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Let them alone: they be blind leaders of the blind. And if the blind lead the blind, both shall fall into the ditch.
Matthew 15:14
Brueghel Painting: 'The Blind Leading the Blind'
Pieter Brueghel, The Parable of the Blind (1568).
Oil on canvas, approximately 34 inches x 61 inches (86 x 154 cm). Museo e Gallerie Nazionali de Capodimonte, Naples.

Some Background: Hieronymus Bosch previously painted the parable of the blind with two beggars; Cornelis Massys with four beggars. Brueghel chose to paint six beggars. His beggars' faces show an unusual intensity, strongest in the beggar about to lose his balance. All beggars are blind, but their individuality is startling. Indeed, some art critics have stated that our own view of blindness originated from Brueghel's paintings, a number of which depict blind people. The background contains the church, a strong building pointing towards the sky. Click on the image to see an enlarged version.


Information Cascades and Rational Herding:
An Annotated Bibliography and Resource Reference

Available at www.info-cascades.info

Sushil Bikhchandani
David Hirshleifer
Ivo Welch

ivo_welch@brown.edu

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October 2007 NOTICE:

With the exception of this part, this web page has not been updated since 2004. It will become a Wiki shortly to allow more intelligent collaborative editing and to resume updating. Please check back over the next few months. This web page should be improving.

Some quick observations as to the impact of information cascades. As of October 2007:

Of course, be very cautious in interpreting these statistics. They are not particularly good at anything. They are only mildly indicative. (Anyone who trusts that the google or webofscience simple cite counts have much meaning should get their head checked.) My plan is to create better statistics, at citation.info in about 2-3 years.

To me, the most interesting aspect is that a number of these cites appear in non-economics journals---biology, political science, sociology, marketing, and elsewhere. If you are working in a non-economics academic discipline, and you would like to learn more information from us, feel free to contact us. We will try to help if we can.

The New York Times John Tierney also just posted a nice writeup (October 8, 2007), which is what prompted me to accelerate my restart of a long-intended revision of this page.

Here is the Palgrave Dictionary entry on Information Cascades (joint with [and mostly written by] Sushil Bikhchandani and David Hirshleifer), 2006


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Introduction and Purpose

These Web pages are an attempt to help coordinate information and permit interaction among authors interested in the informational cascades and rational herding literature. The intention of this WWW page is to (eventually) be comprehensive. This is quite an undertaking, especially at the boundaries where it is not clear whether a paper should be included or not. (Eventually, we hope to write a survey article of relevant literature for publication in a standard economics journal, but this is still a while away.) Moreover, this is both an early draft and a "living" document which is constantly changing. We would like your help to update and improve it. Please be forgiving: in its current state, it is sketchy, subjective, and includes background information not suitable for formal publication. Naturally, this page also reflects some of the authors' biases. If you feel that work has been misrepresented, we would like to hear from you. We are especially interested in corrections, additions, new references, email addresses to authors not yet hot-linked, etc.

If you want to suggest the inclusion of additional papers, please send an email to ivo welch and request a password to edit this page when it becomes a wiki (web-collaborative document). State your research affiliation, please---this page is not for commercial linking, but for university-level research---and include a link in the email to at least one cascades-related paper or page.

In the references that will follow, within each category, we mostly present papers in alphabetical order of the first author's last name, although we have also sometimes added papers at the end out of convenience. Because this file is HTML, it can be searched, printed, downloaded, etc. Email contact addresses (where available) have been added as hyperlinks, either via an obvious icon or via a link in the author's name. The bibliography is also accessible in BiBTeX format, and there is a separate author listing.

If this WWW page has helped you, please cite it:

Sushil Bikhchandani, David Hirshleifer, Ivo Welch. June 1996. Information Cascades and Rational Herding: An Annotated Bibliography. Working Paper: UCLA/Anderson and Ohio State University and Yale/SOM (Note: The World-Wide Web)

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A Quick Introduction to Information Cascades

Intuition and Aspects

A Simple Example: Let us presume that you and a lot of other people have to find your way to a new destination, and you come to a crossway where you can only either go left or right. Everyone has a private imperfect signal (call it "judgment" or "opinion"). For simplicity, let everyone have a private signal "left" ("right") with probability 2/3 if the true best choice is to go left (right). So, the signal helps but it is not perfect. Everyone's signal is equally good.

Now, assume that you are the third person to choose, and you first saw a man and then a woman go left. I claim that it is optimal for you to go "left" even if your private signal/intuition says "right". Why? You know that the man must have had an "l" signal, because he went left. The woman saw the man go "left." She would have figured out that the first individual's signal was "left". If her private signal was "left", she would have surely walked left, too. If her signal was "right", she would have been aware of one right and one left signal. She might have walked either way.

Now it is your turn. Having seen both the man and the woman walk "left," you know that the man had a "left" signal and the woman had a better than even chance of having had a "left" signal. Loosely speaking, the actions of your predecessors give you more than 1 "left" signal. Even if your private information is 1 "right" signal, net-in-net you should choose "left" if you are acting rationally---and so will everyone choosing after you. Now, everyone after you will know that what you did had nothing to do with your private information---but they will be in the same boat. The optimal decision will be to do the same thing and go left. One major consequence of information cascades is that you may get a million rational individuals walking "left" just because the first two individuals walked "left", even if the true best choice was "right." (This will happen with more than 1/3*1/3=1/9 probability [first two individuals got incorrect "left" signals].)

So, what does this mean for society? Cascades predict that you can get massive social imitation, occasionally leading everyone (the "herd") to the incorrect choice. (Because everyone knows that there is very little information in a cascade, cascades are "fragile"; a little bit of new public information can make a big difference).

Definition: An information cascade is a situation in which every subsequent actor, based on the observations of others, makes the same choice independent of his/her private signal.

Erroneous Mass Behavior: In an information cascades everyone is individually acting rationally. Still, even if all participants as a collective have overwhelming information in favor of the correct action, each and every participant may take the wrong action. The probability that everyone is taking the wrong action is less than 50%, but it is easy to construct examples in which everyone is wrong with 30-40% probability.

Fragility: A little bit of public information (or an unusual signal) can overturn a long-standing informational cascades. That is, even though a million people may have chosen one action, seemingly little information can induce the next million people to choose the opposite action. Fragility is an integral component of the Informational cascades theory!

Overviews and Surveys

There are other intuitive explanations and/or similar surveys in:

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The Academic Literature

Origin

Information Cascades first appeared in the following three papers:

The first drafts of Banerjee (1992) and Welch (1992) were both independent and contemporaneous. Banerjee (1992) and Bikhchandani, Hirshleifer and Welch (1992) independently show in different settings that information cascades (or "herding", in Banerjee's terminology) will eventually occur with certainty. (Bikhchandani, Hirshleifer and Welch generalized a result in Welch (1992).) Welch (1992) and Bikhchandani, Hirshleifer and Welch (1992) assume discrete actions. Banerjee (1992) assumes continuous actions, but discontinuous preferences. Bikhchandhani, Hirshleifer, and Welch (1992) prove the generality of information cascades, their fragility, and discuss their applications. Welch (1992) examines the pricing of common-value goods (such as shares in Initial Public Offerings [IPOs] of stock) by a seller when purchasers cascade; it also examines the effect of price-setting by an informed seller.

Direct Methodological Extensions/Improvements

Although the papers in this section may offer models outside the cascades realm as well, at least one part of the following papers offers an analysis of information cascades under assumptions different from those in the original papers.

The literature tells us that the two crucial ingredients of an information cascades model are: [1] sequential decisions with subsequent actors observing decisions (not information) of previous actors; and [2] a limited action space (e.g., an adopt/reject decision). Assumptions that are mostly technical, in that cascades are robust to their (possibly gradual) relaxation are: [3] private information that is bounded and imperfectly informative; [4] homogeneity of actors; [5] constant cost of adoption; [6] exogenous ordering. While relaxation of [3-5] generally decreases the speed with which cascades form, relaxation of [6] can increase the speed.

Applications

Theoretical Applications

Laboratory Experiments

Please note that there is a better and more up-to-date bibliography available at http://www.people.virginia.edu/~cah2k/cascy2k.htm.

Empirical Work

Papers Citing Information Cascades

The following paper's authors considered information cascade to be relevant enough to cite at least one of the three original cascades papers. This relieves us of having to judge ourselves whether the paper is relevant.The quoted papers need not find that information cascades is a dominant factor or may even reject the presence of information cascades. It is important in our opinion to understand whenmodels fit and when they fail. More than one cite indicates more than casual concern with informational copying/imitation/herding/cascading.

Papers Admitting an Information Cascades Interpretation

A good number of papers offer empirical evidence that, in our opinion, cries out for a cascades interpretation as a partial explanatory theory. Many papers in this category precede the information cascades literature. Such papers are indicated with a . Further, some papers/examples were themselves prominently cited by information cascades papers (indicated with a papername). While this does not mean that the authors of the original studies agree with the interpretation of the work, it means that authors of followup papers felt comfortable enough to have a referee see their interpretation of this work. Some information cascades papers quote a number of earlier papers' empirical evidence as examples that can be reinterpreted as information cascades. (We hope the authors will forgive us.)

Casual Examples

Not only did we claim in our published paper that earlier papers contained some evidence of information cascades behavior, we are now going a step further and are speculating about other examples ourselves.

The Press

Information Cascades Featured

Information Cascades Based Soundbites

Are there other stories in the press that you think are related to information cascades, but which do not specifically mention it? Any other anecdotes we should mention? These will not be integrated into the main text, but they will be accessible by clicking on .

Books On Imitation


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Final Thoughts and Further Reading

  1. Here, we will eventually offer links and explanations to models that are not informational cascades models. There will be at least two subsections: one on informational herding models and one on non-informational herding models. This writeup will be necessarily weak, because it is neither the focus of this survey nor are we experts in that literature. Still, the material is intrinsically related and thus relevant, and well worth reading to researchers interested in working on imitation.

Not Yet Processed


Last Compile: Mon May 31 10:16:37 2004.


Pure Chronological List

Pure Alphabetical List

Not Yet Described and Classified

Too much to do. I wish I had added: