahneman and Tversky asked a group of 72 students to state a preference between prospect A and B below. It turned out that 82% of the participants preferred prospect B to A.

A: $2,500 with probability 0.33 B: $2,400 with certainty

$2,400 with probability 0.66

$0 with probability 0.01

It can be easily verified that the expected monetary value of prospect A is slightly higher than that of prospect B. However, this is of course not sufficient for concluding that the students are irrational. It cannot be excluded that they preferred B to A simply because their marginal utility is decreasing in the interval between $2,400 and $2,500. To make a stronger case against the expected utility principle, Kahneman and Tversky also asked the same group of students to state a preference between prospects C and D below.

Summary

Before you make a decision you have to determine what to decide about. Or, to put it differently, you have to specify what the relevant acts, states and outcomes are. Suppose, for instance, that you are thinking of taking out fire insurance on your home. Perhaps it costs $100 to take out insurance on a house worth $100,000 and you ask, “Is it worth it?” Before you decide, you have to get the formalization of the decision problem right. In this case, it seems that you face a decision problem with two acts, two states, and four outcomes. It is helpful to visualize this information in a decision matrix; see Table 2.1.

To model one's decision problem in a formal representation is essential in decision theory, because decision rules are only defined relative to a formal representation. For example, it makes no sense to say that the principle of maximizing expected value recommends one act rather than another unless there is a formal listing of the available acts, the possible states of the world and the corresponding outcomes. However, instead of visualizing information in a decision matrix it is sometimes more convenient to use a decision tree. The decision tree in Figure 2.1 is equivalent to the matrix in Table 2.1.

The square represents a choice node, and the circles represent chance nodes. At the choice node the decision maker decides whether to go up or down in the tree. If there are more than two acts to choose from, we simply adds more lines. At the chance nodes nature decides which line to follow. The rightmost boxes represent the possible outcomes. Decision trees are often used for representing sequential decisions, i.e. decisions that are divided into several separate steps. (Example: In a restaurant, you can either order all three courses before you start to eat, or divide the decision-making process into three separate decisions taken at three points in time. If you opt for the latter approach, you face a sequential decision problem.) To represent a sequential decision problem in a tree, one simply adds new choice and chance nodes to the right of the existing leaves.

Summary

It is hard to think of any minimally reasonable decision rule that totally ignores how much utility an act brings about. However, the concept of utility has many different technical meanings, and it is important to keep these different meanings apart. In Chapter 2 we distinguished three fundamentally different kinds of measurement scales. All scales are numerical, i.e. utility is represented by real numbers, but the information conveyed by the numbers depends on which type of scale is being used.

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13 - Social Choice Theory

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9 - Causal vs. Evidential Decision Theory

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Chronology

Glossary

6 - The Mathematics of Probability

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5 - Daoism and the Daodejing

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7 - The Philosophy of Probability

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Contents

6 - The Mingjia and the Later Mohists

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1 - Chinese Philosophy

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9 - The Yijing and Its Place in Chinese Philosophy

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3 - Decisions under Ignorance

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8 - The Zhuangzi

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Preface

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14 - Overview of Descriptive Decision Theory

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Contents

4 - Decisions under Risk

2 - The Decision Matrix

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Index

5 - Utility

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