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Demonstration: Decision-Making Under Uncertainty
21.03 • Decision-Making Under Uncertainty
We will demonstrate the principles using a simple (but real) example.
• This is a personal investment decision.
• The outcome is uncertain.
• The potential gains/losses are real.
What is the most that you are willing to invest?
31.03 • Decision-Making Under Uncertainty
1. The selected participant plays the game once.
2. The cost to play is 20.
3. Payment is cash or check; no refunds.
Thumbtack Sweepstakes Rules
VISA MasterCard
4. I will “flip” a thumbtack.
5. The player calls: “Point up”“Point down”
6. If the call is correct, the player wins and keeps 100.
7. If the call is incorrect, the player wins nothing.
8. I keep the amount paid to play, regardless of the outcome.
41.03 • Decision-Making Under Uncertainty
A decision tree organizes and displays important factors of a decision in chronological sequence.
Invest
Don’t Invest
Decision
– 20
Decision
Correct Call
Incorrect Call
Uncertainty
Uncertainty
Outcome
100
0
0
– 20
Net Profit
80
0
Time
51.03 • Decision-Making Under Uncertainty
We define a decision as an “irrevocable” allocation of resources.
We have a certificate acknowledging this first “decision” of the day.
61.03 • Decision-Making Under Uncertainty
Probabilities quantify the player’s judgment about the likelihood of winning.
Correct Call
Incorrect Call
Probability = p
Probability = 1 – p
This uncertain situation is called a “deal” or a “lottery.”
71.03 • Decision-Making Under Uncertainty
To evaluate the tree, we must establish a value for the deal, assuming that we’ve made the investment.
Invest
Don’t Invest
Decision
0
– 20
Correct Call
Incorrect Call
Uncertainty Outcome
100
0
p =
1 – p =
Correct Call
Incorrect Call
Uncertainty Outcome
100
0
p =
1 – p =
Deal
To value the deal going forward, ignore the “sunk” 20; that’s behind us now.
81.03 • Decision-Making Under Uncertainty
The value of the deal is the player’s minimum selling price or “certain equivalent.”
The player is indifferent between having the deal or its certain equivalent.
Correct Call
Incorrect Call
Uncertainty Outcome
100
0
p =
1 – p =
Deal
CertainEquivalent
91.03 • Decision-Making Under Uncertainty
Another way to value the deal is to calculate its “expected value” (probability-weighted average).
The expected (or “mean”) value is the average return from each flip if it were repeated many times.
Correct Call
Incorrect Call
Uncertainty Outcome
100
0
p =
1 – p =
Deal
p x 100 + (1 – p) x 0
ExpectedValue
101.03 • Decision-Making Under Uncertainty
The difference between “expected value” and “certain equivalent” reflects attitude toward risk.
This is a matter of preference; there is no “correct” risk attitude.
MonetaryValue
RiskAverse
RiskNeutral
RiskPreferrin
g
Expected Value
Risk Attitude
Certain Equivalent
111.03 • Decision-Making Under Uncertainty
Is it worthwhile to gather information to reduce or to eliminate uncertainty?
Correct Call
Incorrect Call
Uncertainty Outcome
100
0
p =
1 – p =
No Info
Buy Information
Decision
?–?
What is the most that our player should pay for perfect information?
121.03 • Decision-Making Under Uncertainty
CertainEquivalent
Perfect information about the outcome of the flip guarantees winning the 100.
Correct Call
Incorrect Call
Uncertainty Outcome
100
0
p =
1 – p =
Decision
No Info
Buy PerfectInformation
100Correct Call
p = 1.0 –?
Here the value added by perfect information is 100 – the certain equivalent.How many opportunities do you have to buy perfect information in your business?
ValueAdded
131.03 • Decision-Making Under Uncertainty
Perfect information may not be available. Here are imperfect sources.
• Experiments—5 trial flips of the tack
• Opinion polls
• Experts
• Mathematical models
SURVEY
141.03 • Decision-Making Under Uncertainty
What is your call?
Point up? Point down?
151.03 • Decision-Making Under Uncertainty
We must distinguish between good decisions and good outcomes.
Preferred Results
Good Outcomes
Balances the probabilities of good and
bad outcomesconsistent with preferences
Good Decisions
40
–6
15
4
.6
.4
.7
.3
161.03 • Decision-Making Under Uncertainty
Making good decisions may not lead to good outcomes.
Good decisionsguarantee
good outcomes.
Decisions with Certainty
CorrectInvest
Don’t Invest
Good decisionsdo not guaranteegood outcomes.
Decisions with Uncertainty
Correct
Incorrect
Invest
Don’t Invest
The goal of decision analysis is make the best decisions in the face of uncertainty.
171.03 • Decision-Making Under Uncertainty
Several insights emerge from the demonstration.
• A decision is an irrevocable allocation of resources.
Invest
Buy Info.
... 30% ...• Probability is the quantitative language for communicating about uncertainty.
• Probabilities represent judgment, which includes experience and information.
• The value of an uncertain deal depends on its characteristics and one’s attitude toward risk.
• The economic value of gathering more information can be calculated before making a decision.
• We must distinguish between the quality of the decision and its outcome.
