风险的跨学科视角

2006 · report · 原文约 2569 词

译文与英文原文逐段对齐可在本页展开英文，也可打开发布者原址核对上下文。

LEGG MASON 资产管理公司

LEGG MASON CAPITAL MANAGEMENT

August 15, 2006

迈克尔·J·莫布森跨学科视角下的风险 2006 年 7 月 26 日在格林威治圆桌会议上的演讲摘录

Michael J. Mauboussin Interdisciplinary Perspectives on Risk Excerpts from a presentation given to the Greenwich Roundtable, July 26, 2006

晚上好。这种圆桌会议总能激励我把一个重大主题的想法理清楚。今晚的话题——风险的多学科视角——尤其引人入胜，就算花上几天时间讨论也未必能说透。我只希望自己的发言能引发思考，提供一些视角。

Good evening. These roundtable meetings always encourage me to organize my thoughts on an important theme. This evening’s topic, an interdisciplinary perspective on risk, is particularly fascinating and we could spend days on it without doing it full justice. I only hope my comments serve to provoke thought and add some perspective.

我想把我的讲话分成三个部分：

I’d like to break my comments into three parts:

首先，我想强调一下经典的奈特式区别，即风险与不确定性之间的界线。我认为这种区分至今仍有价值，尤其是当我们思考如何管理风险的时候。

• First, I’d like to underscore the classic Knightian distinction between risk and uncertainty. I believe this distinction remains useful, especially when we think about how to manage risk.

• 其次，我将探讨风险与不确定性背后的一些机制。我会特别强调区分两类系统：一类是复杂系统中风险或不确定性源自内生（即内部）因素，另一类则是风险或不确定性由外生（即外部）因素引起。

• Second, I’ll discuss some of the mechanisms behind risk and uncertainty. I will place a particular emphasis on differentiating between complex systems where risk or uncertainty is endogenous, or internal, versus situations where risk or uncertainty is due to exogenous, or external, factors.

• 最后，我还会分享一些关于风险管理的想法，包括简要谈谈概率评估。

• Finally, I’ll share some thoughts about managing risk, including a brief look at probability assessment.

在日常语言，甚至在金融领域，人们往往把风险与不确定性混为一谈。但经济学家弗兰克·奈特（Frank Knight）在 1920 年代做出过一个区分，我觉得相当有用。他提出，风险描述的是这样一种系统：我们不知道结果，但我们知道结果背后的概率分布是什么样的。想象一下轮盘赌——当荷官转动轮盘时，你不知道球会落在哪里，但你确实知道所有可能的结果以及它们各自的概率。风险还包含了“损失”这个概念——也就是说，你是可能输钱的。

In our day-to-day language, and even in finance, people tend to use the terms risk and uncertainty interchangeably. But in the 1920s economist Frank Knight made a distinction that I find quite useful.1 He argued that risk describes a system where we don’t know the outcome, but we do know what the underlying probability distribution of outcomes looks like. So think of a roulette wheel—when the croupier spins the wheel, you don’t know where the ball will land, but you do know all the possibilities and their associated probabilities. Risk also incorporates the notion of harm—that is, you can lose.

相比之下，不确定性描述的是这样一种情形：你不仅不知道结果是什么，连底层系统的分布状况也不清楚。不确定性不一定意味着损害，尽管它常常如此。所以不难看出，现实世界中我们打交道的大多数系统其实是不确定的，而不是有风险的。用不确定性来描述恐怖主义、禽流感乃至市场之类的问题，更为贴切。

In contrast, uncertainty reflects a situation where you don’t know the outcome, but you also don’t know what the distribution of the underlying systems looks like. Uncertainty also doesn’t necessarily imply harm, although it often does. So it’s not hard to see that most systems we deal with in the real world are really uncertain, not risky. Uncertainty better describes issues like terrorism or the avian flu, or even markets.

下面我为什么强调这个区别：我们可以用概率演算来建模风险。事实上，风险的统计相对直接。相比之下，我们很难对不确定性建模。而当我们用风险的数学工具去建模不确定的系统时，真正的麻烦就来了。这恰恰是许多人在金融市场以及其他领域中做的事。我们稍后会回到风险或不确定性量化这个问题上。

Here’s why I’m stressing this distinction: we can model risk using probability calculus. In fact, the statistics of risk are relatively straightforward. In contrast, we can’t model uncertainty easily. And real trouble arises when we model uncertain systems using the mathematical tools of risk. Yet this is precisely what many people do in financial markets and in other domains as well. We’ll come back to this issue of risk or uncertainty quantification in a moment.

II.

现在我来谈第二个话题。过去十余年间，我有幸与圣塔菲研究所有所关联，这是一家致力于研究复杂系统的多学科研究机构。2 我与那里的科学家——包括物理学家、生物学家和网络理论家——的交流，促使我更深入地思考风险与不确定性背后的机制。坦率地说，目前这些机制实际上只能帮助描述正在发生什么，预测价值有限。3 但我相信，这些机制为理解复杂系统如何运作提供了洞见，也是我们应对这些系统的第一步。

Let me now turn to the second topic. Over the past decade or so, I’ve had the pleasure of being affiliated with the Santa Fe Institute, a multidisciplinary research institute dedicated to the study of complex systems. 2 My interaction with the scientists there—including physicists, biologists, and network theorists—has encouraged me to think much more about the mechanisms behind risk and uncertainty. To be frank, today these mechanisms can really only help describe what’s going on, and are of limited predictive value. 3 But I believe these mechanisms provide insights into how complex systems work, and a first step in how we might deal with them.

但让我先把一点说清楚：当我们谈论风险或不确定性时，我们不太关心那些乏味的事件——股市小幅波动或一场阵雨。我们关心的是极端事件——市场崩盘或毁灭性的飓风。这些极端事件是如何发生的？

But let me first be clear about a point: when we discuss risk or uncertainty, we’re not so much interested in the boring events—a small move in the stock market or a rain storm. We’re interested in the extreme events—a market crash or a devastating hurricane. How do these extreme events come about?

我发现一个有用的区分方法，是将风险分为内生和外生两大类（尽管前面做了区分，但在讨论中我会互换使用“风险”和“不确定性”这两个词）。顾名思义，内生风险产生于系统内部。内生风险是复杂系统固有的，但人们对它的理解仍然非常有限。我们将试着对此做一些说明。

A distinction I find useful is between endogenous and exogenous sources of risk (notwithstanding the prior distinction, I will use the terms risk and uncertainty interchangeably for discussion purposes). As the word implies, endogenous risk arises within the system. Endogenous risk is inherent in a complex system, yet remains poorly understood. We’ll try to shed some light on that.

当然，外生风险来自系统外部。它本质上是一种施加于系统之上的条件。

Exogenous risk, of course, comes from outside the system. It’s basically a condition imposed on a system.

我想从内生风险说起，它的本质具有跨学科属性。别担心，我会给出一些具体案例，把这些概念与现实世界联系起来。但为了充分呈现这一分析角度，我需要勾勒三种分析框架。

I’d like to start with endogenous risk, which is by its nature interdisciplinary. Don’t worry, I’ll offer some concrete examples to link these ideas to the real world. But to do this approach justice, I need to sketch out three frameworks.

第一个框架是“群体的智慧”，作家吉姆·苏罗维茨基几年前在他同名著作中精彩阐述过这一点。基本思想简单且有些反直觉：如果你召集一群来自不同背景的人一起解决问题，这个群体的答案通常比任何个体——哪怕是专家——都要好。群体的智慧是描述某种复杂适应性系统的一种更常见说法，这也是圣塔菲研究所工作的核心，并且是对股票市场的一个恰当描述。

The first framework is the wisdom of crowds, which writer Jim Surowiecki laid out well a couple of years ago in his book of the same title. 4 The basic idea is simple and somewhat counterintuitive: if you get a diverse group of people together to solve a problem, the group’s answer will typically be better than that of any individual, even an expert. The wisdom of crowds is a more common way of describing a type of complex adaptive system—the heart of the Santa Fe Institute’s work—and is an apt description of the stock market. 5

关键在于，群体只有在特定条件下才是明智的。你需要参与者多样性、一个聚合机制，以及某种激励。当这些条件中有一项或多项被违反时，一切就都不作数了。在人类系统中，多样性是最容易被违反的条件。当你消除多样性时，复杂系统会变得脆弱，某些情况下还会引发大规模变革。繁荣与崩盘就是市场中多样性崩塌的典型例子。潮流和风尚也说明了这一概念。而这引出了第二个框架：扩散理论。

The key is that the crowd is only wise under certain conditions. You need agent diversity, an aggregation mechanism, and some sort of incentives. When one or more of these conditions is violated, all bets are off. In human systems, diversity is the most likely condition to be violated. When you take away diversity, the complex system can become fragile and in some cases will lead to large-scale changes. Booms and crashes are good examples of diversity breakdowns in markets. Fads and fashions also illustrate the concept. And that leads to the second framework: diffusion theory.

技术、理念和疾病的传播，往往遵循 S 形曲线模式。6 因此，举例来说，一项新技术一开始只有少数使用者，早期增长速度相对缓慢。

Technologies, ideas, and illnesses tend to diffuse following an S-curve pattern. 6 So, for example, a new technology will start with only a few adopters, and will grow at a relatively slow rate early

这之后，速度开始加快，技术便进入爆发式增长。这个领域已被深入研究过，尤其受到流行病学家和技术专家的关注——仅举这两类人群。关键在于，增长率并非稳定不变：它起初较低，随后上升，接着又会放缓。同样重要的一点是，大多数技术或想法并不会扩散开——它们只是草草收场。

on. The rate then accelerates, and the technology takes off. This field has been studied in detail, and is of prime interest to epidemiologists and technologists, just to name two groups. The key point is the growth rate is not stable: it’s low to start, rises, and then slows down again. Also important is that most technologies or ideas don’t diffuse—they simply sputter out. 7

最终的框架是网络理论，也就是网络中的各个节点是如何相互连接的。

The final framework is network theory, or how the individual nodes in a network are connected.

网络理论涉及的现象极为广泛，从你的朋友圈、电网上的输电装置，到疾病的传播，无一不包。近年来，科学家们在理解网络本质方面取得了重大进展。我们现在已经认识到，网络的结构对于理解事物如何在网络上传播至关重要。

Network theory bears on a wide variety of phenomena, including your network of friends, transmitters on the power grid, or the spread of disease. In recent years, scientists have made major advances in understanding the nature of networks. We now know that the structure of the network is important in understanding how things get transmitted over the network. 8

这些框架有两个值得强调的特征。第一，它们是非线性的。例如，“群体智慧”的情形：你可以不断减少多样性，减少多样性，再减少多样性，一开始什么都不会发生。然后你再减少一点点，系统就会剧烈反应——正所谓压垮骆驼的最后一根稻草。你们很多人知道这个概念，叫“引爆点”。

There are two features of these frameworks worth emphasizing. First, they are non-linear. For example, in the case of the wisdom of crowds you can reduce diversity, reduce diversity, and nothing happens. Then you reduce it a bit more and the system reacts violently—the proverbial straw that broke the camel’s back. 9 Many of you know this idea as the tipping point. 10

这就引出了第二个特征：缺乏比例性。扰动的规模与结果之间并非总是存在关联。有时微小的扰动会导致巨大的后果，反之亦然。当你将非线性与缺乏比例性结合起来，就不难看出预测是困难的，而因果思维往往徒劳无益。

That leads to the second feature: lack of proportionality. The size of the perturbation and the outcome are not always linked. Sometimes small perturbations lead to large outcomes, and vice versa. 11 When you combine a lack of linearity with a lack of proportionality, it’s not hard to see that predictions are difficult and cause and effect thinking is often futile.

我来举两个例子，让这个概念更具体。

Let me discuss two examples to make this more tangible.

第一个例子来自市场，与长期资本管理公司（LTCM）有关。正如其创始人之一迈伦·舒尔茨所描述的，LTCM 利用统计套利来“吸镍币”（vacuum up nickels）。他们投资组合的一个核心要素是高度分散化：各个头寸之间的历史相关性非常低——在 10% 或以下。为了保守起见，LTCM 在其风险价值模型中假设相关性可能跃升至 30%，这远高于他们在历史数据中看到的任何水平。

The first is a market example, and deals with Long Term Capital Management (LTCM). LTCM used statistical arbitrage to “vacuum up nickels”, as one of the founders, Myron Scholes, described it. One essential component of their portfolio was that it was highly diversified: the correlations between the positions were historically quite low—10 percent or less. To be conservative, in their value at risk models LTCM assumed correlations could jump to 30 percent, vastly higher than anything they saw in their historical data.

然而，1998 年夏季却出现了真正的蔓延——一场规模空前的多样性崩溃。

However, the summer of 1998 saw a real contagion—a diversity breakdown of epic proportions.

尽管套利机会相当可观，却找不到任何套利者，而相关性则急剧攀升至大约 70%。把高相关性、杠杆以及资产价格下跌加在一起，故事就这样成了。 12

Notwithstanding the substantial arbitrage opportunities, there were no arbitrageurs to be found, and correlations rocketed higher, to about 70 percent. Add high correlations, leverage, and declining asset prices, and you have the story. 12

第二个例子是 2003 年 8 月东海岸的大停电事故。那次停电的起因是俄亥俄州一个相当常见的电力问题——这类问题在全国各地都相对频繁地发生。由于我们的国家电网是一个网络，某个点的故障通常会被邻近区域吸收。但在 2003 年，俄亥俄州向密歇根州索取电力，密歇根州无法承受便向加拿大索取电力，加拿大同样无法承受便向纽约索取电力。

The second example is the large East Coast blackout in August 2003. That blackout started with a fairly routine power problem in Ohio—a problem that happens relatively frequently all over the country. Since our national power grid is a network, a failure in one spot is typically absorbed by a neighboring area. In 2003, Ohio demanded power from Michigan, which couldn’t handle it so it demanded power from Canada, which couldn’t handle it so it demanded power from New York.

在这条链条上，情况不断恶化，最终演变为大范围停电。这是一个典型的级联失效案例。

All along the chain things got worse until we ended up with a widespread blackout. It was a classic example of a cascading failure. 13

这些例子中有几点值得强调。第一，结果与触发因素极不成比例。两起事件中，确实都存在引发最终结果的实际问题，但这些导火索完全算不上异常——异常的只有结果本身。

There are a couple of points worth underscoring in these examples. First, the outcomes were grossly out of proportion with the perturbation. In both cases, there were real issues that triggered the ultimate events, but those catalysts were not at all out of the ordinary—only the outcomes were.

其次，事件发生之后——1987 年的股灾也是如此——人们自然会去寻找因果联系并试图解决问题。正如我前边提到的，我们根本无法简单地理解其中的因果，而这些行为本身就是复杂系统的固有组成部分。只要这些系统存在，我们就难免会遭遇周期性的、灾难性的崩溃。

Second, after the events—and this is true of the crash of 1987 as well—people automatically seek to understand the cause and effect and to fix the problem. 14 As I mentioned a moment ago, there’s no way to understand cause and effect simply, and these behaviors are part-and-parcel of complex systems. As long as these systems exist, we will suffer periodic, catastrophic failures.

另一方面，这些系统为社会带来了很多好处，是解决问题的有效途径。

On the flip side, these systems bring a lot of good to society, and are a useful way to solve problems.

一个系统面临的另一类风险是外生性风险。当今的例子包括禽流感威胁、恐怖主义和飓风。虽然这些威胁中的每一种，单独来看，都可以被视为一个复杂系统，但我们通常认为这些事件是发生在我们身上的，而不是源于我们的日常活动。所以，当我们考虑灾难防范时，我们通常想的是外生性风险。

The other kind of risk a system faces is exogenous. Examples today include the threat of the avian flu, terrorism, and hurricanes. While each of these threats, viewed individually, can be treated as a complex system, we often think of events happening to us rather than arising from our day-to-day activities. So when we think about disaster preparedness, we’re often thinking of exogenous risks.

III.

让我以第三部分来收尾，提出一个问题：我们对此该怎么办？以下是一些想法——有些具有建设性，有些则令人担忧。

Let me wrap up with the third part of my comments by asking the question, what should we do about all of this? Here are some thoughts—some constructive, some concerning.

在积极的一面，值得注意的是，复杂系统的结果通常有一个特征——幂律分布。幂律——通俗来说就是 80/20 法则——表明大事件不常发生，而小事件则频繁出现。幂律的精妙之处在于，可以用一个特定的数学公式来表达这种关系。幂律描述了从战争死亡人数、地震规模、停电范围、股票价格变动、城市规模，到动物代谢率在内的广泛现象。15 即便具体的预测能力有限，了解这种统计特性也极为有用。

On the constructive side, it’s useful to note that the outcomes of complex systems often have a signature—a power law distribution. A power law—colloquially known as the 80/20 rule—says that large events happen infrequently and small events happen frequently. What’s elegant about power laws is there is a specific mathematical formula that can express this relationship. Power laws describe a wide range of phenomena, from deaths in wars, to earthquake sizes, to the size of blackouts, to stock price changes, to city sizes, to the metabolic rate of animals. 15 Awareness of the statistical properties, even with limited specific predictive ability, is very useful.

接下来，在建设性方面，我们现在有了所谓的预测市场，至少可以帮助我们评估各种事件的概率。这些是真金白银的市场，已被证明在预测经济和政治结果方面相当准确。让我读出今天早上（2006 年 7 月 26 日）我在市场中看到的一些概率：

Next, on the constructive side, we now have so-called prediction markets that can at least help us assess probabilities of various events. These are real-money markets that have proven quite accurate in predicting economic and political outcomes. 16 Let me read off some of the probabilities I found in the markets this morning (July 26, 2006): 17

2006 年 7 月 26 日事件发生概率（%） 2006 年 8 月 15 日事件发生概率（%）

Event Probability of Happening (%) as of July 26, 2006 as of August 15, 2006

至 2006 年 12 月 31 日美国确认禽流感病例	33	39
欧洲先于美国确认禽流感病例	88	85
至 2006 年 12 月 31 日禽流感疫苗	33	31
布什总统任内美国遭伊斯兰恐怖分子袭击	54	48
恐怖分子先袭击欧洲后袭击美国	69	70
2006 年大西洋飓风超过 9 个	43	39

Confirmed case of avian flu in U.S. by 12/31/06   33   39
Confirmed case of avian flu in E.U. before U.S.   88   85
Avian flu vaccine by 12/31/06   33   31
Islamic terrorists hit U.S. while Bush is president   54   48
Terrorists attack E.U. before U.S.   69   70
More than nine Atlantic hurricanes in 2006   43   39

自然，对分布和概率有一定了解，就能设计出某些保险形式或防范措施，用来抵御其中一种或多种事件。

Naturally, some understanding of the distributions and probabilities allows for forms of insurance, or preparedness, that can protect against one or more of these events.

但这引出了我的最后一个想法，而这个想法并不乐观。心理学家已经证明，那些在我们脑海中不够鲜明的事件，往往被赋予极低的概率——远低于事实所应得的权重。¹⁸ 我猜想，作为一个社会，我们要真正动员起来应对像全球变暖或能源约束这样的风险，就需要一起甚至多起 9/11 式的事件——一场悲剧性的事故，揭示出真实情况。

But that leads to my final thought, which is not optimistic. Psychologists have demonstrated that events that are not vivid in our minds get assigned very low probabilities—much lower than the facts warrant. 18 I suspect for us to mobilize, as a society, to address risks like global warming or energy constraints we will need one or more 9/11-type events—a tragic incident that reveals what’s really going on.

总结来说，我想留给你们这样一个想法：我们人类在应对风险或不确定性方面仍然并不擅长。我们依然是线性思维者，对把因果串联起来有着近乎无法满足的需求，而且我们对概率的评估也很差劲。不过，现在我们确实更了解了一些构成复杂系统基础的机制，这些知识在防范未来灾难性事件时能发挥很大作用。

In summary, I want to leave you with the notion that we humans are still not very good at dealing with risk or uncertainty. We are still linear thinkers, we have a nearly-insatiable need to link cause and effect, and we assess probabilities poorly. However, we do now better understand some of the mechanisms that underlie complex systems, and that knowledge can be very helpful in preparation for future catastrophic events.

格林威治圆桌会议是一家非营利研究和教育组织，面向那些将资本配置于另类投资的投资者。

The Greenwich Roundtable is a non-profit research and educational organization for investors who allocate capital to alternative investments.

尾注 1 弗兰克·H·奈特，《风险、不确定性与利润》（波士顿：霍顿·米夫林出版公司，1921 年）。 2 参见 www.santafe.edu。

Endnotes 1 Frank H. Knight, Risk, Uncertainty, and Profit (Boston: Houghton and Mifflin, 1921). 2 See www.santafe.edu.

3 关于复杂系统中的预测问题，可参阅迪迪埃·索内特的《股市为何崩盘：复杂金融系统中的临界事件》（普林斯顿，新泽西州：普林斯顿大学出版社，2003 年）。

3 For some thoughts about prediction in complex systems, see Didier Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems (Princeton, N.J.: Princeton University Press, 2003).

4 James Surowiecki, 《群体的智慧：为什么多数比少数更聪明，以及集体智慧如何塑造商业、经济与国家》（纽约：兰登书屋，2004 年）。

4 James Surowiecki, The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, and Nations (New York: Random House, 2004).

5 Michael J. Mauboussin，“重新审视资本理念”，《莫布森谈战略》，2005 年 3 月 30 日。6 Everett M. Rogers，《创新的扩散》第 5 版（纽约：自由出版社，2003 年）。7 Geoffrey A. Moore，《跨越鸿沟：向主流客户营销和销售技术产品》（纽约：哈珀柯林斯，1991 年）。

5 Michael J. Mauboussin, “Capital Ideas Revisited,” Mauboussin on Strategy, March 30, 2005. 6 Everett M. Rogers, 5th ed., Diffusion of Innovations (New York: Free Press, 2003). 7 Geoffrey A. Moore, Crossing the Chasm: Marketing and Selling Technology Products to Mainstream Customers (New York: HarperCollins, 1991).

8 邓肯·J·瓦茨，《六度分隔：互联时代的科学》（纽约：W.W. 诺顿，2003 年）。

8 Duncan J. Watts, Six Degrees: The Science of a Connected Age (New York: W.W. Norton, 2003).

9 史蒂文·斯特罗加茨，《同步：自发性秩序的新兴科学》（纽约：亥伯龙图书公司，2003 年）。

9 Steven Strogatz, Sync: The Emerging Science of Spontaneous Order (New York: Hyperion Books, 2003).

10 马尔科姆·格拉德威尔，《引爆点：如何制造流行》（纽约：利特尔·布朗出版社，2000 年）。

10 Malcolm Gladwell, The Tipping Point: How Little Things Can Make a Big Difference (New York: Little, Brown, 2000).

11 John H. Holland，《隐秩序：适应性如何构建复杂性》（马萨诸塞州雷丁：Helix Books，1995 年）。

11 John H. Holland, Hidden Order: How Adaptation Builds Complexity (Reading, MA: Helix Books, 1995).

12. Donald MacKenzie，《引擎，而非相机：金融模型如何塑造市场》（剑桥，马萨诸塞州：麻省理工学院出版社，2006 年），第 218-236 页。

12 Donald MacKenzie, An Engine, Not a Camera: How Financial Models Shape Markets (Cambridge, MA: MIT Press, 2006), 218-236.

13 迈克尔·J·莫布森与克里斯汀·巴索尔森，《瓦特论瓦特（以及更多）》，《融合观察者》，第 2 卷，第 16 期，2003 年 9 月 9 日。

13 Michael J. Mauboussin and Kristen Bartholdson, “Watts on Watts (and Much More),” The Consilient Observer, vol. 2, 16, September 9, 2003.

14 戴维·M·卡特勒、詹姆斯·M·波特巴和劳伦斯·H·萨默斯，《什么在推动股票价格？》

14 David M. Cutler, James M. Poterba, and Lawrence H. Summers, “What Moves Stock Prices?”

《投资组合管理期刊》，1989 年春季刊，第 4-12 页。

The Journal of Portfolio Management, Spring 1989, 4-12.

15 Mark Buchanan, 《无处不在：历史的科学……或者为什么世界比我们想象的更简单》（纽约：Crown Publishers, 2000 年）。

15 Mark Buchanan, Ubiquity: The Science of History . . . Or Why the World is Simpler Than We Think (New York: Crown Publishers, 2000).

16 参见 Justin Wolfers 和 Eric Zitzewitz 合著的《预测市场》，NBER 工作论文 10504 号，2004 年 5 月。另见 Justin Wolfers 和 Eric Zitzewitz 合著的《将预测市场价格解读为概率》，工作论文，2005 年 2 月。

16 See Justin Wolfers and Eric Zitzewitz, “Prediction Markets,” NBER Working Paper 10504, May 2004. Also Justin Wolfers and Eric Zitzewitz, “Interpreting Prediction Market Prices as Probabilities,” Working Paper, February 2005.

17 见 www.tradesports.com；www.newsfutures.com。

17 See www.tradesports.com; www.newsfutures.com.

18 Paul Slovic、Melissa Finucane、Ellen Peters 与 Donald G. MacGregor，“情感启发式”，载于《启发式与偏差：直觉判断的心理学》，Thomas Gilovich、Dale Griffin 与 Daniel Kahneman 编（剑桥：剑桥大学出版社，2002 年），第 397-420 页。

18 Paul Slovic, Melissa Finucane, Ellen Peters, and Donald G. MacGregor, “The Affect Heuristic,” in Heuristics and Biases: The Psychology of Intuitive Judgment, ed. Thomas Gilovich, Dale Griffin, and Daniel Kahneman (Cambridge: Cambridge University Press, 2002), 397-420.

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