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S19 SOCI 111: Social Networks Homework 3 – 91 points total DUE: 5/28/19
Instructions:
As before, these problems give you an opportunity to use the concepts and techniques we’ve learned in class to analyze interesting social systems. This time I’ve leaned more toward interesting conceptual puzzles rather than brute calculations. I encourage you to work in groups (of no more than 5), but each student should prepare her or his own solutions, along with a note at the top of your assignment crediting other members of the working group. Please make sure you truly understand the solution to a problem, and please: DO NOT COPY SOLUTIONS. This includes copying solutions from earlier years. We will figure it out. In particular, do not go to the testbank at SAC, do not go to Course Hero, and do not get solutions from friends who have taken the course in the past. This will impede your learning, it will not prepare you for the final exam, and I will treat it as academic misconduct.
In general, you should show your work rather than just writing down a number. This makes it easier for us to see that you know what you are doing, and easier for you to see when you’ve made a trivial mistake. On the other hand, don’t just throw everything vaguely relevant at the wall and hope that something sticks. You need to be judicious!
Please turn in a hard copy of your solutions to the TA at the beginning of class. Your submission should be neat and legible: you can type it up or write it out by hand, but we aren’t going to engage in decipherment here. Please follow the breakdown of questions into parts (a, b, c, etc.) to make these easier for your TA to grade.
Q1. Suppose a network exchange theory experiment is run on the graph depicted below using the one-exchange rule.
a. Say which node or nodes you would expect to make the most money (i.e., receive the most favorable exchanges). (2 points)
b. Explain why you would expect these nodes to make the most money. (3 points)
c. Do you think the advantage experienced by the most powerful nodes in this graph will be more similar to the advantage experienced by the most powerful node on a 3-node path, or more similar to the advantage experienced by the most powerful node on a 4-node path? (2 points)
d. Give a brief (1-3 sentence) explanation for your answer to part c, and be sure to compare the advantage experienced by the most powerful nodes in this graph to the most powerful nodes in the 3-node path and the 4- node path. (You do not need to give actual numbers for the amounts of money the nodes would receive). (4 points)
Q2. Now consider the following outcome of a network exchange experiment:
Bold lines represent the matching (who exchanges with whom), while the numbers give the values.
a. Is this outcome stable? (2 points)
b. Explain how you know whether or not the outcome is stable. (2 points)
c. Is this outcome balanced? (2 points)
d. Explain your answer to part c and show your work. Make sure you do the appropriate calculation for all edges in the matching.
i. Calculation for A-B (2 points) ii. Calculation for C-D (2 points) iii. Calculation for E-F (2 points) iv. How do these calculations allow you to see whether or not the outcome is balanced? (1 point)
Q3. Now consider the following outcome for a network-exchange theory experiment:
a. If you performed the experiment with real people, would you expect to see these precise values? (2 points)
b. Why or why not? Explain! (3 points)
Q4. Competing teams of sociologists at Bruin State University (BSU) and Southern Trojan University (STU) have each claimed to discover a different, “universal” human social behavior. The sociologists from Bruin State University are proud of the fact that they recruited over 10,000 student subjects from Bruin State University for their study. The sociologists at Southern Trojan University carried out their study in six societies: in the US, China, Sweden, as well as three small-scale societies. Each of these experiments by the STU sociologists had 100 subjects.
a. Which study provides better evidence for “universal” human social behavior? (2 points)
b. Explain why. Be sure to address both the Bruin State University and the Southern Trojan University studies. (4 points)
Q5. We know that it is rare for a directed graph to have more than one giant strongly connected component.
a. Define a strongly connected component (2 points)
b. Describe a graph with two giant strongly connected components, each of which contains 10,000 nodes. Clearly, you don’t need to draw the full graph; rather, you should describe it in words. You may find it helpful to draw a schematic picture as well. (2 points)
c. Explain how you could reduce the number of giant strongly connected components from two to one by adding at most two edges. Make sure you describe how those new edges reduce the number of giant strongly connected components. (3 points)
Q6. Josephina Bruin runs a website called “Bruin Bytes,” which delivers delicious snacks to students working late at night. But her site doesn’t even show up on the first page of search results for Google queries like “late night food UCLA.” She looks into search engine optimization and receives proposals from two companies. The first company says that she needs to increase her PageRank by linking to the websites of other popular restaurants, which they will help her do for a modest fee. The second company says that she needs to optimize her Authority score, which they can do for her by creating several pages with high Hub scores that link to Josephina’s site. Josephina knows that Google uses both PageRank and Hubs & Authorities to rank search results. The second company asks for a lot more money, but Josephina chooses it anyway. When her business partner, who has not taken SOC 111, asks her why, she says that the first company’s approach definitely would not have worked, while the second company’s approach made sense. Explain her decision!
a. Why won’t the first company’s approach work? Make sure you provide a (brief) explanation of how you get a high PageRank score and why the first company’s approach is unlikely to change her PageRank. (3 points)
b. Why will the second company’s approach work? Make sure you provide a (brief) explanation of how you get a high Authority score and why the second company’s approach can improve Josefina’s Authority score. (3 points)
Q7-Q8 concern the following scenario:
Suppose that 10% of all extra-terrestrial civilizations are evil: when they find out about another planet with intelligent life, they will immediately try to conquer it. This means that Pr ???????????????? = 0.1 and Pr ???????????????? = 0.9. You can get a hint of whether a civilization is “good” or “evil” by looking at the signals it sends. But this is unreliable. If a civilization is good, its signals will be friendly 80% of the time: Pr ????????????????????????????????|???????????????? = 0.80. However, some evil civilizations are SO tricksy that they will send friendly messages too: Pr ????????????????????????????????|???????????????? = 0.10. [NOTE: Make sure you write out the entire answer to Q7 and Q8 in symbolic form before you substitute in the values] Q7. What is the probability that a signal from an extra-terrestrial civilization will be friendly, i.e., what is Pr ???????????????????????????????? ? Make sure you write out your calculation in full detail. (5 points) Q8. Suppose that we receive a friendly message from an extra-terrestrial civilization.
a. What is the probability that this civilization is evil, i.e., what is Pr ????????????????|???????????????????????????????? ? Make sure to write out the calculation. (4 points)
b. Given this probability, should we write back? (1 point)
Q9. You are running a focus group on an ad campaign for a new energy drink called Slurm. All twenty participants are seated around a conference table. You decide to go around the table and ask each participant what he or she thinks of the ad. The first participant, Scruffy, says he loves it. The second participant, Zoidberg, says he loves it, too. The third participant, Leela, says she is also in favor of Slurm’s campaign (i.e., she loves it).
a. What will the other 17 participants say? Assume that each will say that they like the ad if the majority of independent signals suggest that the ad is Good. (2 points)
b. Is it possible to infer Scruffy’s private signal from his behavior? If so, state
what the private signal is; if not, say why not. Be sure to explain. (2 points)
c. Is it possible to infer Zoidberg’s private signal from his behavior? If so, state what the private signal is; if not, say why not. Be sure to explain. (2 points)
d. Is it possible to infer Leela’s private signal from her behavior? If so, state
what the private signal is; if not, say why not. Be sure to explain. (2 points)
Q10. In this problem we will explore the power of experts in creating and destroying information cascades. Let’s keep the same setup as in lecture and Chapter 16; ordinarily, individuals can see the behaviors but not the private signals of all previous individuals. Each individual receives a private signal (“High” or “Low”) and must decide whether to Accept or Reject the technology, belief, behavior, practice, etc., in question. To be concrete, let’s assume we are talking about a technology—say, a new virtual reality device. Individuals want to Accept Good technology and Reject Bad technology. Good technologies are more likely to generate High private signals; Bad technologies are more likely to generate Low private signals. Finally, suppose we have two types of individuals: Ordinary and Expert. Ordinary people have no special knowledge, and so they only get one private signal. Experts have special knowledge relevant to the decision, and so they get two private signals (they always get the same signal – two High or two Low). Assume that everyone knows who is an Expert and who is Ordinary. Everyone also knows that an Expert gets two private signals and an Ordinary person gets only one.
a. Imagine that Person 1 is an Expert and Person 2 is Ordinary. Person 1 receives two High signals and Accepts. Person 2 receives a Low signal. What should she do? Explain your answer. (3 points)
b. Does Person 2’s action reveal anything about her private information?
Why or why not? (3 points)
c. Now imagine that Person 3, 4, 5, etc. arrive and make their decisions. These people are all Ordinary. Explain why an information cascade will occur. (3 points)
d. Now imagine that after some number of Ordinary people (say 50),
another Expert arrives as Person 51. She receives two Low signals. What will she do? Explain your answer, and the consequences for the information cascade. (3 points)
e. Can an information cascade occur despite multiple Experts acting
sequentially? Imagine that Persons 1, 2, and 3 are all Experts. See if you can find a scenario in which an information cascade will nonetheless occur and describe it; if such a scenario is impossible, explain why. (3 points)
