June 14, 2009
June 14, 2009
June 17, 2009
14.782.1 - 14.782.10
Interesting Different Decision Problems
Consider a choice among three used cars based upon three criteria, miles, price, and year. Year is used as a proxy for other features, such as an adjustable seat and so forth, that have been added to cars over time. The three cars have the following values on the criteria:
Criterion miles price year 1 45K $8K 2000 Car 2 100K $9K 1995 3 60K $10K 1998 Figure 1: choice among three cars
Because Car 1 has the lowest miles, lowest price, and newest year, it is better than the other two cars on every criterion and the decision is easy. Car 1 dominates the other Cars. We call a decision problem containing a dominated alternative “not interesting.” We call a decision problem containing no dominated alternative “interesting.”
Assuming no ties in preferences among alternatives, we can represent a decision problem with 3 alternatives and 3 criteria in a 3 x 3 matrix; an example is shown in Figure 2, where B indicates the best value on that criterion, W the worst value, and M the middle value. Each column must have one B, one M, and one W.
Criterion C1 C2 C3 A1 B M M Alternative A2 W B M A3 M W B Figure 2: Representation of a decision problem
Now compare the matrices in Figures 2 and 3.
Criterion C1 C2 C3 A1 B M M Alternative A2 W M B A3 M B W Figure 3: Matrix equivalent to Figure 2
Each of these matrices contains no dominated alternative, so they are interesting, but the matrices can be obtained from each other by switching C2 and C3. We want to focus on the structure of the decision problems, not the labels for the criteria (or the alternatives), so we call these two
Fraser, J., & Tsai, R. (2009, June), Interesting Different Decision Problems Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. https://peer.asee.org/5598
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