Rivalrous and Risky Decisions

1
Rivalrous and Risky Decisions

• Sciences Po
• F.H. Buckley
• Goetz 49-75

2
When does it make sense to gamble?
3
How would you react to the following gambles?

• The president of a pharmaceutical company has to
  decide whether to market a newly discovered drug.
  He is uncertain about how many patients will be
  cured, how many might actually be harmed by the
  drug, and the demand for the drug at a certain
  price. Advise him.

4
How would you react to the following gambles?

• A doctor does not know if a patients sore throat
  is caused by a virus or by strep. Failure to
  prescribe the appropriate antibiotics for strep
  can lead to serious illness, but over-prescribing
  antibiotics is harmful also. Advise the doctor.

5
How would you react to the following gambles?

• Your fairy godmother asks you to toss a six-sided
  die. She will pay you 20 if 2 turns up and 40
  if 4 turns up. You will lose 30 if 6 turns up,
  and neither win nor lose if a 1, 3 or 5 turns up.
  
• Would you pay anything to be allowed to
  participate in such a bet?

6
Exhibit 2.1 Representing the wagerGoetz p. 50
A fair die
7
Representing the wagerWould you pay anything to
take the wager?
A fair die
8
Representing the wagerWould you pay anything to
take the wager?
Expected Value 5
9
What if the Wicked Witch of the East switches the
payoffs?What would you pay not to take the wager?
10
The Wicked Witch of the EastWhat would you pay
not to take the wager?
Expected Value -15
11
Are you an EMVer?

• You are presented with a gamble with a 50
  probability of a payoff of 1 and a 50
  probability of a payoff of -1. Would you take
  the bet?

12
Are you an EMVer?

• You are presented with a gamble with a 50
  probability of a payoff of 1 and a 50
  probability of a payoff of -1. Would you take
  the bet?
• Same coin toss, but now the stakes are 1000.

13
Are you an EMVer?

• You are presented with a gamble with a 50
  probability of a payoff of 1 and a 50
  probability of a payoff of -1. Would you take
  the bet?
• Same coin toss, but now the stakes are 1000.
• In the latter case, would you pay money NOT to
  take the gamble?

14
Dispersion of outcomes matters to non-EMVers


x
All three Bell Curves have the same mean value
(x) but different risk (dispersions from the
mean).
15
Three kinds of people

• EMVers are risk neutral.
• Most people are risk averse.
• Risk lovers are risk prone.

16
A new concept Utility

• Utility is the economists measure of well-being
  (cf. utilitarianism)
• Ordinal Utility measures preferences without
  weighing them (first, second, third, etc. are
  ordinal numbers)
• Cardinal Utility (Benthams utils) weighs
  utility (one, two, three are cardinal numbers)

17
Cardinal Utility
Utility
For EMVers, utility is linear with money

18
Cardinal Utility
For the risk averse, the marginal utility of
money declines (more money generates
increasingly smaller increases in utility).
Utility

19
Cardinal Utility
In what follows we posit risk aversion through a
non-linear utility function U 100M1/2
Utility

20
Cardinal Utility
With U 100M1/2, utility increases with money,
but at a decreasing rate
Utility

21
Goetzs Exhibit 2.2, p. 52U 100M1/2Fill in
the Marginal Utility blanks
22
Goetzs example U 100M1/2Fill in the Marginal
Utility blanks
23
Goetzs example U 100M1/2Fill in the blanks
24
Goetzs example U 100M1/2Fill in the
remaining blanks
25
Goetzs example U 100M1/2Fill in the
remaining blanks
26
Goetzs question 2 on p. 54You have 100 and are
offered a coin toss for 19

• Is this an attractive prospect?
• Recall that U 100M1/2

27
Goetzs question 2 on p. 54You have 100 and are
offered a coin toss for 19

• Is this an attractive prospect?
• How does U100 compare to (.5U81 .5U119)

28
Goetzs question 2 on p. 54You have 100 and are
offered a coin toss for 19

• Is this an attractive prospect?
• How does U100 compare to (.5U81 .5U119)
• U100 1,000

29
Goetzs question 2 on p. 54You have 100 and are
offered a coin toss for 19

• Is this an attractive prospect?
• How does U100 compare to (.5U81 .5U119)
• U100 1,000
• The utility level of the risk
• .5100811/2 .51001191/2
• 450 545.44
• 995.44

30
Goetzs question 2 on p. 54You have 100 and are
offered a coin toss for 19

• U100 1,000
• Urisk 995.44
• So youre worse off with the wager. Can we
  quantify this in dollars?

31
Goetzs question 3 on p. 54You have 100 and are
offered a coin toss for 19

• What income level would give you U995.44?

32
Goetzs question 3 on p. 54You have 100 and are
offered a coin toss for 19

• What income level would give you U995.44?
• 100M1/2 995.44

33
Goetzs question 3 on p. 54You have 100 and are
offered a coin toss for 19

• What income level would give you U995.44?
• 100M1/2 995.44
• M1/2 9.954
• M 9.9542
• 99.0892

34
Goetzs question 3 on p. 54You have 100 and are
offered a coin toss for 19

• You would therefore pay (100 99.0892) 0.918
  to avoid the risk

35
Law of the Leaning TreeGoetz p. 54
36
Law of the Leaning TreeGoetz p. 54

• The tree costs 385 to remove and the damages
  will be 760 if it does fall.
• Probability of it falling is 60
• EMV .6(-760) -456.
• Suppose Abbot owned both properties what would
  happen? (Internalizing the externality).

37
Law of the Leaning TreeGoetz p. 54

• Suppose liability amounts to a coin toss. What
  would happen?
• Each partys exposure .5(.6)(760) 228
• No one would fix the tree.

38
Law of the Leaning TreeGoetz p. 55, Question 4

• What do non-homogenous expectations do?

39
Law of the Leaning TreeGoetz p. 54, Question 4

• What do non-homogenous expectations do?
• Each party thinks his own liability is
  (.4)(.6)760 182.40 and that that of the other
  party is (.6)(.6)760 273.60
• Will the parties agree to fix the tree in these
  circumstances?

40
Can you now say something about the desirability
of clear legal rules?

• Goetz p. 55, question 5.

41
Mrs. Crispys Chicken Goetz p. 55

• Let me leave this for youquestions about it?

42
In re John LynchGoetz p. 56
How would you penalize the flasher?
Is a sentence with an indefinite term cruel and
unusual punishment?
43
An optimal sentencing policy depends on the
probability of detection

• What should the penalty for flashing be if the
  probability of detection is 100?
• The rational criminals calculus
• Commit crime if B gt pApGP, where
• B Benefit of crime
• pA probability of arrest
• pG probability of being found guilty
• P criminal penalty

44
Is there such a thing as too little crime?

• Suppose that B is much smaller than pApGP.
• Does that mean that we should adjust pApGP?
• Too many policemen are we in a police state?
• Are our criminal procedure laws too tilted
  towards the prosecution (i.e., do we convict too
  many innocent people?)
• Are our criminal sentences cruel and unusual?

45
Suppose youre designing a criminal justice system

• What does this tell you about the number of
  policemen to employ?
• Could we reduce our police budget by levering up
  penalties?
• What are the limits on this way of thinking?

46
Suppose youre designing a criminal justice system

• What does this tell you about the number of
  policemen to employ?
• Could we reduce our police budget by levering up
  penalties?
• What are the limits on this way of thinking?
• Cruel and unusual
• Jury nullification
• Overdeterence and risk aversion

47
Richards v. AllstateGoetz p. 60

• Legal Jargon
• Diversity jurisdiction
• Jury verdicts
• Compensatory and punitive damages

48
Richards v. AllstateGoetz p. 60

• What did Allstate do that was wrong?

49
Richards v. Allstate

• What did Allstate do that was wrong?
• Retained Exclusion 2 for non-covered cars
• Denied coverage for a non-covered car.
• Why wouldnt compensatory damages suffice?

50
Richards v. Allstate

• What did Allstate do that was wrong?
• Retained Exclusion 2 for non-covered cars
• Denied coverage for a non-covered car.
• Why wouldnt compensatory damages suffice?
• Why did Allstate retain Exclusion 2?
• Did the plaintiff get what he bargained for?

51
How is this case like In re John Lynch?

• Lets say that compensatory damages amounted to
  2500. What would you award, if anything, as
  punitive damages?

52
How is this case like In re John Lynch?

• Lets say that compensatory damages amounted to
  2500. What would you award, if anything, as
  punitive damages?
• How do you feel about 750,000 in punitives?

53
How is this case like In re John Lynch?

• Lets say that compensatory damages amounted to
  2500. What would you award, if anything, as
  punitive damages?
• How do you feel about 750,000 in punitives?
• Saul Levmore on interstate exploitation as a PD
  game. The Fifth Circuit remitted to 350,000

54
How is this case like In re John Lynch?

• Lets say that compensatory damages amounted to
  2500. What would you award, if anything, as
  punitive damages?
• How do you feel about 750,000 in punitives?
• Cass Sunstein on juries and outrage

55
More probability theory Craig v. BorenGoetz p.
62

• What happened in the case?
• Nor shall any state deprive any person of life,
  liberty, or property, without due process of law,
  nor deny to any person the equal protection of
  the laws (Fourteenth Amendment).

56
More probability theory Craig v. BorenGoetz p.
62

• Could a state discriminate on the basis of sex on
  the sale of beer?
• What is the standard for review Trial Court
  asked if Oklahoma had a rational basis for the
  discriminatory standard?
• Is a heightened scrutiny standard more
  appropriate in the case of discrimination?

57
More probability theory Craig v. BorenGoetz p.
62

• Is the difference in treatment attributable to
  mere prejudice?
• Is the difference between 0.18 (female) and 2
  (male) significant?
• Is this attributable to chivalrous police
  officers, as Brennan suggests?