Which is true for the following decision problem of Alice? Sunny Cloudy RainyBeach 1 2 2Park 2 3 3Mall 1 3 1 A. Beach is a strongly dominated choice for Alice B. Alice has no strongly dominated choices C. Mall is a strongly dominated choice for Alice D. Park is a strongly dominant choice for Alice
Question
Which is true for the following decision problem of Alice? Sunny Cloudy RainyBeach 1 2 2Park 2 3 3Mall 1 3 1 A. Beach is a strongly dominated choice for Alice B. Alice has no strongly dominated choices C. Mall is a strongly dominated choice for Alice D. Park is a strongly dominant choice for Alice
Solution
The correct answer is C. Mall is a strongly dominated choice for Alice.
Here's why:
A strongly dominated choice is one where every other option is always better, regardless of the state of the world.
If we compare the options row by row:
- Beach vs Park: Beach is better when it's sunny (1 < 2), but worse when it's cloudy or rainy (2 > 1).
- Beach vs Mall: Beach is the same when it's sunny (1 = 1), but better when it's cloudy or rainy (2 < 3).
So, Beach is not a strongly dominated choice.
- Park vs Beach: Park is worse when it's sunny (2 > 1), but better when it's cloudy or rainy (3 > 2).
- Park vs Mall: Park is better in all weather conditions (2 > 1, 3 > 3, 3 > 1).
So, Park is not a strongly dominated choice.
- Mall vs Beach: Mall is the same when it's sunny (1 = 1), but worse when it's cloudy or rainy (3 > 2).
- Mall vs Park: Mall is worse in all weather conditions (1 < 2, 3 < 3, 1 < 3).
So, Mall is a strongly dominated choice.
Therefore, the correct answer is C. Mall is a strongly dominated choice for Alice.
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