COU 2: Summarizing Another Expected Utility Model
In COU 1, you were guided step-by-step through the processes of extracting the required elements of an expected utility model from a narrative description. This COU will not go step-by-step. Instead it will describe all the elements of an expected utility model in a single chunk of text. Your job is to extract and summarize each of the four essential elements of the model.
Imagine a person choosing whether or not to join an anti-government guerilla or terrorist group, as in the models explored in several of the COUs from Lesson 5. Specifically, this person must choose whether to join or to not join the group. Suppose this person cares about two outcomes of her decision: Whether the group is effective or ineffective and whether or not she is a member of the group. Obviously, whether or not she is a member of the group will be directly determined by whether or not she joins. But she is uncertain about whether the group is effective or ineffective. Thus her choice to join or not join will result in one of four possible outcomes:
- The group is effective and she is a member.
- The group is ineffective and she is a member.
- The group is effective and she is not a member.
- The group is ineffective and she is not a member.
She believes that the group is effective with probability \frac{1}{10} and ineffective with probability \frac{9}{10}. Therefore, if she joins the group, the group will be effective and she will be a member with probability \frac{1}{10}, and the group will be ineffective and she will be a member with probability \frac{9}{10}. On the other hand, if she does not join, the group will be effective and she will not be a member with probability \frac{1}{10}, and the group will be ineffective and she will not be a member with probability \frac{9}{10}.
As for her utility level, the person prefers to be a member of the group if it is effective and prefers to not be a member if it is not effective. Specifically, her utility function from any given outcome is: \begin{Bmatrix} 20 & \text{if the group is effective and she is a member} \\ 0 & \text{if she is not a member} \\ -1 & \text{if the group is ineffective and she is a member} \end{Bmatrix}
Summarize the required elements of this model by filling in the following list:
- Available Actions:
- Possible Outcomes:
- Conditional Probability Distribution:
- Utility Function:
In specifying the conditional probability distribution, use the tabular format for specifying conditional probability distributions that we’ve used in a number of places in Lessons 5 and 6, i.e.:
| Outcome | Probability |
|---|---|
| [one of the outcomes] | [probability of that outcome] |
| [another outcome] | [probability of that other outcome] |
| Outcome | Probability |
|---|---|
| [another outcome] | [probability of that outcome] |
| [another outcome] | [probability of that outcome] |
Rubric
There is one correct summary of each of the four required elements, although that summary may be expressible in a number of ways. For each of the four required elements, you get one point if you specify it correctly and zero points otherwise.