Chapter 8 from The Complete Problem Solver:

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Chapter 8 from The Complete Problem Solver

• Dealing with chance in decision making
• ME 5211 / HUMF 5211 / IE 5511
• Human Factors

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Dealing with chance in decision making

• Risk there are several possible outcomes, but
  the probability of those outcomes can be
  calculated or estimates. (e.g. card games).
• Uncertainty there are several possible outcomes
  but it is not possible to calculate probabilities
  for the outcomes. (career choice)
• Unknown an event or outcome that was not even
  anticipated or thought of. (what you might
  encounter in space exploration)
• Conflict many outcomes are possible, and an
  enemy is trying to outwit you and foil your
  strategy. (chess)

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Decision MakingCertainty vs Uncertainty

• In making decisions under
• Certainty the task is to choose the alternative
  that is best. Assume that you will get that
  choice.
• Uncertainty You might not get what you choose.

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Decision Making Strategies

• Decision making strategies in Chapter 8
  (Complete Problem Solver) provide a way of
  addressing uncertainty it is uncertain how much
  value one will actually derive from an
  alternative under different conditions.
• Some decision making strategies accommodate
  different decision makers tolerance for risk (or
  lack of tolerance).

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Expected Value

• Expected Value (EV) average payoff from a
  decision.
• Example coin toss games
• Game 1 Win 2 automatically
• Game 2 Heads win 10 tails loose 5
• Which game should you play?

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Expected Value

• Calculate the expected value of each
• EV p(heads)v(heads) (tails)v(tails)
• where p probaility, vvalue
• Game 1
• EV 0.5 (2) 0.5 (2) 2
• Game 2
• EV 0.5 (10) 0.5 (-5) 2.50
• The expected value of Game 2 is greater.
• This means that if you play many times, you will
  likely earn more (on average) if you play Game 2.

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Expected Value

• Calculate the expected value of each
• EV p(heads)v(heads) (tails)v(tails)
• where p probaility, vvalue
• Game 1
• EV 0.5 (2) 0.5 (2) 2
• Game 2
• EV 0.5 (10) 0.5 (-5) 2.50
• The expected value of Game 2 is greater.
• This means that if you play many times, you will
  likely earn more (on average) if you play Game 2.

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Expected Value

• Calculate the expected value of each
• EV p(heads)v(heads) (tails)v(tails)
• where p probaility, vvalue
• Game 1
• EV 0.5 (2) 0.5 (2) 2
• Game 2
• EV 0.5 (10) 0.5 (-5) 2.50
• The expected value of Game 2 is greater.
• This means that if you play many times, you will
  likely earn more (on average) if you play Game 2.

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Difficulties with Expected Value

• Suppose you have the choices
• Win a million dollar for certain,
• Take a 50/50 chance on winning
• either 4 M or nothing!
• Choice 1
• EV 1 M
• Choice 2
• EV .5(4M) .5(0)
• 2 M

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Difficulties with Expected Value

• Suppose you have the choices
• Win a million dollar for certain,
• Take a 50/50 chance on winning
• either 4 M or nothing!
• Choice 1
• EV 1 M
• Choice 2
• EV .5(4M) .5(0)
• 2 M

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Difficulties with Expected Value

• Many people would take the sure thing (choice
  1 1 M for sure), over the riskier choice
  (choice 2)
• Others choose to take the best expected value.
• Yet others choose the chance at the best possible
  outcome.

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Difficulties with Expected Value

• Expected value may not matter to some decision
  makers if
• You are only playing once (there is no average
  result).
• You cannot afford to loose (e.g. retirement
  savings).
• You are a risk adverse person. It makes you
  uncomfortable to loose.
• Different decision makers have different risk
  tolerances.

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Decision Making Strategies that accommodate risk
tolerance

• Optimistic choose option with highest value,
  best return on investment, smallest cost/benefit
  ration.
• Hurwicz Strategy a blend of optimistic and
  pessimistic strategies.
• Pessimistic choose option with the least
  terrible worst case (i.e. minimize regret under
  the worst of circumstances).

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Hurwicz Strategy Procedure

• Choose a value between 0 and 1 for the decision
  makers coefficient of optimism, A. (A 0 is
  very pessimistic, A 1 is very optimistic)
• Find the min and max value for each alternative
  (under the best and worst possible
  circumstances).
• Compute Hurwicz value, H-value, for each
  alternative
• H-value (A)max (1 A)min
• 4. Choose alternative with best H-value.

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Example of Hurwicz Strategy

• Three brothers own a bakery.
• They are choosing between 4 possible investment
  options to increase sales
• Expand bread production
• Add a line of pastries
• Invest in stock market
• Start a bread delivery service
• However, they anticipate each option has risks
  including different probabilities of success
  under different future economic conditions.

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Example of Hurwicz Strategy
Option 4, Delivery, is eliminated because it is
dominated by the first 2 options (it does not
need to be dominated by all options to be
eliminated, one is enough.)