Is Justin Timberlake a Product of Cumulative Advantage?

This weekend’s New York Times Magazine has an article from Duncan Watts on the topic of network effects. The article covers many of the topics that we have covered in class, including the “rich get richer” effect and the MusicLab experiment. Watts draws from examples such as Harry Potter and Madonna in his magazine piece, and he uses language that will hopefully be more approachable to the layman.

However, those in INFO 204 have already had exposure to some of these topics, so you can read between the lines to see what Watts is implying. For example, take this excerpt.

In our artificial market, therefore, social influence played as large a role in determining the market share of successful songs as differences in quality. It’s a simple result to state, but it has a surprisingly deep consequence. Because the long-run success of a song depends so sensitively on the decisions of a few early-arriving individuals, whose choices are subsequently amplified and eventually locked in by the cumulative-advantage process, and because the particular individuals who play this important role are chosen randomly and may make different decisions from one moment to the next, the resulting unpredictably is inherent to the nature of the market. It cannot be eliminated either by accumulating more information — about people or songs — or by developing fancier prediction algorithms, any more than you can repeatedly roll sixes no matter how carefully you try to throw the die.

The few “early arriving individuals” strongly parallels the information cascade example that we have covered repeated in class. The start of the information cascade also causes future individuals to be “locked in by the cumulative-advantage process”.

For those that attend class regularly, this article offers just a new description of a subject that you already understand. For those new to this blog (or those skipping class), Watts offers a succinct description of many of the topics we have covered in the last three weeks.

http://newsroom.eworldwire.com/view_release.php?id=16672

The problems caused by information cascades are clearly exemplified in the case of popular websites that display videos submitted by web-users for viewing by the general public. Most of these sites allow users to rank the videos, which are then sorted based on these ranks and the number of times they were viewed. The idea is that the most entertaining, or “best” in some way shape or form, videos will be ranked higher and will be more accessible to casual viewers of the site. However, the linked article mentions that there is an intrinsic problem with this system. If the first one or few viewers gives a certain video a high ranking, even if the video is poor or not of interest to most of the general public, the video will achieve a high ranking. This will cause more and more people to watch the video until a full-blown information cascade has developed. This ultimately could lead to situations where poor videos have been viewed far more times than superior videos.

In order to tackle this problem, a company called CrowdRules has devised a system in which they organize people together into “crowds” and select videos for people in the crowds to watch. All ratings are kept private from others in the crowd, meaning one voter is unable to see any other voter’s rating for any video, and each video is rated the same number of times. The results are compiled, and a cumulative ranking is formulated free of the detrimental effects of information cascades.

While the above case of on-line video ratings is inconsequential in the large scheme of society’s problems today, the solution proposed by CrowdRules could be applicable to situations that are more important. Information cascades can cause significant problems in political elections if a few people spread positive words about a candidate who is unqualified or unfit for the job. To fix this problem, certain individuals could interview all candidates early in the process and rank them individually such that their perceptions do not depend on what others say or believe about a certain candidate. This solution essentially is an extension of that used by CrowdRules for ranking video games, and presents a potential solution to a more imporant problem.

In their essay Movie Marketing Strategy Formation with System Dynamics: Towards a multi-disciplinary adoption/diffusion theory of cinema-going, authors David Lane and Elke Hussman provide a thorough review of the adoption/diffusion mechanism and propose a model of “reinforcing and balancing loops” to explain the process. We discussed cinema-advertising as an example of adoption/diffusion during class, and this article is an in-depth study into how the general theory can be applied to a narrow, specific industry and marketing technique.

The authors begin their essay with the example of a basic model of disease transmission and infection. Although this example is not immediately similar to that of cinema advertising, it nevertheless features the same sort of feedback-loops that ultimately determine the spread of information (or, in the example, the disease). Furthermore, slight changes in the model’s parameters can have profound differences in the model’s output: in some cases, the disease spreads to infect entire populations, while in others relatively few individuals become infected. This directly correlates with the success of movie marketing: some movies are hits, while others are flops.

In both cases, diffusion requires a “patient-zero”. In disease spread, this refers to the initial infected person, while in advertising it refers to the first group of consumers to try a product (in class we discussed these groups and the use of “free-giveaways” to entice their support).

Ultimately, the authors find both similarities and differences between movie-marketing and traditional diffusion. First, the authors claim that advertising reduces the need for “free giveaways.” Next, they claim that the advertising produces consumers who are able to “act in a way which allows the reinforcing loop to operate.” Because advertisements can reach a sufficiently large group of consumers, the requisite feedback loops will have enough users to generate strong consumer sentiment either in favor of, or opposed to, the particular film. Third, the authors find that, after a relatively short period of time during which advertising is crucial, the “reinforcing effect” of the feedback loop becomes critical to a movie’s continued success. Finally, the authors find that, if a movie is unable to generate a positively reinforcing word-of-mouth feedback loop, it is virtually impossible to use advertising to stimulate sales.

This model can be used to create an “ideal” movie launch scenario. Ideally, a movie is advertised to a sufficiently large target audience (ie, the “tipping point”). This audience not only sees the film during its early release, but likes the film enough to create a positive reinforcement loop and recommend the film to those who might not have been interested enough by the advertisement alone to see the film. At this point, the filmmakers can stop spending money on new advertising and instead rely more heavily on word-of-mouth to generate new sales. The authors cite the example of Saving Private Ryan, a tremendously expensive project that was able to become profitable after only 3 weeks in theatres thanks to both its large initial advertising budget and its overwhelmingly positive feedback.

Lothar Krempel and Michael Schnegg (2005) “About the Image: Diffusion Dynamics in an

Historical Network”, Structure and Dynamics: eJournal of Anthropological and Related Sciences:

Vol. 1: No. 1, Article 10.

http://repositories.cdlib.org/imbs/socdyn/sdeas/vol1/iss1/art10

This paper discusses how the structure of a social network influences history and the spread of ideas in a medium-sized German town.  This is accomplished by creating and analyzing several graphic representations of the data.  First, they link the villagers to different historical events, sorting the graphs by political persuasion and occupation.

When they plotted the diffusion of political ideas, it became clear that the merchants and craftsmen were vital in the first stage of spreading ideas.  Ideas spread from the center of the graph towards the edges, so the occupations on the “fringes” of the social network only became involved in the second phase of political action.

Recently, much work has been done to investigate the structure and dynamics of large social networks. Through datasets from online social networking sites, computer scientists are given an unprecedented look into the networks many of us form everyday. One of the key research questions that has arisen is about the growth of online communities. How do groups form online? How does the number of a given person’s friends who have already joined a group influence his decision? What about the community’s social density? Is a person’s decision influenced by the network structure of his group of friends who have joined the group? What about the structure of the group as a whole? By examining the development of online communities and seeking to answer such questions, sociologists can infer a great deal about how humans interact, whether online or off.

In fact, such issues do play important roles in the development of online communities. For the sake of this blog post, however, I intend to address just one: the trend of “triadic implosion” in the growth of online communities. In “Group Formation in Large Scale Social Networks: Membership, Growth, and Evolution”, the authors use LiveJournal to examine these network phenomenon. One interesting (and someone counter-intuitive) finding of the paper was that growth increased with the ratio of closer to open triads only to a certain value, at which point it dropped sharply.

But before I explain the sudden drop in growth, let me elucidate the logic behind the initial correlation. Based on the concept of weak ties, one could say that there is a trust advantage to joining a community in which your friends know each other. Specifically, a new community member would theoretically be supported by a richer social structure in such a community. Another point, consistent with the findings of “Cascade Dynamics of Multiplex Propagation”, is that successful social diffusion commonly occurs in “highly clustered networks” since a “coordination effect” may come into play, in which a non-member receives a greater net endorsement of a community if there is a “shared focus of interest among a group of interconnected friends.”

Once the closed to open triad ratio hits 0.15, however, there is a tipping point, and the rate of growth drops suddenly. This phenomenon has been colloquially dubbed “triadic implosion.” There are a couple of hypotheses for this phenomenon. The first is that the high ratio of closed to open triads implies a sense of “cliqueishness.” In other words, the community is so tightly connected that it is either too hard to break into, or becomes undesirable for potential members. Another possible explanation is that the high density of the group implies that it has reached a stage when it has stopped gaining new members and has subsequently begun densifying, (i.e. forming edges between its current set of nodes). Both of these hypotheses beg further research and would make interesting projects for continued work.

L. Backstrom, D. Huttenlocher, J. Kleinberg, X. Lan.

Group Formation in Large Social Networks: Membership, Growth, and Evolution.

Proc. 12th ACM SIGKDD Intl. Conf. on Knowledge Discovery and Data Mining, 2006

at http://www.cs.cornell.edu/home/kleinber/kdd06-comm.pdf

Informational Cascades in the Laboratory: Do They Occur for the Right Reasons?

(Postscript reader/Download required)

This is an older article about information cascades and how laboratory experiments can give results which coincide with theory, but perhaps may not be for the right reasons. There are more than a few sources which I have read which cite this article, so I thought it would be helpful to see where their ideas originated.

In this study, Bayesian probability was tested versus a subset of undergraduate students who had recently completed a study in Bayesian decision making. The question was administered as part of an exam. However, instead of previous studies, in which the subjects were shown the previous results of other subjects, in this study the information given to the subjects was purposefully prepared, in order to test how well Bayesian theory holds in a real-life setting.  Instead of seeing what others had answered, the experiments purposefully manipulated the subjects’ beliefs about the previous decision(s). Out of a sample of 63 subjects, approximately half responded in accordance to Bayesian theory, but even if they were in accordance, a scant few could respond correctly how they used it to obtain the answer.

From the results of the study, it can be said that Bayesian probability “works” – that is to say, it works when it possibly coincides with other heuristics, such as following one’s own signal, or following the majority. From there, cascades appear to form, but for different reasons than the probability would predict. As discussed in class, the “follow one’s own signal” approach is the resolution when trying to work through a cascade situation, when given conflicting data in equal amounts (i.e. 3 high signals, and 3 low signals).  But according to the paper, appearance of this phenomena appears much more readily than simply when signals are in conflict – approximately 66% of the results are in line with a “follow your signal” approach more than Bayesian logic (~49%). As stated in the paper, there are reasons why cascades form, but the reasons behind such may not be as predictable as the mathematical models might immediately suggest - the probabilities, for example, might be skewed more than the Bayesian conditional model would immediately predict.

http://www.chass.utoronto.ca/~wellman/publications/viruspaper/version.PDF

We’ve been discussing network diffusion in class recently – namely, how a trend propagates throughout a network. The paper above analyzes viruses, one such “trend.” It explores the effect of tightly- and loosely-knit networks on several types of viruses. Specifically, the paper compares biological viruses, computer viruses, and viral marketing.

The paper first identifies two extremes in network structure. Densely knit groups involve members who are in frequently contact with each other and infrequent contact with those outside the group. Ramified networks are just the opposite: fewer members are in contact with each other, and each member has a wider range of contacts.

Networks with densely knit groups tend to reinforce each other, so if a virus can infect even a single member of the group, it can quickly spread to the rest of the group. Biological viruses spread based physical contact; so if a family member catches a cold, the rest of the household might soon get sick. Moreover, groups often share certain characteristics that make them more susceptible to a particular virus. Business computer networks often have identical hardware and software configurations for each of the workstations in the building. A computer virus that takes advantage of a security flaw in one system can also compromise every other system in the network with the same tactic. In both biology and computing, viruses are more effective if they can “stick” to a host for longer. The paper refers to this as the “stickiness factor.” Viruses that kill a person or wipe a hard drive quickly have a low stickiness factor and cannot stay around long enough to spread well. In viral marketing, people in the same group often have similar tastes and interests. Thus, introducing a new product to a single member helps the rest of the group discover the product quickly. The entire group is likely to use the product shortly thereafter.

Ramified networks contain a number of weak ties that bridge different groups together. These “structural holes” are the means by which viruses can spread to a more heterogeneous population. This the means by which HIV was eventually able to spread outside the gay population into the general public. Modern computer viruses often spread by e-mailing a copy of themselves to everyone on a person’s contact list. This includes both a person’s strong and weak ties, enabling a virus to extend outside that person’s close circle of friends. Structural holes can be used with great success in viral marketing as well. Free e-mail services such as Yahoo! Mail and Hotmail tag a footer onto all outgoing e-mails, advertising the e-mail service to the recipients. In fact, the Internet virtually eliminates physical distance barriers to viral marketing. Blog posts, social networking sites, forums, and newsgroups can serve to explode the popularity of ideas, trends, and products.

In summary, most kinds of viruses spread similarly in particular types of networks. Densely-knit and ramified networks are two extreme cases; real social networks are always somewhere in between. The paper refers to these as “glocalized” networks. These types of networks spread rapidly within clusters, but more slowly across clusters.

The author of the paper is Barry Wellman, a professor at the University of Toronto. He studies network interactions and communications for both social and computer networks.

While doing one of my normal perusals of Wikipedia, I came across some assertions on the value of social networks relative to their sizes. Metcalfe’s law, which was originally applied to early Ethernet networks, states that the value of a network is proportional to the square of the number of users. This makes sense, because for a network of size n, the total number of possible connections between people is n(n-1)/2, which is proportional to n^2.

Reed’s law, however, says that size plays an even bigger factor in the value of a social network. David P. Reed, in an essay called That Sneaky Exponential (linked from the wiki article), claims that the value of a social network is not quadratic, but exponential. This is because, he says, the value of a network does not rely on the number of possible pairings, but on the number of possible subsets. It’s easy to see that the number of subsets is roughly 2^n, because for each element, one can either choose it or not choose it, and we use our multiplication rules from set theory. Communication on the internet is not merely one-to-one; there are communities of large numbers of people, so we can that it is not pairs, but groups, that are important.

This connects in with our discussion of network cascades, and how people will be more likely to join the instant messaging or other network that their friends already use. However, this looks at the total value of a network instead of its value for only one person. While if we divide by the number of people, Metcalfe’s shows the value being directly proportional to the number of users, Reed’s way of looking at things is still exponential, just with a slightly smaller exponent. Therefore, the value per person still increases very quickly with the number of people using the network. Finding the exponential the per-person value winds up is left as an exercise for the reader.

http://www.atsweb.neu.edu/w.carl/PDFs/colleagues/LSE_AdvocacyDrivesGrowth.pdf

This paper summarizes the results of a study conducted on the effects of word of mouth advocacy on the growth of businesses. The study observed word of mouth communication in two areas: Postive Word of Mouth (PWOM) and Negative Word of Mouth (NWOM). The authors used a point scoring system developed by Net Promoter (TM) that measures WOM rates as a parameter with reference to growth. What they found was that companies with a relatively high NetPromoter Score and relatively low NWOM rates grew 4 times as fast as their competitors. These results were found across many different industries ranging from automobile manufacturing to retail banking. Apparently there is a direct corellation between success and how positive one’s image is.

Specifically the factors that the paper declares most important are:

1) The rate at which customers recommend a brand to friends

2) The rate at which investors recommend investing in a specific company to friends or colleagues

3) The rate at which the employees recommend working for a specific company

Interestingly, the paper claims that with these 3 rates, one can accurately predict a company’s performance. These findings magnificently justify that the small mechanisms at work (the simple recommendation from one friend to another) on a large scale have a tremendous impact. In the UK industry, a total 1% decrease of NWOM would result in a 24.84 million pound increase in revenue for the 1000+ companies surveyed. In addition the paper delves into various techniques that can be used in order to increase PWOM. These include: referral programs, Tryvesting (a recently popular technique that combines free trials but selectively for those consumers who are most likely to advocate the product the service), and also advocacy tracking.

One interesting question that comes to mind with this paper that is not fully answered is how much of a factor is the value of the actual product. If there is more of an information cascade system occuring then one possible technique would be for companies to pay artificial PWOM advocates (advocates that otherwise wouldn’t be advocates if they weren’t getting paid) to generate enough positive communication so that growth will increase. I’m pretty sure this is already a commonly used technique, but I wonder if there is a distinction between artificially produced PWOM and genuine PWOM (eg., is PWOM enough to boost a companies growth or does it have to be genuine PWOM?).

Payoff Effects in Information Cascade Experiments

A question in problem set 5 describes an experiment involving information cascades. Subjects were paid if they can guess correctly whether an urn contain more black balls or more red balls; and they were given a private

signal of a draw of a ball from the urn and the guess of all the previous subject. An information cascade does in fact occur in this setting, and its effects is explored in Anderson’s paper.

Anderson’s expriment is identical to the one described in our problem, with number of subjects equal to 6 conducted over 9 sessions. The subjects’ behavior is not always consistent with our cascade model discribed in class. Some of the subjects’ decisions are inconsistent with Bayes’ rule; that is, they sometimes choose to ignore the plausible guess based on the guesses of previous subjects and even their own private signals. The experiment’s data also shows that an incorrect cascade can occur sometimes given the right (or wrong, depending on your point of view) conditions. Although having a non-zero payoff to guessing the correct urn decreases the decision error of subjects, increasing the payoff (when it is already non-zero) has no significant effect.