Racial networks can be represented, in network theory, by groups that have links to each other, and fewer individual links to other racial networks. These groups help sustain triadic closure between other racial networks, which creates a great amount of stability with the whole worldwide racial network. Several articles I have read talk about how racial networks can spread positive or negative cascading effects within a population.

http://rss.sagepub.com/cgi/content/refs/17/2/191

This link talks about how a population of Bayesians are given observations and concepts from outside sources, and the people are forced to choose what to believe in: Their private preferences or the preferences of others. This experiment tests how potentiatlly negative and unpopular norms emerge within a population of heterogeneous beliefs and preferences.

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=251645

          In another abstract, the article mentions health-related cascading within an African population. The information that spreads around the medical arena makes a huge impact on the health effects of Black behavior. As a result, they decide to implement a democratic structure so that unpopular information can be spread more quickly and easily, as long as it will provide positive effects on the health of African Americans.  

        These two cascades of distinct racial groups show how influential information can affect the health or behavioral conditions of the whole population. The so-called tipping point is the point when people convert their beliefs to an uncommon belief, and these situations should be examined closely so that a population’s health will not be undermined in the future.

The Erdös Number Project

Just as the idea of the small-world phenomenon famously inspired “Six Degrees of Kevin Bacon” in the movie industry, so too do mathematicians have their own version of the game. This one centers around the late Hungarian mathematician Paul Erdös, who had a reputation for, among other things, publishing an incredibly vast body of academic work. After his death, his friends invented the Erdös number, a tongue-in-cheek measure of how closely all other mathematicians were “related” to Erdös. In fact, the Erdös number is much older than the Kevin Bacon game — the former was created in the late 1960s, the latter in the early 1990s.

In the Erdös-number sense, if two people have co-authored an academic paper, they are said to be connected. The Erdös number itself is a measure of the shortest path of connections from any person to Erdös. Of course, Erdös himself has a number of 0. All those who have collaborated with him have an Erdös number of 1, all those who have collaborated with his collaborators have a number of 2, and so on. The description given by the website strengthens this definition with some formalities:

In graph-theoretic terms, the mathematics research collaboration graph C has all mathematicians as its vertices; the vertex p is Paul Erdös. There is an edge between vertices u and v if u and v have published at least one mathematics article together. (There is no reason to restrict this to the field of mathematics, of course.) We will usually adopt the most liberal interpretation here, and allow any number of other coauthors to be involved; for example, a six-author paper is responsible for 15 edges in this graph, one for each pair of authors. Other approaches would include using only two-author papers (we do consider this as well), or dealing with hypergraphs or multigraphs or multihypergraphs. The Erdös number of v, then, is the distance (length, in edges, of the shortest path) in C from v to p. The set of all mathematicians with a finite Erdös number is called the Erdös component of C. It has been conjectured that the Erdös component contains almost all present-day publishing mathematicians (and has a not very large diameter), but perhaps not some famous names from the past, such as Gauss. (We have some information about the conjecture on this site.) Clearly, any two people with a finite Erdös number can be connected by a string of coauthorships, of length at most the sum of their Erdös numbers.

It’s intriguing to see how some famous people stack up using this metric. The page “Famous paths to Paul Erdös” lists some distinguished professionals — Nobel Prize winners, Fields Medalists, etc. — and their respective numbers. As expected, mathematicians generally have the lowest numbers. Andrew Wiles, who solved Fermat’s Last Theorem, has a number of 3. Einstein’s is 2. Bill Gates has a number of 4. And the only mathematician said to be as prolific as Erdös is Euler, whose number is…well, undefined. Of course, like the Kevin Bacon game, the Erdös number was never meant to be taken seriously, and interestingly, because Euler lived so long before the 20th century, no definitive link has been found between his works and those of Erdös.

As a side note, an Erdös-Bacon number also exists, which is defined as the sum of a person’s Erdös and Bacon numbers. As given by Wikipedia, Paul Erdös has a Bacon number of 3, although it would seem that Kevin Bacon doesn’t have an Erdös number.

article:  The Sky-high Club

James Surowiecki, the author of The Wisdom of Crowds, wrote an article for the New Yorker on the finding that CEO connections lead to increased pay.  He begins the article by discussing the ex-CEO of Home Depot, who was given two hundred million dollars despite the fact that he did not do an exceptional job.  Surowiecki accounts this surprising severance to the fact that the independent board members are not truly independent.  He notes that the people on Home Depot’s board sit on an average of two other boards and these connections to other companies lead to a continuous increasing of CEO pay.  However, the downside of this happening is that increased compensation does not necessarily lead to better performance.

First, this article shows how information cascades can lead to bad decisions.  Surowiecki describes how the idea of high pay travels from one board to another through its well-connected members.  Thus, in the same way companies may adopt new strategies for competition, they adopt the idea of supporting high paid CEOs.  In short, if many boards seem to pay their executives well, you should too.  In fact, to keep a good CEO, you should pay them more.  As the board of a company gains connections (from sitting on other boards), there becomes an increased chance that they will become a “friend of a friend” to the executives.  Thus, the connections between independent board members and the executives become friendlier and more “you help me, I’ll help you”.  At the end of the article, Surowiecki notes that while people join boards to be more connected, this often leads to less valuable decisions.  In short, the wisdom of the crowd is lost when people are too connected.

Perhaps this can also be a literal example of the “rich-get-richer” model.  Since, in an ideal world, compensation would relate to how well someone performs, a high-paid CEO would be thought to do a very good job.  Thus, when trying to attract a new CEO or retain a good one, the board must take into consideration how much money the CEO currently makes.  Consequently, high-paid CEOs, who are thought to be good, would then be paid even more in an attempt to attract/retain their expertise.

if you’re interested in seeing the actual study Surowiecki talks about(it’s 62 pages): Director Networks, Executive Compensation and Firm Performance

http://www3.interscience.wiley.com/cgi-bin/abstract/112726409/ABSTRACT 

 In the paper “Hierarchical Reporting, Aggregation, andInformation Cascades”, the authors (Anil Arya, Jonathan Glover and Brian Mittendorf ) illustrate how a cascade can decide the outcome of a decision in a hierarchical organization and how that can be prevented. In their model, a firm consists of 3 tiers – there are 3 lowest level managers, a middle manager, and a top manager. The firm needs to make a Yes/No decision (whether it should accept a project, etc.). Each of the 3 lowest level managers make private decisions (according to their own signals), which are forwarded to the middle manager. He updates his decision after considering their recommendations and his own signal. The top manager then makes the final decision after observing the decisions of the tiers below him.

The authors argue that rather than letting the middle and top manager have the knowledge of the votes of each lowest level manager, the lowest tier should submit an aggregated vote, i.e. a single decision representing the majority of the lowest tier. This prevents a cascade from forming as the middle and top managers, uncertain about whether the aggregated vote was mixed or unanimous, harbor a certain level of doubt about the recommendation. As a result, they rely more on their own discretion instead of merely rubber stamping the decision of the lower tiers.

By modifying their model, the authors investigated the consequences when the opinion of one of the lowest managers is deemed more valuable than those of the other two. This simulates the real-life situation in which the opinions of prominent voters who are regarded as more knowledgeable hold more weight. They found that an intermediate aggregation of information, in which the final decision makers are told of the number of votes, but not the identities of the voters, is the optimal solution to prevent excessive influence of a few individuals.

The practical application of their findings is that restriction of statistical information or identities of voters not only safeguards the privacy of individuals, but also prevents information cascades from forming during the decision making process.

Stanley Milgram’s small-world experiment, popularly termed as the “six degrees of separation” model, claimed that two perfectly random people were typically only six connections away from each other, assuming a connection to be an acquaintance they knew by name. The threory essentially made the world seem a lot small, by proving that we were all much more interconnected in the global network than anyone ever imagined. Ever since Milgram publicized the findings of this experiment, popular culture has been enamored with his theory. Hollywood has made frequent use of the idea from the popular game of Six Degrees of Kevin Bacon, to using it as a base for the overwhelmingly opportunistc connectedness of characters on shows like Lost. These are all human networks, but the theory’s applicability does not stop there.

Wikipedia, arguably one of the most popular sources of online information, is a network of linked articles written by whoever wants to contribute preferrably unbiased information on any topic whatsoever. The author of an article can include links to other already existing articles. Articles are accessible to anyone else who wishes to edit or add to the information, or perhaps put in more links to more articles relevant to the subject. The articles are put into larger categories based on their subject matter with other articles that share relevant characteristics. Wikipedia represents an excellent example of an electronic network, where the articles represent the nodes and the links between them represent edges. Many of the principles that can be applied to social networks between people can also be applied to the network of Wikipedia articles. One such principle is the idea of Six Degrees of Separation.

The Six Degrees of Wikipedia is a tool that claims that any two articles listed on Wikipedia can be connected by six or fewer steps, assuming you’re using the full, properly disambiguated names of articles. Having tested this a number of times, including finding the number of steps between popular South African group Ladysmith Black Mambazo and the 1990s popular television show Boy Meets World , and between New Age musician Enya and classical composer Maurice Ravel, I found that articles with the most unrelated topics are in fact linked by less than six steps.  In the first search above, the links went from Boy Meets World to ABC (a relatively strong link considering that Boy Meets World was in fact aired on ABC) to Life Savers to Ladysmith Black Mambazo. There is a tiny mention of Life Savers in the article for ABC, and the connection to LBM is that they sang the Life Savers theme song a capella at some point. The connection in the second link is equally as random, with the connection between the two musicians being that both have had an asteroid named after them.

What I found to be the more interesting extension of the Six Degrees of Separation model is the fact that random links tend to be the ones that more successfully link pages together in under six steps than stronger closer links. Thinking about Wikipedia in almost geographical terms, if two articles are very closely related in topic, then they are “closer” together, whereas if two topics are completely unrelated, they are farther apart and have only random connections. In the two examples above, it took very random far reaching connections to find a path of under six steps to the target. If the search was forced to go through only close links, such as Enya having to go through New Age Music (since Enya and Maurice Ravel are both musicians) to Classical Music to Maurice Ravel, the path would get extended (although not significantly in this case).

One major difference between Milgram’s Six Degrees of Separation model and its extension to Wikipedia is that in Milgram’s experiment, random people were told to find the shortest path to a Boston stock broker by sending a letter, but they didn’t have the goal of keeping it close to 6 connections, and had no information as to how close their acquaintance was to their target. Basically, people sent letters to acquaintances they figured would be more likely to know a Boston stock broker, and potentially missed shorter but more random paths as a result. In the case of Wikipedia, we have perfect information in finding the shortest path between two articles, so this is not necessarily a perfect example of Milgram’s findings.

Three years before the Cuban Missile Crisis, noted philosopher Bertrand Russell compared nuclear brinkmanship to a game of Chicken; the idea that superpowers should stockpile nuclear weapons and make generally vague yet scary threats against each other in order to create situations more advantageous to them was analogous to two reckless car drivers waiting until the last moment to swerve out of the way. Events like the Cuban Missile Crisis demonstrated how dangerous waiting until reaching the verge of severe global conflict could be during the Cold War. This power play between the two superpowers can be described in more economic terms as a game, with severely negative payoffs if both players choose the aggressive strategy, and not particularly exciting results if both players choose the safe one.

While the Cold War has ended, the concept of nuclear weapons as deterrents has not, and many more recently modernized nations are hoping to add themselves to the list of nuclear powers. With so-called “rogue nations” such as North Korea and Iran, the issue is often more one of diplomatic negotiation and empty threats than a serious prelude to nuclear war. That said, the diplomatic negotiations can often seem like a game of Chicken between a monster truck and a motorcycle. Naturally the US and Europe don’t want new nuclear powers with their own agendas, but, likewise, cannot seem to be capitulating too quickly to their demands. Likewise, a rogue nation’s leader cannot wither under international pressure and expect to keep the respect of his country’s population. Both parties make decisions on how to proceed with negotiations by analyzing which negotiation strategy will likely give them a better payoff in the future, and, when an evolutionarily stable strategy is found (like, say, multilateral negotiations) the situations can be resolved.

Expecting countries at opposite ends of the negotiating table to act unselfishly is a bit of a stretch. Here’s to hoping that, at the very least, evolutionarily stable strategies can be found where all parties involved, at the very least, can escape a conflict without dire consequences.

I have been a major league baseball fan for years, but it was not until last week during one of my routine visits to my favorite baseball team’s website (which shall remain nameless as I am embarrassed by their performance), that I realized a small ad in the lower left corner of the screen. The ad linked me to protrade.com where I came across the world’s only online forum for trading and exchanging professional sports teams and players. The site has established a formula that computes a player’s (or team’s) value based on a their current performance. I immediately could see the connections the our class.

If members of the site think that a player or team is undervalued they will choose to buy a certain number of shares sold at a given price. When a player is overvalued the community will choose to sell the player which will result in their values dropping. After I joined the free website, I found that the site has set up a perfect scenario for the forming of information cascades to occur. If a player is receiving a lot of attention, the site will reveal how the community is reacting as they post a list with the best and worst movers over the last 24 hours. The protrade member will be able to see how much of a percentile gain (or loss) a player has experienced and furthermore will show the general leaning toward that player. Thus a player might be titled a ’strong buy’, a ’strong sell’, or a ‘hold’. Thus when the next person examines a player’s earning potential they will see where the market is leaning in regards to that player, thus triggering an information cascade. Even if it is a odd occurrence of the phenomenon, nonetheless the website clearly exhibits the concept of an information cascade.

Normally, social networking sites are designed to allow people to make connections that they previously would not have been able to make. This one is different. Instead of helping you find new social links, famiva.com simply brings out the ones that are already there. Not just any links, only the most important ones: Family.

The premise of this site is that one person starts a family site, which includes a family tree, family network, and profiles for each family member. This person then invites their family members to join. As each new person joins, they are added to the tree and family group, and are also allowed (and encouraged!) to add their other family members. One can only imagine how large this can grow, considering that you can end up with distant relatives of your distant relatives. I don’t know any of my second cousins, and I definitely don’t know any of their second cousins. While you watch your family grow before your eyes, you can also keep in touch with anyone on your family site, via a profile with vital information, photo sharing, a forum for sharing stories, and a world map. I would recommend this to anyone who is interested in genealogy or staying in touch with distant relatives.

In lecture we have been talking about the six degrees of separation, particularly in the context of Milgram’s experiment. When trying to get a letter to the stock broker in Boston, the participants had the disadvantage having to guess which path to start with. They had no way of seeing the entire social network. If they had this information available, the six degrees that we always hear about would be an overestimate. This site does not show your entire social network, but it does show your entire family, which brings will bring your degree of separation from distant relatives down significantly. If this had been around at the time of Milgram’s experiment, one of the random letter recipients in Nebraska may have discovered that his cousin Bob happened to have a cousin on the other side of his family who worked at the same company as the stock broker. I could see this being particularly useful in countries with very little immigration, such as Iceland (Iceland is famous for having a very homogeneous population, and many hereditary studies are done there). Since most people there are (distantly) related, one could easily create a family network that contains most of the country, which could possibly eliminate most of the country’s social distance. And this is just with familial links!

http://www.bloomberg.com/apps/news?pid=20601101&sid=a8XwoOb8Nczo&refer=japan

This article deals with Toyota’s new division called Scion. Scions are marketed towards younger people. Toyota’s plan is simple; they sell cheap reliable cars, and market them solely to “edgy young dudes of the world.” This means that they are not advertising through the usual mediums of TV and print. Instead all advertisements are being done on the internet and targeted towards younger people. The people then get hooked and keep on buying Toyotas.

This got me thinking about how this is essentially (like all viral marketing campaigns) forming a cascade. This is because they want people to spread the word of how good these cars are to their friends, and hopefully it spreads through word of mouth. In addition they are getting you to buy more Toyotas in the future. I say this because the article states “Customer surveys show 80 percent of Scion buyers wouldn’t have bought another Toyota vehicle, the company said. So far, Scion customers are also mainly choosing Toyota models for their next purchase.” So it would seem as if there is a cascade forming, because normally people would not buy a Toyota, but after being tricked into buying one they like it.

http://shirky.com/writings/powerlaw_weblog.html

This article discussed the emergence of power law models and popularity imbalance in the popularity of web-blogs. Addressing the common observation that a small group of web-blogs account for a disproportionally large amount of web traffic, the article explains that it is not individuals’ behaviors, but “Diversity plus freedom of choice [that] creates inequality.” In fact, the greater diversity a community has, the more extreme the inequality will be. In a system where there is freedom to choose from many options, a power law distribution occurs.

In 2003, when this data was gathered, the top two blogs of 433 accounted for 5% of all inbound links. The top dozen counted for 20%, and the top 50, which make up only 12% of the blogs, counted for half of all inbound links. Such power law models are prevalent, emerging within many online communities. Livejournal users ranked by number of friends and Yahoo! Groups ranked by number of subscribers both are power laws.

This kind of system has both fair and unfair aspects. This kind of natural sorting is inevitable when people’s choices are influenced by other people’s choices. This kind of extreme popularity for a small subset is not necessarily unfair because it relies on “distributed approval that would be hard to fake.” However, power laws tend to set in quickly, preserving a system in a homeostatic state at an early time. This makes it harder for new members to gain popularity and is aversive to change.

Thus, this shows that power laws are ubiquitous occurrences that arise out of any community that allows democratic free choice and public opinion. Though it may cause unbalanced popularity for a few, it also shows that all it takes is one small step to cause a chain reaction that would lead to inclusion in this few.