Model Thinking – Decision Tree problem

Currently I am taking Model Thinking from Coursera and I’d like to share interesting problem solving technique using a decision tree model.

Concept

Basic is very simple. You use tree like model to support your decision. See more info here. Without knowing the tool/model, we use this technique often in our real life. Really interesting thing about decision tree is you can quantify your decision with numbers.

Example problem

Here is one of the questions from the week 2 quiz.

You want to go to a concert in Detroit, but you have only $80. The cost of driving will be $30. When you get to the concert, there’s a 40% chance you’ll be able to get a ticket for $50, and a 60% chance that tickets will cost more than $50. If it’s worth $130 to you to go to the concert, should you drive to Detroit to attend this concert? To solve, use a decision tree.

Solution

 

Answer to the question is “Yes” because “Go” decision will give me $2 gain.

In the decision tree, there is no point of exploring “No Go” option because I don’t gain anything from not going. Let’s look at “Go” decision. When I decided to go, I have two possibilities: 40% of getting a ticket at $50, 60% of not getting a ticket. I need to exam each possibilities.

With 60% chance that tickets will be over $50, I can’t buy a ticket due to lack of money. I only have $80, so I ended up loosing the cost of driving which is $30. With 40% chance that ticket will be $50, it requires little bit of calculation. One important statement is that I have to see if it is worth spending $130 for the whole thing. This means my net gain calculation should be based on $130. Starting from $130, subtract driving cost $30 and concert ticket $50, so I have $50 of net gain.

From “Go” decision, I need to calculate overall net gain, so my total net gain from “Go” decision is $2 (see above picture). This means it is worth for me to “Go”.

Conclusion

I found this technique is fascinating. It allows you to think rationally with numbers and possibilities, also allows you to see your reasoning clearly. One of the challenges are understanding the problem from the model thinking. It seems easy when you look at the solution, but actually it is hard to apply the concept to the scenario. Just like every problem solving technique, you will get better as you spend more and think more about the problem.