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In the previous lecture, we had an introduction
to the field of decision analysis.
Today we'll introduce some tools that we
can use to structure and evaluate our decisions.
The first of these is the decision tree.
Consider this simple scenario, the decision
that I'll need to make.
I don't like carrying an umbrella with me.
I already have too much to carry around,
and I know from past experience that if I carry an umbrella,
there's a good chance that I'll lose it.
But worse than the hassle of carrying an umbrella,
I really don't like getting wet in the rain.
And the weather forecast today reported a 25% chance of rain,
so that leaves a 75% chance that it won't rain.
Should I bring my umbrella or should I leave it at home?
Using a decision tree, I can start
to structure this question in a way that
will help me to evaluate my identified courses of action.
And those courses of action are bring an umbrella
or leave my umbrella at home.
In this case, my decision tree begins
at a decision node, which is conventionally
represented as a square box.
The possible courses of action are represented
by branches, or action lines.
Each action line terminates in a chance node, which
is represented by a circle.
The chance node represents a state of nature
or a chance event, something I have no control over
and I can't absolutely predict.
The alternative outcomes for each chance event
are represented by lines leaving the chance nodes.
The values of the probability of each outcome occurring
is noted on the branch.
In this case, the chance node might consider the likelihood
of me getting wet.
If I bring an umbrella, regardless
of what the weather does, I can assume
there is only one outcome, which is me staying dry.
Excellent, but if I make that decision every day,
I'm going to do a lot of umbrella
carrying on sunny days, and probably a lot of umbrella
losing.
If I leave my umbrella safely at home,
there are two possible outcomes based on two identified
states of nature.
If the weather is fine, I'll stay dry.
But if it rains, I'm going to get wet.
So what is the best decision for me to make?
In most cases, I need more information
to answer that question.
I need some measure of how much I
don't like the hassle of carrying
an umbrella on a sunny or a rainy day,
as well as a measure of how much I don't like getting wet.
Getting wet is worse, but how much worse?
Well, that depends on my personal preferences.
But if I can quantify them I can start
to develop the maths to answer this question.
Now, would my answer change if the weather forecast changes?
What if rain becomes more or less likely?
How would we factor that into the equation
that we are developing?
Think about it, and we'll talk about it in class.
But before you come, I want you to have a go
at drawing a simple decision tree with one decision
and at least two chance nodes.
It can be any type of decision and you
can make up the numbers.
But I want to see your general design concept.
At the start of the class, I'm going to randomly select
a few students who I'll ask to come up and present
their decision tree on the white board.
It won't need to be amazing.
I'll just want to see that you've
given the idea some thought.
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