This week our goal is to become familiar with using utility in decision-making. We will also map our utility with respect to money. Finally, we will build decision trees to solve practical problems.
Note. There is no pre-workshop assignment. All assignments, homework, or exercises mentioned in the videos and articles are optional.
Instructional Material
- What Utility Is and Isn’t provides our working definition of utility in context of decision-theory, and explain how this is distinct from other definitions of utility you may have used in the past.
- The Certain Equivalent explains a powerful tool for helping you quantitatively value outcomes that may feel very emotionally different.
- Utility in Money provides the means by which we calculate our own utility curve for money.
- Building and Using Decision Trees walks you through a detailed example of building a full decision tree from a real-life example, using all the skills and concepts we have learned up to this point.
Cohort Activity: Crisis Point at Station Seven
You are on an emergency space mission to retrieve a vital fuel source for your home space station's reactor. Even under best-case assumptions, your odds of retrieving the payload are only 75%.
Halfway to the asteroid where the fuel source can be mined, your life support system fails. You rig a modified CO2 scrubber that you estimate has 70% odds of keeping you alive. Even if the scrubber fails and you die, your ship has a 10% chance of retrieving the fuel payload automatically using its robotic autopilot.
You have the option of abandoning the mission and crash-landing on a nearby planet. Your odds of survival are 95%, but you will fail the mission, putting your colony in further jeopardy.
Complete the exercises below with your cohort. Try to stay within the time limit defined for each exercise.
Initial evaluation [5 minutes]
Make a copy of the Crisis Point at Station Seven spreadsheet. It has been filled out with most of the relevant values and equations. Discuss the utility valuations in the Outcomes column, and answer the following questions.
- In which outcome branches do you live?
- Based on these utility valuations, what can you say about how you value your own life in this scenario?
An alien offer [10 minutes]
An alien vessel suddenly appears and offers to transmit to you blueprints for a CO2 scrubber patch that will work at nearly 100% odds, or a landing trajectory that will ensure your own survival if you choose to abort. Which option should you choose, and why?
Utilicoins [5 minutes]
You have with you 100 Utilicoins, a special currency that, using unfathomably advanced technology, is equal to exactly 1 utility in all situations. How many of your Utilicoins would you be willing to give the alien in exchange for the CO2 scrubber patch?
Exploding offer! [5 minutes]
You took too long to decide! The alien entirely withdraws its offer, and instead zaps your robotic autopilot, upgrading its AI and raising the odds of a successful retrieval to 100%, as long as your ship reaches the asteroid – even if the scrubber fails and you die. What is the best choice now?
Wrap up [5 minutes]
Discuss whether you would personally find it reasonable to make a life or death decision this way.
Pre-Workshop Assignment (optional)
Note. This assignment is optional.
Fill in the table below with your certain equivalents on a 50% coin flip, and plot your own utility curve in money. (Use your own familiar currency, as appropriate.) You do not have to share your results, but be prepared to discuss anything you learned from the experience.
| Value ($) | Certain Equivalent |
|---|---|
| 5 | |
| 100 | |
| 500 | |
| 1000 | |
| 2000 | |
| 5000 | |
| 10000 | |
| 50000 |