Problem Set Week 08

### Before Second Class

Q165. What's the difference between an "equation-based model" and an "agent model"? What are some other synonyms we might hear for these terms?

Q164. Sketch a flowchart that represents the logic of setting up a Schelling "tipping model":

To Create Schelling Model

1. Set up the model.
2. Run the model until everyone is content to stay where they are.

To Set Up

2. Identify a number of type A residents and a number of type B residents such that A+B is less than N2.
3. Randomly place As and Bs on grid.

To Run the Model

1. For each resident, evaluate move/stay choices
2. For each resident, find new location for all those that choose move.

To Evaluate choice

1. Identify the resident
2. Count all neighbors
3. Count similars
4. Compute ratio
5. If larger than threshold, mark as stay, otherwise mark as move

To Move

1. Select a random square
2. If empty, move there. Otherwise try again.

Q169. Consider the 12 block neighborhood bounded by parks on the north and south and major thoroughfares on the east and west. Green houses are supporting Obama, purple houses Romney.

Using the facing blocks delineated by the red dashed lines as units (it yields 15 of them), calculate the index of dissimilarity.

Q170. Suppose you have a population of one hundred persons. It is divided into five categories of willingness to join a protest all of which depend on people's expectations of how many others will appear at the protest. The thresholds range from very low (I'll go if anyone else is going) to the very high (I won't go unless basically everybody else is going).

Assume the population is divided among these categories as follows:

Challenge of Recruiting Very Easy Easy Average Hard Very Hard
Participation Threshold 1 10 40 60 99
Number at this threshold 10 20 40 20 10

a. If news reports suggest that 15 people will show up, how many actually will?

b. If last week saw participation of 41 and this is widely reported so that everyone knows, how many will come out this week? And then next week? And after that?

c. What if 91 came last week?

Q171. A common phrase to describe processes in which people engage in imitative behavior is "bandwagon effect." Explain the appropriateness of this metaphor.

Q172. Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. If news reports suggest participation will be at 20 people, how many people's threshold is met or exceeded? How about if the number is 70?

Q173. Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. If news reports suggest participation will be at 20 people, how many people's threshold is met or exceeded? How about if the number is 70?

Q174. Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. How does this system behave when the expected number is 10? 20? 50? 60? 90?

Q175. Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. Plot the cumulative distribution on a chart with a 45 degree line.

### In Class/Lab

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