This week, we learned about decisions under ignorance and the various methods for choosing the most rational decision under specific conditions. Now, its your turn to take the concepts we learned this week and apply them to a real$-$world problem.

This week, you$$ll take the role of our decisionmaker. In this homework, you must answer an important question: $$Should I buy AppleCare for my new device?$$

Read the information below to answer the following homework assignment. Be sure to submit your responses by our deadline, which is outlined in our course Syllabus.

The Facts

Today is an exciting day. Apple is releasing a brand new device that will revolutionize your mobile computing experience forever. The AppleJuice is a brand new, lightweight wearable device that$$s part phone and part watch. It requires charging only once every three months. Gone are the days of being tethered to a wall or running out of power when you least expect it$.$

You are an early adopter of all new technology. You were so excited for the release of the AppleJuice that you camped outside of the Apple Store for $3$ days to be one of the first to own it$.$ When the doors finally open, you grab the shiny new product from the shelves. As you go to make your purchase, the sales associate asks you:

$$Would you like to purchase our AppleCare protection plan?$$

The AppleCare protection plan for the new AppleJuice will replace your AppleJuice with no questions asked for any defects, accidents, and other issues for $2$ years after your original purchase date. If you do not buy the protection plan, the sales associate tells you that you will not be covered if anything malfunctions on the device or if you accidentally break the device. If you are not covered by AppleCare, you will need to buy a brand new AppleJuice.

You$$ve been reading up on the technology for months. Unfortunately because this is a product that has never been seen in the history of wearable computers, there have been no reviews that speak about how durable or reliable the AppleJuice truly is$.$ There is no way, at this moment in time, for you to assign any probability to how the AppleJuice will be when it$$s in use.

As a true decision theorist, you ask the Apple associate for an iPad and a stylus as you think about this question.

NOTE: Prices have been omitted to simplify this question and to focus on the concepts of decisions under ignorance. Please do not factor the price of the AppleJuice purchase and the price of the Warranty in this specific calculation!

Objectives

By the end of this exercise, you should be able to:

Construct a decision table based on a real scenario

Rank and value each outcome in your decision table

Use a pre$-$filled decision table to answer several decision under ignorance questions

Apply informal writing to decision theory concepts

Instructions

Part A

Using the information provided in the question above, map out a decision table with two alternatives and two states of nature that represents your decision problem with the issue $$Should I buy the AppleCare protection plan?$$ You can use the pre$-$made decision matrix below to get started:

ISSUE: Should I Buy the AppleCare Protection Plan?

S$1.$ S$2.$

A$1.$

A$2.$

$2.$ Rank all of the outcomes from your matrix based on your preferences. Then, provide values for all of your stated outcomes in an ordinal scale.

Part B

Assume that your decision matrix for this problem has the following values:

ISSUE: Buy the AppleCare Protection Plan?

S$1.$ S$2.$

A$1.24$

A$2.13$

Answer Questions $3,4,$ & $5$ using the information provided in the matrix in Part B$.$

In questions $3-5,$ be sure to show your reasoning along with your answer in order to receive full credit for your work!

Based on the decision matrix in Part B$,$ which Act should you choose under the Dominance Principle? Why?

Based on the decision matrix in Part B$,$ which choice would the MAXIMIN rule suggest that you make? Why?

Based on the decision table and rankings in Part B$,$ which choice would the MAXIMAX rule suggest that you make? Why?

Part C

Based on your own observations and your own experience with buying any new technology: which would you choose? Why did you make your selection?