Chapter 14 Utility Axioms,Paradoxes and Implications

1
Chapter 14Utility Axioms,Paradoxes and
Implications

• Wang YU

2
Axioms

• These axioms are the foundations of utility
  theory because that people who behave according
  to the axioms should make choices consistent with
  the maximization of expected utility.
• People dont always behave according to theses
  axioms.

3
Axioms

• 1. Ordering and transitivity (Loop)
• 2. Reduction of compound uncertain events
• 3. Continuity
• 4. Substitutability
• 5. Monotone

• 6. Invariance
• 7. Finiteness
• Conclusion Axioms are just assumptions. Based on
  these assumptions, we can introduce ordinal
  utilities.

4
Paradoxes

• 1. Framing effects
• Where do you put the status quo?
• Peoples tend to be risk-averse in dealing with
  gains but risk-seeking in deciding about losses.
• Axiom 6 Invariance. Both the probabilities,
  paid offs and frames of the problems should be
  taken into consideration.

5
Paradoxes Contd

• 2. Certainty Effect
• People tend to place too much weight on certainty
  outcome relative to uncertain outcomes. Allais
  Paradox
• We should behave according to sure-thing
  principles.

6
Implications

• Utility assessment
• Basic Idea Hold three of Gain, Loss, Probability
  and CE fixed and find the remaining one.
• CE with gain, more risk-averse
• With loss, more risk-seeking
• PE Certain forms of probability distortion
• New method to assess utility are needed.

7
Implications Contd

• 1. Reference set and status quo sunk cost and
  viewpoint to modeling a decision problem.
• 2. Mania for certainty. ( protest for nuclear
  power plant).

8
Conclusion

• Decision analysis is a constructive mean to help
  the decision maker to gain insight from analysis
  and get consistent decisions.
• 1. Utility and personal preferences assessment.
• 2. Modeling the problem.
• Systematically and consistently.