COU 4: Mass Uprisings
For the Lesson 7 COUs due on November 24, you are only required to do ONE of either this COU or COU 3. If you choose to do both COU 3 and COU 4, any points beyond the 12 available on either one of them will count for extra credit.
In this COU you’ll explore a model based on one by Timur Kuran (Kuran 1991) of mass uprisings. Kuran developed and described his model in a 1991 paper that attempted to explain why the mass uprisings that occurred in Eastern Europe in 1989 and 1990 were so surprising to those familiar with the politics of the region – surprising even the persons who participated in the uprisings!
Kuran’s model is based on the same ideas developed in the models in COU 1 and COU 2 of this lesson: When persons consider whether or not to participate in protest against a regime that rules through violence, they recognize that there is power in numbers. Participating in a protest with just a handful of other persons can get you killed, and may strengthen the regime’s hold on power. But participating in a protest with thousands of others carries little personal risk, and can cause the regime to collapse.
Kuran adds one additional feature to this logic: Persons differ from one another in their willingness to participate in a protest of any given size. For instance, some persons are very cautious: They will only participate in a protest if they are sure that thousands of other persons will also participate. Others are more bold: They will participate in a protest involving just a dozen or so participants. More generally, we can think of each person in a population as having a “threshold” that determines when they will or will not participate in protest. If a person expects the total number persons participating in a protest to be below her threshold, she will not participate. If a person expects the total number of persons participating in a protest to be above her threshold she will participate.
Here is the model:
Imagine a population consisting of N persons, where N is some integer greater than or equal to 3. Label the persons “Person 1”, “Person 2”, “Person 3” and so on through “Person N”. Suppose that each person must choose between one of two actions: to participate in a protest or to not participate. Let i be any integer between 1 and N, so that “i” refers to any one of the N persons. Each person i has a threshold given by a proportion T_i which lies between 0 and 1, inclusive. Given Person i’s decision to participate or not participate and given the decisions of the N-1 persons other than person i to participate, person i’s utility level is given as follows:
| Person i’s Action | Proportion of N persons (including Person i) who Participate | Person i’s Utility Level |
|---|---|---|
| Participate | Greater than or equal to T_i | 1 |
| Participate | Less than T_i | 0 |
| Not participate | Greater than or equal to T_i | 0 |
| Not participate | Less than T_i | 1 |
The table above can be difficult to parse at first. Most importantly, it does not draw a clear picture of the strategic interdependence the actors in the model face. So to understand this model better, let’s look at a concrete example. Imagine that N = 100, i.e. there are 100 persons each deciding whether or not to participate in a protest, labeled Person 1, Person 2, Person 3 and so on through Person 100. Imagine just one of these persons. It doesn’t matter which one, so we’ll pick arbitrarily. Imagine…Person 7.
To get a clear picture of the strategic interdependence between Person 7 and the other 99 persons in the model, think of all the possible expectations that Person 7 can have about what the other 99 persons might do. Describe these expectations purely in terms of the number of the other 99 persons that Person 7 expects to participate. We can list all of these possible expectations like so:
| Number of other the 99 persons Person 7 expects to participate |
|---|
| 0 |
| 1 |
| 2 |
| \vdots |
| 25 |
| 26 |
| \vdots |
| 83 |
| 84 |
| \vdots |
| 97 |
| 98 |
| 99 |
To grasp the strategic interdependence between the persons in the model, we want to get a sense of how Person 7’s preferences over her available actions depend on her expectations about what the other 99 persons will do. So, let’s get clear about Person 7’s utility level, depending on whether or not she participates at each of the expectations she can have about how many of the 99 other persons will participate. Remember, strategic interdependence amounts to each person’s preferences over her actions depending on her expectations about what actions other persons will take. So, we want to understand how Person 7’s utility levels from participating as opposed to not participating change depending on her expectations about what the other 99 persons will do.
Since her utility level depends on what actions she takes and the proportion of the entire group that ultimately participates, understanding her preferences over her actions at each possible expectation requires taking account of the proportion of all 100 persons that Person 7 will expect to be participating if she either does or does not participate. Specifically, we need to add in two additional columns of our table like this:
| Number of other the 99 persons Person 7 expects to participate | Proportion Person 7 Expects to Be Participating if She Does Not Participate | Proportion Person 7 Expects to Be Participating if She Participates |
|---|---|---|
| 0 | ||
| 1 | ||
| 2 | ||
| \vdots | ||
| 25 | ||
| 26 | ||
| \vdots | ||
| 83 | ||
| 84 | ||
| \vdots | ||
| 97 | ||
| 98 | ||
| 99 |
Filling these columns in just requires taking account of what proportion will be participating depending on each possible action by Person 7 and the number of the 99 other persons she expects to be participating. For instance, if Person 7 expects that 83 of the 99 other persons will participate, then she will expect that \frac{83}{100} of the group will be participating if she does not participate and that \frac{84}{100} of the group will be participating if she participates. Thus we can fill in our two additional columns like so:
| Number of other the 99 persons Person 7 expects to participate | Proportion Person 7 Expects to Be Participating if She Does Not Participate | Proportion Person 7 Expects to Be Participating if She Participates |
|---|---|---|
| 0 | \frac{0}{100} | \frac{1}{100} |
| 1 | \frac{1}{100} | \frac{2}{100} |
| 2 | \frac{2}{100} | \frac{3}{100} |
| \vdots | \vdots | \vdots |
| 25 | \frac{25}{100} | \frac{26}{100} |
| 26 | \frac{26}{100} | \frac{27}{100} |
| \vdots | \vdots | \vdots |
| 83 | \frac{83}{100} | \frac{84}{100} |
| 84 | \frac{84}{100} | \frac{85}{100} |
| \vdots | \vdots | \vdots |
| 97 | \frac{97}{100} | \frac{98}{100} |
| 98 | \frac{98}{100} | \frac{99}{100} |
| 99 | \frac{99}{100} | \frac{100}{100} |
And with these proportions in hand, we can compute Person 7’s utility level for each of her actions at each expectation. Her utility level depends on whether or not she participates, the proportion of the whole group participating and her threshold. Let’s assume an arbitrary threshold for Person 7. Say…Person 7’s threshold T_7 is equal to \frac{3}{4}. With this assumption in hand, we can write the utility level Person 7 gets at each of her possible expectations depending on her action. For instance, suppose that Person 7 expects that 83 of the 99 other persons will participate. Then if she does not participates, the total proportion participating will be \frac{83}{100} and if she participates, the total portion participating will be \frac{84}{100}. With all this in mind, look again at the table specifying the utility level any of the persons gets depending on their action:
| Person i’s Action | Proportion of N persons (including Peron i) who Participate | Person i’s Utility Level |
|---|---|---|
| Participate | Greater than or equal to T_i | 1 |
| Participate | Less than T_i | 0 |
| Not participate | Greater than or equal to T_i | 0 |
| Not participate | Less than T_i | 1 |
Reading off this table, we can see that if Person 7 has threshold T_7=\frac{3}{4}, she does not participate and the portion of the entire group participating is \frac{83}{100}, then, since \frac{3}{4} < \frac{83}{100}, Person 7’s utility level will be 0. On the other hand, if Person 7 participates and the portion of the entire group participating is \frac{84}{100}, then, since \frac{3}{4} < \frac{84}{100}, Person 7’s utility level will be 1. Calculating in this way for each expectation that Person 7 could have about what the other 99 persons will do, we can add columns stating Person 7’s utility level to our table like so:
| Number of other the 99 persons Person 7 expects to participate | Proportion Person 7 Expects to Be Participating if She Does Not Participate | Proportion Person 7 Expects to Be Participating if She Participates | Person 7’s Utility of She Does Not Participate | Person 7’s Utility if She Participates |
|---|---|---|---|---|
| 0 | \frac{0}{100} | \frac{1}{100} | 1 | 0 |
| 1 | \frac{1}{100} | \frac{2}{100} | 1 | 0 |
| 2 | \frac{2}{100} | \frac{3}{100} | 1 | 0 |
| \vdots | \vdots | \vdots | \vdots | \vdots |
| 25 | \frac{25}{100} | \frac{26}{100} | 1 | 0 |
| 26 | \frac{26}{100} | \frac{27}{100} | 1 | 0 |
| \vdots | \vdots | \vdots | \vdots | \vdots |
| 83 | \frac{83}{100} | \frac{84}{100} | 0 | 1 |
| 84 | \frac{84}{100} | \frac{85}{100} | 0 | 1 |
| \vdots | \vdots | \vdots | \vdots | \vdots |
| 97 | \frac{97}{100} | \frac{98}{100} | 0 | 1 |
| 98 | \frac{98}{100} | \frac{99}{100} | 0 | 1 |
| 99 | \frac{99}{100} | \frac{100}{100} | 0 | 1 |
This last table makes the strategic interdependence in this model vivid. Notice how the ordering of Person 7’s utility levels from her two possible action reverses once the number of the other 99 persons she expects to participate gets sufficiently large. In fact, we can re-write the table above in a way that makes the dependence of her preferences on her expectations about the behavior of the other persons in the group explicit as follows:
| Number of other the 99 persons Person 7 expects to participate | Proportion Person 7 Expects to Be Participating if She Does Not Participate | Proportion Person 7 Expects to Be Participating if She Participates | Person 7’s Preferences Over Her Actions |
|---|---|---|---|
| 0 | \frac{0}{100} | \frac{1}{100} | prefers to not participate instead of participate |
| 1 | \frac{1}{100} | \frac{2}{100} | prefers to not participate instead of participate |
| 2 | \frac{2}{100} | \frac{3}{100} | prefers to not participate instead of participate |
| \vdots | \vdots | \vdots | \vdots |
| 25 | \frac{25}{100} | \frac{26}{100} | prefers to not participate instead of participate |
| 26 | \frac{26}{100} | \frac{27}{100} | prefers to not participate instead of participate |
| \vdots | \vdots | \vdots | \vdots |
| 83 | \frac{83}{100} | \frac{84}{100} | prefers to participate instead of not participate |
| 84 | \frac{84}{100} | \frac{85}{100} | prefers to participate instead of not participate |
| \vdots | \vdots | \vdots | \vdots |
| 97 | \frac{97}{100} | \frac{98}{100} | prefers to participate instead of not participate |
| 98 | \frac{98}{100} | \frac{99}{100} | prefers to participate instead of not participate |
| 99 | \frac{99}{100} | \frac{100}{100} | prefers to participate instead of not participate |
Finally, one more thing before you do your own analysis: You might be wondering exactly where in the table above Person 7’s preferences over her available actions switch. To figure this out, let K be any integer between 0 and 99 inclusive and suppose person 7 expects that K of the 99 other persons will participate. Then, she expects that if she does not participate, the total proportion of the group participating will be \frac{K}{100}, and if she participates, the total portion of the group participating will be \frac{K+1}{100}. Recall that we assumed that Person 7’s threshold T_7 is equal to \frac{3}{4}. So if \frac{K+1}{100} < \frac{3}{4}, then the proportion of the entire group participating will be less than Person 7’s threshold regardless of whether Person 7 participates, and so Person 7 prefers to not participate instead of participate. On the other hand, if \frac{3}{4} \leq \frac{K}{100}, then the proportion of the entire group participating will be greater than or equal to Person 7’s threshold regardless of whether Person 7 participates, and so Person 7 will prefer to participate instead of not participate. Finally, if \frac{K}{100} < \frac{3}{4} \leq \frac{K+1}{100}, then Person 7 is indifferent between not participating and participating. Her utility level will be 1 regardless of her choice!
All that means that if T_7 = \frac{3}{4}, Person 7’s preferences over her actions switch when the number of the other 99 persons passes from below 74 to above. So if we just take the rows of the above table around 74, the switch looks like this:
| Number of other the 99 persons Person 7 expects to participate | Proportion Person 7 Expects to Be Participating if She Does Not Participate | Proportion Person 7 Expects to Be Participating if She Participates | Person 7’s Preferences Over Her Actions |
|---|---|---|---|
| 72 | \frac{72}{100} | \frac{73}{100} | prefers to not participate instead of participate |
| 73 | \frac{73}{100} | \frac{74}{100} | prefers to not participate instead of participate |
| 74 | \frac{74}{100} | \frac{75}{100} | indifferent between participating and not participating |
| 75 | \frac{75}{100} | \frac{76}{100} | prefers to participate instead of not participate |
| 76 | \frac{76}{100} | \frac{77}{100} | prefers to participate instead of not participate |
Prompt 1
In this and the following Prompts, you’ll work with a version of Kuran’s model in which there are 10 persons (i.e. N=10). The prompts will guide you through depicting the strategic interdependence the persons face in the model.
Start in this prompt by imagining any one of the 10 persons. Write a table in which there is one row for each expectation this person could have about the number of the other 9 persons who will participate – i.e. the first row correspond to the expectation that 0 of the other 9 will participate, the second to the expectation that 1 of the other 9 will participate, and so on through the last row corresponding to the expectation that 9 of the other 9 will participate. The table should have three columns. One headed “Number of the other 9 persons the person expects to participate”, one headed “Proportion of the whole group the person expects will be participating if she does not participate”, one headed “Proportion of the whole group the person expects will be participating if she participates”. So the table should look like this:
| Number of the nine other persons the person expects to participate | Proportion of the whole group the person expects will be participating if she does not participate | Proportion of the whole group the persons expects will be participating she participates |
|---|---|---|
| 0 | ||
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 |
Write the table and fill in all the cells!
Prompt 2
Pick a value for the threshold for the person whose expectations and preferences you modeled in the table you wrote in response to Prompt 1. Keep in mind that the threshold is a proportion, so it must be a number between 0 and 1. That said, to make the analysis interesting, make sure to pick a number that is larger than \frac{2}{10} and smaller than \frac{8}{10}. For threshold values outside that range, her preferences over her actions will be the same regardless of what she expects the other persons to do. Any number between \frac{2}{10} and \frac{8}{10} (non-inclusive), but a nice fraction is easiest to handle!
Once you’ve picked the threshold value, write the threshold value you’ve chosen, as in “The threshold I’ve chosen is \frac{3}{4}”. Then, below that statement, re-write the table you wrote in response to Prompt 2 with two additional columns added. The first addition column should be headed “Person’s utility if she does not participate”. The second should be headed “Person’s utility if she participates”. Fill in all the cells!
Prompt 3
Re-write a new version of the table you wrote in response to Prompt 2. In the new version, replace the columns headed “Person’s utility if she does not participate” and “Person’s utility if she participates” with a single column titled “Person’s preferences over her actions”. Fill in all the cells!
Prompt 4
In no more than one page of double-spaced text, explain how the table you wrote in response to Prompt 3 depicts the strategic interdependence faced by the persons in Kuran’s model.
In formulating your explanation, keep in mind that strategic interdependence only occurs when a person’s preferences over her available actions vary according to her expectations about the actions other persons will take! Thus the key thing your explanation is how a person’s preferences over her available actions switch as her expectations change.
Prompt 5
Pick a different value for the threshold than the one you picked in response to Prompt 2. As above, pick a value between \frac{2}{10} and \frac{8}{10} (non-inclusive). Write the different threshold value, as in “The different threshold value I’ve picked is \frac{1}{4}”. Then, re-write the table you wrote in response to Prompt 3 (changing what is written in each cell as required), assuming the person’s threshold is the different value you’ve picked for this prompt.
Prompt 6
Imagine two different persons depicted by Kuran’s model. Imagine one person has the threshold you picked in responding to Prompt 2. Imagine the other person has the threshold value you picked in response to Prompt 5. In no more than 1 page of double-spaced text and using no mathematical expressions nor any computations, (i) describe how these two persons differ from one another in the relationship between their expectations about the actions the other nine person’s will take and their preferences over their own actions and (ii) explain why the differences you described in (i) occur.
Rubric
Prompt 1
The answer gets one point if it writes the required table and fills in all the cells of the table correctly. It gets zero points otherwise.
Prompt 2
The answer gets one point if it states a threshold between \frac{2}{10} and \frac{8}{10} and then writes the required table and fills in all the cells of the table correctly, given the stated threshold. It gets zero points otherwise.
Prompt 3
The answer gets one point if it writes the required table and fills in all the cells correctly, given the threshold value stated in response to Prompt 2. It gets zero points otherwise. If no threshold value was stated for Prompt 2, any answer to this prompt gets zero points unless the relevant threshold value is made clear in some other way.
Prompt 4
A successful answer does all of the following
- It points out that the person modeled in answer to Prompts 2 and 3 prefers to not participate instead of participate when she expects a small portion of the other nine persons to participate and prefers to participate instead of to not participate when she expects a large portion of the other nine persons to participate.
- It points out that a group of persons are strategically interdependent when each one’s preferences over her actions depend on her expectations about what the other persons in the group will do.
- It must be sufficiently free of errors of spelling, grammar and usage as to be readily and easily comprehensible.
- If hand written, it must be immediately and easily legible.
An answer gets…
- Four points…
- if it meets all of the above criteria.
- Two points…
- if it meets criteria (c) and (d) but misses either criterion (a) or (b)
- Zero points…
- if it misses either (c) or (d).
Prompt 5
The answer gets one point if it states a different threshold between \frac{2}{10} and \frac{8}{10} and then writes the required table and fills in all the cells of the table correctly, given the stated threshold. It gets zero points otherwise.
Prompt 6
A successful answer does all of the following
- It states that the person with the lower threshold switches from preferring to not participate instead of participate to preferring to participate instead of not participate at a lower expectations of how many of the other 9 persons will participate than does the person with the higher threshold.
- It must be sufficiently free of errors of spelling, grammar and usage as to be readily and easily comprehensible.
- If hand written, it must be immediately and easily legible.
An answer gets…
- Four points…
- if it meets all of the above criteria.
- Zero points…
- otherwise.