#### Simulation and Modeling in the Social and Policy Sciences

**Q1** In connection with a program that provides alternatives for youth who have a run in with the criminal justice system, a colleague mentions that the program could be more effective if there were an easy way to predict who might benefit from the alternative program. The data suggests that about 75% of the youth in Ourtown are "good kids" who would benefit from the alternative program and 25% are "bad kids" who will not. Your supervisor also says you should come up with some more acceptable terms than "good" and "bad."

**Q2** Sketch, anew, the decision tree for the embassy party described in the text book.

"The officer in charge of a United States Embassy recreation program has decided to replenish the employees club funds by arranging a dinner. It rains nine days out of ten at the post and he must decide whether to hold the dinner indoors or out. An enclosed pavilion is available but uncomfortable, and past experience has shown turnout to be low at indoor functions, resulting in a 60 per cent chance of gaining $100 from a dinner held in the pavilion and a 40 per cent chance of losing $20. On the other hand, an outdoor dinner could be expected to earn $500 unless it rains, in which case the dinner would lose about $10" (Stokey & Zeckhauser 1977, 202).

**Q3** What is the expected value of a two dice toss if the payoff is whatever comes up on the dice, in dollars? Sketch this as a decision tree with just chance nodes.

**Q4.**Along with the alternative arrest program, a town is considering a mix of extra community policing, after school programs and evening youth programs as a part of their comprehensive efforts.

**Q71.** Consider this little bit of logic that describes a tourist's thinking process (taken from the title of a 1970s movie): “if it’s Tuesday, this must be Belgium. Otherwise, I have no idea where we are.” Sketch a flowchart that represents this flow of thought.

**Q72.** Sketch a flowchart that represents this bit of logic: “if you are a woman then if you are over 40 you should have this test no matter what but if either parent had diabetes women should have the test no matter what. Men only need to take the test if they are overweight.”

**Q73.** Sketch a flowchart that represents this bit of logic: “if cell E$3 is greater than cell G$12 then value is G$12; otherwise, value is G$12-E$3.”

**Q74.** Sketch a flowchart that represents this bit of logic: “if the balance is less than the minimum alternative payment then just pay the balance, otherwise, pay the minimum alternative payment.”

**Q75.** Sketch a flowchart that represents this bit of logic: “If you can get a direct flight for under $1500 take it unless it leaves from SFO before 9 am. Otherwise, see if anything is available on frequent flier miles no matter what the routing. If you can’t find anything, use Expedia to find the cheapest flight out of OAK.”

**Q76.** Sketch a flowchart that represents this bit of logic: If I have anything that is due tomorrow then if I am acing the class already and if I have some money I’ll go out drinking by myself (since all my friends will be busy), but if I don’t have any money I’ll stay home and watch reruns on cable. If, on the other hand, I’m not acing this class, I’ll stay home and study. If I don’t have anything due tomorrow, then if I have some money I’ll see if some friends are around and if so I’ll party with them. Otherwise, I’ll drink alone. If I don’ t have any money I’ll just stay home and watch reruns on cable.

**Q77.** Draw a flow charts that represents "Do A until B" and "While B do A. Then do C".

**Q78.** Sketch a flow chart that represents the following writing protocol: (1) Edit your essay until it is perfect. (2) While the essay still needs work, edit your essay.

**Q79.** Use stepwise refinement to create a flow chart for this set of instructions: Do A and then B. If C, then while E do F and after that do G, otherwise do H. Do I.

**Q80.** If A: until B do C and then, do D if E, otherwise do F while G. Otherwise if H, then if I do J else do K. Do L.

**Q81.** Is a picture worth 548 words? Convert the Rock County, Wisconsin "Drug Court Flow Chart" from text form to diagram form.

**Q82.** Flow chart the following protocols. (a) Record youth name and address. Check in system to see if already there. If there, pull up record and verify information. If not, create new record and ask for information. When done, send record to orientation staff, give youth a number and instruct to wait until number is called. (b) Once stage three in the treatment regimen is completed, clients are not eligible for the next stage in treatment until they have had three consecutive clean weekly drug tests. If they have one failed test they are given a warning. Two failed tests in a row and they have to meet with a counselor. Three failed tests and they are out of the program.

**Q83.** Weimer & Vining (1989) characterize policy problems in terms of market failure and government failure. Any given problem, they suggest, can be placed in one of four categories: (1) market AND government failure; (2) government works (policy corrects for market failure); (3) market works; (4) government failure to correct for market failure. Their suggested strategy is to start by asking whether there is a market failure and then whether there is government failure. Using the two conditionals, "Is there evidence of market failure?" and "Is there evidence of government failure?" construct a flowchart that would permit you to classify any given situation into one of the four aforementioned categories.

**Q84.** If the weather is nice, plant a garden. Otherwise paint the office. For the garden, make a decision between flowers and vegetables. If you go for vegetables, buy compost, seeds, and stakes; till the soil, and hook up the irrigation. If it's flowers this year, go to the garden store and if they have 4 inch plants buy enough for the plot and plant them. If they don't then get flats of smaller plants and bring them home and let them get acclimated for a week and then plant them next week. To till the soil, if the ox is healthy, do it with the animal plow, otherwise get out the rototiller.

**Q85.** A regimen consists of three mandatory sessions, followed by an optional weekend retreat and then, monthly sessions until standard test indicates absence of symptoms.

**Q86.** Sort clients into four categories promising, troubling, recalcitrant, hopeless on the basis of two tests which can be passed or failed.

**Q87.** Sketch a flow chart to represent the following scenario. The Alameda County Waste Management Authority (ACWMA) has decided to spend some money on a public relations campaign to increase the level of composting ("green bin") recylcing. Data on hand says that current levels are 4 kg per household of four per week. The plan is to spend $10,000 on advertising each month until the level has gone over 6 kg per week for four weeks in a row.

Prefatory concern – what does 4 kg / household of 4 / week mean? The amount of compost likely depends on the number of people in a household. We don't want to get the numbers wrong by failing to take this into account. So, in our data collection, we double the number for households of 2, halve it for households of 8, etc. Why not just express it as "kg/person/week"? That would work fine mathematically. Perhaps the PR folks had wanted to focus on households (and families) so as to induce a greater sense of collective responsibility.

**Q88.** Convert the following statement to “pseudo-Excel” formulas (follow the example to see what we mean by that).

Example. "If it is Tuesday, this must be Belgium, otherwise it is France" would become something like

`= if(day="Tuesday","Belgium","France")`

**Q89.**Convert the following statement to “pseudo-Excel” formulas (follow the example to see what we mean by that).

Example. "If it is Tuesday, this must be Belgium, otherwise it is France" would become something like

`= if(day="Tuesday","Belgium","France")`

**Q90.**Convert the following statement to “pseudo-Excel” formulas (follow the example to see what we mean by that).

Example. "If it is Tuesday, this must be Belgium, otherwise it is France" would become something like

`= if(day="Tuesday","Belgium","France")`

**Q91.**Sketch flow chart that captures logic of the following process.

**Q92.**What is wrong with the decision tree here? I need to decide whether to work at home or go down to Stanford today. At home, because of distractions, I work at about 75% efficiency. If I go to my research office at Stanford I work at 100% efficiency. If I work at home I will get 8 hours to work. If I decide to drive down to Stanford, I will get 8 hours minus driving time to work. The normal drive is ^0 minutes each way. But about 20% of the time it is extra light and the round trip takes just 90 minutes. About 30% of the time, though, traffic is awful and round trip is 180 minutes. I made a decision tree to figure out where I should work if I am trying to maximize my output, but I did something wrong. Fix the tree and tell me what I should do.

**Q93.** A new device at your favorite big box store costs $200. It has a one year guarantee from the manufacturer. The cashier offers you a special deal on a three year replacement warranty (assume it's good, will be honored, etc.) — $40. You estimate that the chances of the device failing during second and third years is 25% and that the price of replacement by then will be $150. Should you buy the service plan? What are the parameters of this decision model?

**Q94.** Assuming you are self-interested, what makes more sense: buy a $1.00 lottery ticket with a 1 in five million chance of winning a million dollars, buying a twenty dollar raffle ticket for a local fundraiser with a 1 in 2500 chance of winning a $500 jackpot, or playing a $1 stake game of rock-scissors-paper with the person next to you.

**Q95.** You never know what the weather is going to be around here. Somedays you need a sweater and some days you need sunglasses. The smart person, they say, always brings both. But suppose there is a definite hassle involved in bringing either (e.g., you ride a bike and space is tight). Sketch a decision tree that takes into account a cost to bringing either and a cost to not having either when you need them and the possibility that on a given day you might need one, the other, or both. Use plausible numbers of your own choice.

**Q96.** A college enrolls two types of students. Full-pay students pay $40K tuition and half-pay students pay $20K. At present the school spends $1 million per year to recruit 200 students about 75% of whom are half-pay and 25% full-pay. A consultant submits a proposal to shift resources around and use GIS to target recruitment at zip codes that are more likely to yield full-pay students. She says there is a 75% chance that the results will be a slightly smaller class (190) but one with 40% full-pay and 60% half-pay. Unfortunately there is also a risk things won't turn out so well. There's a 25% chance that enrollment will drop to 170 and only 30% will be full pay. Use a decision tree to advise the college as to its best course of action.

**Q97.** There's an idea in philosophy called "Pascal's Wager" that describes a way of thinking about the existence of god. It goes like this. I have a choice to believe or not believe. And there is a chance that god exists and a chance that there is no god. If I believe and there is a god, I have a chance at eternal salvation. If I don't believe but there is a god, I suffer eternal damnation. If I do believe and it turns out there is no god, I will feel a bit of a chump, but the atheists can feel smug if opposite is the case. Sketch this situation as a decision tree. Should you believe in god?

**Q98.** Sketch the decision tree for the following scenario. I want to buy a used car. The car I am looking at is being offered at $4000. The seller says it is in good shape all around. I look it over and agree, but you never know for sure. Suppose there is a 10% chance that it is a total dog and that buying it will be a $2000 mistake. I know a mechanic who will give it a very thorough inspection, for a price. If my assumptions are correct, what's the most I should pay my mechanic?

**Q99.** We want to apply for a home equity line of credit. The bank says it has to know what your house is worth (It has to be worth a certain amount over what we still owe on the mortgage to get a loan at a good rate). A loan at a bad rate will cost $10,000 more than a loan at a good rate. We think there is a 60:40 chance that our house is in fact worth enough to get a good rate. We have a choice between a cheap appraisal ($100) and an expensive appraisal ($1000). A cheap appraisal, we have learned, has a 40% chance of correctly valuing a property. An expensive appraisal is right 70% of the time. Draw a decision tree that will help us figure out what to do.

**Q100.** How much would you be willing to pay for a forecast that would resolve the contingency in problem 95?

**Q101.** If the farmer plants early and the spring is warm, she can get a 20% increase in her harvest. But if she plants early and there's a late frost she can lose 50% of her harvest. Historically, these late frosts happen one year in four (25% of the time). Use a decision tree to determine how much she would be willing to invest in a perfect forecast.

**Q102.** Kids these days! Of those who get into trouble, it turns out, about 30% are "real trouble-makers" who need some help. The other 70% are normal adolescents who will age out of their trouble-making under normal care. A social worker friend introduces you to a test that you can give to kids who are referred to you to determine which category they are in. Research has suggested the test is 75% accurate. Use tree flipping to describe what to make of the test's results.

**Q103.** Suppose we are running a program to which we want to accept only individuals in the top 25% of the population (on some measurable trait). Unfortunately, our test for measuring the trait is only 80% accurate. Draw event tree and flip to show what kind of faith we can have in the test results. Which test result appears more worthy of taking at face value? Which group would you be inclined to develop a second test for?

**Q104.** House gets another case. There's this funny rash. We won't say where it appears, but it's a funny rash. In 1% of the cases, it means something really, really bad — anxoreisis. Fortunately, there's a test. Unfortunately, it's not a perfect test. Fortunately, it's a pretty good test. Unfortunately, it is wrong 2% of the time. Work it out.

**Q105.** Following on problem 104, suppose the test is not painless or without its own risks. Suppose the "cost" of the test is 5. And suppose the treatment is also not so nice and the cost of the treatment is 15. But if you have the disease and you are not treated, the results are nasty : 50. Do we have enough information to recommend a course of action? What should we do?

**Q106.** She may love you or she may not. It turns out there is a 40% chance she does. You decide to use the buttercup test to find out (hold a buttercup under chin and see if it reflects yellow). The test is 90% accurate. Draw tree and flip to determine what conclusions we can draw from positive and negative buttercup test results.

**Q107.** Our neighborhood association has a ten member board. Each year it plans to add four members. Write the difference equations that describe the size of the board (S) each year.

**Q224.**You are working for an agricultural cooperative which is helping local farmers figure out how to optimize the mixture of crops they plant. A typical farmer has 10 acres to plant in wheat and rye. She has to plant at least 7 acres. However, she has only the equivalent of $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. If the expected profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits? (From Steve Wilson)

**Q225.**Your are the supervisor at a new after-school program. The program will serve 100 boys and 100 girls. Activities will include chess, games, and crafts. Materials, supervision, and the like have been priced out at $2/person for chess, $10/person for games, and $5 for crafts. Space needs are such that we can get 8 chess players at a table, 4 games players, or 2 crafters. The center has 50 tables. Solid research has shown that activity preferences among this population of children is somewhat gender specific. Boys and girls like chess the same but games are 70% girls and 30% boys while crafts tend to be 30% girls and 70% boys. What is the most economical division of activities subject to these constraints?

**Q226.**"You have $12,000 to invest, and three different funds from which to choose. The municipal bond fund has a 7% return, the local bank's CDs have an 8% return, and the high-risk account has an expected (hoped-for) 12% return. To minimize risk, you decide not to invest any more than $2,000 in the high-risk account. For tax reasons, you need to invest at least three times as much in the municipal bonds as in the bank CDs. Assuming the year-end yields are as expected, what are the optimal investment amounts?" (From PurpleMath.com)

**Q227.**A gold processor has two sources of gold ore, source A and source B. In order to kep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? (From Steve Wilson)

**Q228.**A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus. Calculate how many buses of each type should be used for the trip for the least possible cost. (From VITutor)

**Q229.**Bob builds tool sheds. He uses 10 sheets of dry wall and 15 studs for a small shed and 15 sheets of dry wall and 45 studs for a large shed. He has available 60 sheets of dry wall and 135 studs. If Bob makes $390 profit on a small shed and $520 on a large shed, how many of each type of building should Bob build to maximize his profit? (From solution here)

**Q230.**A store wants to liquidate 200 of its shirts and 100 pairs of pants from last season. They have decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants which will sell for $30. Offer B is a package of three shirts and a pair of pants, which will sell for $50. The store does not want to sell less than 20 packages of Offer A and less than 10 of Offer B. How many packages of each do they have to sell to maximize the money generated from the promotion? (From VITutor)

**Q231.**A transport company has two types of trucks, Type A and Type B. Type A has a refrigerated capacity of 20 m3 and a non-refrigerated capacity of 40 m3 while Type B has the same overall volume with equal sections for refrigerated and non-refrigerated stock. A grocer needs to hire trucks for the transport of 3,000 m3 of refrigerated stock and 4 000 m3 of non-refrigerated stock. The cost per kilometer of a Type A is $30, and $40 for Type B. How many trucks of each type should the grocer rent to achieve the minimum total cost?

**Q239.**I need to take a certification exam this year. The exam cost is $200. There is a prep course for the exam, but I don't know if I need it or not. It costs $300 and if one takes it, one is certain to pass the exam. If I do not take the prep course there is a 50% chance of passing and a 50% chance of failing in which case I'd have to take the prep course anyway and then retake the test (total cost = prep course + twice the exam fee). Should I take the prep course??

**Q240.**This is an event tree problem, that is, there are no choices to be made. Work out the probabilities of each of the final outcomes.

There is a 72% chance that candidate A will win the presidency over candidate B. There is a 55% chance that candidate A's party will win control of the senate and a 30% chance that his party will win control of the house.

**Q241.** If my new study method works, I should earn a 98 on the test. If it does not work, I will get a 79. Research suggests that there is a 75% chance it works. What is the expected value of my grade?

A. |
87.5 | B. |
93.25 | C. |
95.5 | D. |
79 | E. |
98 |

**Q242.** Draw a flowchart that represents the following protocol for enjoying a Saturday afternoon.

If it is sunny, go to the beach. If it is not sunny go to the movies.

If you go to the beach, if you are by yourself, take an umbrella and a good book. If you are with friends, take a bottle of wine and some nice cheese.

If you go to the movies alone, buy a monster popcorn and sit right up front. If you go with friends, be more restrained with the snacks and sit midway back.

Have a nice dinner afterwards.

**Q243.**Consider the following instructions for funding your NGO and then draw a flow chart representing this logic

Write the grant. Find a funder. Submit the grant. Wait to see if it is funded. If it is funded, start the project. Otherwise go back to finding a funder.

**Q244.**This question extends problem 243. You've learned the following things during your professional training. Represent this information as a three level stepwise refinement.

- Preparing to write a grant consists of identifying a need and putting together a logic model that shows what new inputs are needed to generate desired outcomes
- Finding a funder requires identifying a list of funders, looking up the kinds of projects they are funding, and finding matches for your project
- Writing a grant involves (1) preparing to write the grant; (2) finding template appropriate to particular funders; (3) producing drafts and reviewing with staff
- Draft and review protocols vary, but one you like is to produce a draft, post it on Google docs for the team to comment on, send a prodding email to team members every few days until it looks like there are no more comments on that draft, make revisions and repeat this process until the deadline is near.

**Q245.** Offer a critique of this flow chart diagram

**Q246.** What's wrong with this flow chart? How would you fix it?

**Q247.** What's wrong with this flow chart? How would you fix it?

**Q248.** What criticism would you offer if the diagram below were my first stab at a flow chart for an organizational process? How would you fix it?

**Q249.** Translate each of the flow charts below into everyday English.

**Q250.** What's wrong with this flow chart? How would you fix it?

**Q251.** Suppose the (time) cost of waiting behind someone with a big shopping cart in the super market checkout line is 10 minutes while the time behind someone with a very few items is 2 minutes. Consider three cities, A, B, and C. Suppose the probability of running into someone again soon in the grocery store is 0.1, 0.2, and 0.4 in cities A, B, and C, respectively. What do we predict? Which "path to cooperation" does this illustrate?

**Q252.** Consider this network in which green agents are cooperators and violet are defectors and the cost of cooperating is 2 while the benefit of being cooperated with is 5. Where is the equilibrium is people's behavior changes based on their network experiences?

**Q253.** Consider this network in which green agents are cooperators and violet are defectors and the cost of cooperating is 2 while the benefit of being cooperated with is 5. Where is the equilibrium is people's behavior changes based on their network experiences?

**Q254.** Just based on reasoning, explain the relation among relatedness, cost of cooperation, and benefit of cooperation in kin selection as a mechanism for achieving cooperation in the face of prisoner's dilemma scenarios.

**Q255.** Work through the section on direct reciprocity in Nowak and Sigmund, "How Populations Cohere."

**Q256.** Consider the collective action model described in Lecture 17.4: Collective Action and Common Pool Resource Problems where $x_j$ is the cost to me to "pitch in" and do my part in some collective effort. Each member of the collective reaps benefits from the contributions of those who decide to pitch in. In particular, they receive some fraction $\beta$ of all the contributions. Their net benefit is thus, this amount minus the effort they contribute. In other words,

**Q257.** (a) Explain the equations for common pool resource problems as discussed in Lecture 17.4: "Collective Action and Common Pool Resource Problems":

**Q258.** Insofar as particulars matter, what's the difference between cows, lobsters, and whether you live up stream or downstream?

**Q259.** What are the 5+2 means of achieving cooperation in the face of structural arrangements that "mandate" non-cooperation in human relationships?

**Q260.** Explain how "group selection" can give rise to cooperative behavior in human society.

**Q321.**: Our consulting firm, NGOsRus, has developed a new organizational assay protocol to help characterize the financial health of community organizations. We have tested the instrument on many organizations whose financial well-being has been determined by other, much more expensive means. Here's what we know:

**Q322.** Say what's wrong with these flow charts and redraw them correctly.

**Q323.** What flow chart concept does this diagram illustrate? Explain what it means and how we use it. Draw the series of flow charts implied by this diagram.

**Q324.** You are the board chairperson of a small non-profit and you are hiring new executive director. It has come down to two candidates, one rather plain vanilla and, frankly, a bit boring, but rock solid, and the other quite exciting and edgy. After all the interviews and due diligence, you and your board estimate that that with the boring candidate there is a 94% likelihood that she'll be OK, a 5% chance that she'll be amazing, and a 1% chance that she'll be a disaster. You estimate the "value" of OK to be 25, the value of amazing to be 100 and the value of disaster to be -100.

**Q325.** Have a look at the paper shown below about immunization in Uganda. Look especially at the causal loop diagrams on pages 102(146) and 103(147). Explain what is going on in each of the labeled/shaded loops. In some cases, there might be a sign missing. Based on your reading of the diagrams, supply these and explain.

**Q326.** (A) Consider this plot of P_{n+1} vs. P_{n}. Without worrying about what sort of system it might be, show that you understand how the chart works by describing the behavior of this system if it starts at time i at P_{i}=30. How about 70?

**Q327.** Our agency provides three types of client service: A, B, and C. And we have 3 kinds of staff: X, Y, and Z.

**Q328.** Have a look at this recent release from Bureau of Labor Statistics (BLS). The data separates those without a job into unemployed but "in the labor force" and "marginally attached to the labor force" and a subset of these called "discouraged" - the former would like to work but have not looked in the last four weeks and so are not counted as unemployed. The latter are not actively looking for work having given up on the idea that its possible to find. These groups are **not** included in the denominator when the unemployment rate is calculated. The simple version of the unemployment rate is, then,

**Q329.** Create for yourself a one page cheat-sheet/course summary illustration that captures what you have learned/want to take away from the course. Be prepared to show it at oral exam and explain it to instructor as if he were a fellow student who has not taken this course. This can take any form at all within the constraints of being no more than one sheet of paper. Just for fun, here are some examples from other courses: Social Theory, GIS, Social Control. Focus, of course, on content, not artistic flair.

**Q330.** **Equilibrium** came up many times in this course. Briefly catalog several and describe the concept and its importance. Be sure you can address (1) whether it is a normative concept (2) stable vs. unstable (3) different examples.

**Q331.** Studying for an exam could raise a student's grade by a whole letter grade. But it turns out to not be a sure thing. Suppose research has shown that six hours of studying has a 60% chance of increasing your grade by one letter grade, a 25% chance of having no effect, and a 15% chance of actually lowering it by one letter grade (perhaps due to increased anxiety and not enough sleep).

Calculate the expected value of the investment of 6 hours of study time in terms of "letter grades per hour."

**Q410.** Show what you know about Schelling's "micromotives macrobehavior" models by explaining this diagram.