How to construct a decision tree

1
How to construct a decision tree

1. List each decision nodes its alternatives.
2. List each chances nodes its alternatives.
3. Draw the nodes and links.
4. Add costs probabilities along links
5. Calculate utilities for utility (leftmost) nodes
6. Calculate expected utilities

2
Example

• You need to decide whether to do a fancy project
  or a mundane project. Either project can succeed
  or fail. There is a 10 chance of success for
  the fancy project, and 80 chance of success for
  the mundane project. The fancy project costs 1M
  to execute, and if it succeeds, you get 11M. If
  you lose, you get nothing. The mundane project
  costs 0.5M to execute, and you get 1.5M if it
  succeeds. If it fails, you get nothing. Which
  project should you do?

3
1. List each decision nodes its alternatives.

• Which project?
• Fancy
• Mundane

You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
4
2. List each chance nodes its alternatives.

• Outcome?
• Success
• Failure

You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
5
3. Draw nodes as tree
You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
Success
Failure
Fancy
Project?
Mundane
Success
Utility nodes are like diamonds
Decision nodes are square
Failure
Chance nodes are oval
6
4. Add costs and probabilities to links
You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
Successp0.1
Failurep 0.9
Fancycost 1M
Project?
Mundanecost 0.5M
Success p0.8
Failurep0.2
7
5. Calculate utility values for utility nodes
You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
Benefit 11M Cost 1M
Successp0.1
Failurep 0.9
Fancycost 1M
Project?
Mundanecost 0.5M
Success p0.8
Benefit 0 Cost 0.5M
Failurep0.2
8
6. Calculate expected utilities, moving leftward
You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
EU 0.1101.0
Successp0.1
EU 0.9(-1)-0.9
Failurep 0.9
Fancycost 1M
Project?
EU 0.810.8
Mundanecost 0.5M
Success p0.8
EU 0.2(-0.5)-0.1
Failurep0.2
9
6. Calculate expected utilities moving leftward
You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
EU 0.1101.0
EU 1.0-0.9 0.1
Successp0.1
EU 0.9(-1)-0.9
Failurep 0.9
Fancycost 1M
Project?
EU 0.810.8
EU 0.8-0.10.7
Mundanecost 0.5M
Success p0.8
EU 0.2(-0.5)-0.1
Failurep0.2
10
6. Calculate expected utilities moving leftward
You need to decide whether to do a fancy project
or a mundane project. Either project can succeed
or fail. There is a 10 chance of success for
the fancy project, and 80 chance of success for
the mundane project. The fancy project costs 1M
to execute, and if it succeeds, you get 11M. If
you lose, you get nothing. The mundane project
costs 0.5M to execute, and you get 1.5M if it
succeeds. If it fails, you get nothing. Which
project should you do?
EU 0.1101.0
EU 1.0-0.9 0.1
Successp0.1
EU 0.9(-1)-0.9
Failurep 0.9
Fancycost 1M
Project?
EU 0.810.8
EU 0.8-0.10.7
Mundanecost 0.5M
Success p0.8
EU 0.2(-0.5)-0.1
Best choice
Failurep0.2
11
A more complex example

• Your show dog has cancer. If you do nothing,
  there is a 90 chance she will die. If she has
  surgery, there is a 40 chance of curing the
  cancer, 10 chance of dying from the surgery, and
  a 50 chance that the cancer will survive, in
  which case, she has the usual 90 chance of
  dying. If she gets chemo, there is a 20 chance
  of curing the cancer, and an 80 that the cancer
  will remain, in which surgery can be performed,
  with the same risks and outcomes as mentioned
  above. Chemo cannot be done after surgery, by
  the way. The dog is worth 900K if she is alive,
  and nothing if she is dead. Surgery costs 10K
  and chemo costs 4K. What should you do?

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1. List each decision nodes its alternatives.

• Which treatment?
• surgery
• chemo
• Nothing
• After chemo fails, which treatment?
• surgery
• nothing

Your show dog has cancer. If you do nothing,
there is a 90 chance she will die. If she has
surgery, there is a 40 chance of curing the
cancer, 10 chance of dying from the surgery, and
a 50 chance that the cancer will survive, in
which case, she has the usual 90 chance of
dying. If she gets chemo, there is a 20 chance
of curing the cancer, and an 80 that the cancer
will remain, in which surgery can be performed,
with the same risks and outcomes as mentioned
above. Chemo cannot be done after surgery, by
the way. The dog is worth 900K if she is alive,
and nothing if she is dead. Surgery costs 10K
and chemo costs 4K. What should you do?
13
2. List each chance nodes its alternatives.

• Outcome?
• Cancer cured
• Died due to surgery (only for surgery node)
• Cancer not cured

Your show dog has cancer. If you do nothing,
there is a 90 chance she will die. If she has
surgery, there is a 40 chance of curing the
cancer, 10 chance of dying from the surgery, and
a 50 chance that the cancer will survive, in
which case, she has the usual 90 chance of
dying. If she gets chemo, there is a 20 chance
of curing the cancer, and an 80 that the cancer
will remain, in which surgery can be performed,
with the same risks and outcomes as mentioned
above. Chemo cannot be done after surgery, by
the way. The dog is worth 900K if she is alive,
and nothing if she is dead. Surgery costs 10K
and chemo costs 4K. What should you do?
14
3. Draw nodes

• Your show dog has cancer. If you do nothing,
  there is a 90 chance she will die. If she has
  surgery, there is a 40 chance of curing the
  cancer, 10 chance of dying from the surgery, and
  a 50 chance that the cancer will survive, in
  which case, she has the usual 90 chance of
  dying. If she gets chemo, there is a 20 chance
  of curing the cancer, and an 80 that the cancer
  will remain, in which surgery can be performed,
  with the same risks and outcomes as mentioned
  above. Chemo cannot be done after surgery, by
  the way. The dog is worth 900K if she is alive,
  and nothing if she is dead. Surgery costs 10K
  and chemo costs 4K. What should you do?

Cured
Die
uncured
Live
Surgery
Surgery kills
Treatment?
chemo
Cured ?
Surgery
Nothingcost 0
Uncured
Treatment?
Die
Die
Nothing
Live
Live
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4. Add costs probabilities

• Your show dog has cancer. If you do nothing,
  there is a 90 chance she will die. If she has
  surgery, there is a 40 chance of curing the
  cancer, 10 chance of dying from the surgery, and
  a 50 chance that the cancer will survive, in
  which case, she has the usual 90 chance of
  dying. If she gets chemo, there is a 20 chance
  of curing the cancer, and an 80 that the cancer
  will remain, in which surgery can be performed,
  with the same risks and outcomes as mentioned
  above. Chemo cannot be done after surgery, by
  the way. The dog is worth 900K if she is alive,
  and nothing if she is dead. Surgery costs 10K
  and chemo costs 4K. What should you do?

Curedp0.4
Diep0.9
uncuredp0.5
Livep0.1
Surgerycost 10K
Surgery killsp 0.1
Treatment?
chemocost 4K
Cured p0.2
Surgerycost 10K
Nothingcost 0
Uncuredp0.8
Treatment?
Diep0.9
Diep0.9
Nothing
Livep0.1
Livep0.1
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5. Calculate utility values for utility nodes

• Your show dog has cancer. If you do nothing,
  there is a 90 chance she will die. If she has
  surgery, there is a 40 chance of curing the
  cancer, 10 chance of dying from the surgery, and
  a 50 chance that the cancer will survive, in
  which case, she has the usual 90 chance of
  dying. If she gets chemo, there is a 20 chance
  of curing the cancer, and an 80 that the cancer
  will remain, in which surgery can be performed,
  with the same risks and outcomes as mentioned
  above. Chemo cannot be done after surgery, by
  the way. The dog is worth 900K if she is alive,
  and nothing if she is dead. Surgery costs 10K
  and chemo costs 4K. What should you do?

Curedp0.4
Diep0.9
uncuredp0.5
Livep0.1
Surgerycost 10K
Surgery killsp 0.1
Treatment?
chemocost 4K
Cured p0.2
Surgerycost 10K
Nothingcost 0
Uncuredp0.8
Treatment?
Diep0.9
Diep0.9
Nothing
Livep0.1
Livep0.1
17
6. Calculate expected utilities

• Your show dog has cancer. If you do nothing,
  there is a 90 chance she will die. If she has
  surgery, there is a 40 chance of curing the
  cancer, 10 chance of dying from the surgery, and
  a 50 chance that the cancer will survive, in
  which case, she has the usual 90 chance of
  dying. If she gets chemo, there is a 20 chance
  of curing the cancer, and an 80 that the cancer
  will remain, in which surgery can be performed,
  with the same risks and outcomes as mentioned
  above. Chemo cannot be done after surgery, by
  the way. The dog is worth 900K if she is alive,
  and nothing if she is dead. Surgery costs 10K
  and chemo costs 4K. What should you do?

Curedp0.4 EU365
Diep0.9EU -9
uncuredp0.5 EU80
Livep0.1 EU89
Surgerycost 10K EU444
Surgery killsp 0.1EU-1
Cured p0.2 EU179.2
Treatment?
chemocost 4KEU619.2
Surgerycost 10KEU440
Nothingcost 0EU90
Uncuredp0.8EU440
Treatment?
Diep0.9 EU0
Diep0.9 EU-3.6
NothingEU86
Livep0.1 EU90
Livep0.1EU89.6
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My disk drive is flakey. Tech says that there is
a 10 chance it will crash in the next week, and
replacing the disk and data will cost me 200.
If I replace the disk, it will cost me 70 and it
will not crash. If I save its contents to DVD,
reformat and restore it, then it costs me 4 hours
(equivalent to 40) but reduces the chance of
crashing to 3.
EU 0.03(-240)0.97(-40) -46
Yes p0.03
Nop 0.97
Yes
Save, reformat, restore?
Yes p0.1
No
No
Replace disk?
Yes
Nop0.9
EU 0.10(-200)0.90(0) -20
EU -70
19
Quiz question

• You will be drilling a water well in your
  backyard, and you have to decide where to dig it.
  If you just dig where you think it is best,
  there is a 40 chance youll hit water. If you
  hire a seismologist, the chances increase to 60
  but it costs you 10K. If you hire a water
  witch, the chance of hitting water is 50 and the
  cost is 1K. If you get 50K for hitting water,
  what should you do
• Draw the decision tree
• Evaluate alternatives
• Indicate best choice
• Put your name on the paper and hand it in.

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You will be drilling a water well in your
backyard, and you have to decide where to dig it.
If you just dig where you think it is best,
there is a 40 chance youll hit water. If you
hire a seismologist, the chances increase to 60
but it costs you 10K. If you hire a water
witch, the chance of hitting water is 50 and the
cost is 1K. If you get 50K for hitting water,
what should you do?
Yes p0.5 EU24.5
Nop 0.5 EU-0.5
Water witchcost 1KEU24
Yes p0.6EU24
Seismologist Cost 10K EU20
Detector?
Nop0.4 EU-4
Yes p0.4 EU20
Nothing Cost 0 EU20
Nop 0.6 EU0