Analytical Methods
for Lawyers
v Idea of the Course
¯ Brief survey of lots of areas useful to lawyers
¯ Many of which could be a full course--my L&E
¯ Enough so that you won't be lost when they come up, and É
¯ Can learn enough to deal with them if it becomes necessary.
v Mechanics
¯ Reading is important
¯ Discussion in class
¯ Homework to be discussed but not graded--way of testing yourself
¤ Prefer handout hardcopy or on web page? URL on handout
¯ Midterm? First time.
v
Topics
¯
Decision Analysis
¯
Game Theory
¯
Contracting: Application of Ideas
¯
Accounting.
¯
Finance
¯
Microeconomics.
¯
Law and Economics.
¯
Statistics.
¯ Multivariate
Statistics: Untangling one out of many causes. Death penalty
v First Topic:
Decision Analysis
¯ Way of
formally setting up a problem to make it easier to decide
¯ Typically
¤ Make a
choice.
¤ Observe the
outcome, depends partly on chance
¤ Make another
choice.
¤ Continue
till the end, get some cost or benefit
¤ Want to know
how to make the choices to maximize benefit or minimize cost
¯ Simple
Example: Settlement negotiations
¤ Accept
settlement (known result) or go to trial
¤ If trial win with some probability and
get some amount, or lose and have costs
¤ Compare settlement offer to average
outcome at trial, including costs.
¯ Fancy example: Hazardous materials
disposal firm
¤ You suspect employees may have cut some
corners, violated disposal rules
¤ First choice: Investigate or don't.
á
If you
don't, probably nothing happened (didn't violate or don't get caught)
á
If you do,
some probability that you discover there is a problem. If so É
¤ Conceal or report to EPA
á
If you
conceal, risk of discovery--greater than at previous stage (whistleblowers)
á
If you
report, certain discovery but lower penalty
¯ In each case, how do you figure out what
to do? Two parts:
¤ If you knew all the probabilities and
payoffs, how would you decide (Decision Analysis)
¤ What are the probabilities and payoffs,
and how do you find them?
¯ Simple case again: Assuming numbers
¤ First pass
á
Settlement
offer is $70,000
á
Trial cost
is $20,000
á
Sure to win
á
Tree
diagram
á
Lop off
inferior branch--easy answer
¤ Second pass: As above, but 60% chance of
winning
á
Square for
decision, circle for chance node
á
On average,
trial gives you $40,000
á
Is that the
right measure?
á
If so,
inferior. Lop off that branch
á
Settle
¤ Risk aversion
á
If you are
making similar decisions many times, expected value.
á
If once,
depends on size of stakes.
¯ Where do the numbers come from?
¤ Alternatives: Think. Talk to client,
colleagues, É Think through
alternatives.
á
Partly your
professional expertise
á
Forces you
to think through carefully what the alternatives are.
¤ Probabilities
á
Might have
data--outcome of similar cases in the past. Audit rate.
á
Generate
it--mock trial. Hire an expert.
á
By
intuition, experience. Interrogate. What bets would I accept?
¤ Payoffs
á
Include
money--costs, profits, fines, É Past cases, experts, É .
á
Reputational
gains and losses
á
For an
individual, moral gains and losses? Other nonpecuniary?
¯ Sensitivity analysis
¯ (Land Purchase Problem?)
¯ Is ethics relevant?
¤ Criminal trial--does it matter if you
think your client is guilty?
¤ EPA--does it matter that concealing may
be illegal. Immoral?
á
What if not
looking for the problem isn't illegal, but É
á
Finding and
concealing is?
v
Query re Becca
v Mechanics
¯ Office Hours
handout
¯ Everyone
happy with doing stuff online?
v Review:
Points covered
¯ Basic
approach
¤ Set up a
problem as
á
Boxes for choices
á
Circles for chance outcomes
á
Lines joining them
á
Payoffs, + or -, and probabilities.
¤ Calculate
the expected return from each choice, starting with the last ones
á
Since the payoff from one choice
á
May depend on the previous choice or chance.
¤ If one
choice has a lower payoff than an alternative at the same point, lop that
branch
¤ Work right
to left until you are left with only one series of choices.
¯ Complications
¤ Expected
return only if risk neutral
¤ You have to
work out the structure, with help from the client and others
¤ Estimate the
probabilities, and É
¤ Payoffs, not
all of which are in money.
¯ Sensitivity
analysis to find out whether the answer changes if you change your estimates.
v Handout
problems
¯ Settle or go
to trial
¯ Which
contract to offer
¤ Easy answer
for the team
¤ Note that we
have implicitly solved the player's problem too.
á
Upper contract, if he has back pain, playing costs him $2 million,
gets him nothing, not playing neither costs nor gets, so don't play
á
Lower contract, if he has back pain, playing costs him $2 million,
gets him $10 million. Not playing gets and costs nothing. So he plays.
¤ Note also a
third option, that we didn't mention--no contract.
á
Better than the first
á
Could change the numbers to make it better than the second
á
Demonstrating that one has to figure out the structure of the
problem.
v Questions?
v More book
problems
¯ Land
purchase problem
v
v Game Theory
Intro: Show puzzling nature by examples
¯ Bilateral monopoly
¤ Economic case--buyer/seller, union/employer
¤ Parent/child case
¤ Commitment strategies
á
In economic
case
á
Aggressive
personality.
1/17/06
v Move to front of the room
v Strategic Behavior: The Idea
¯ A lot of what we do involves optimizing
against nature
¤ Should I take an umbrella?
¤ What crops should I plant?
¤ How do we treat this disease or injury?
¤ How do I fix this car?
¯ We sometimes imagine it as a game against
a malevolent opponents
¤ Finagle's Law: If Something Can Go Wrong,
It Will
¤ "The perversity of inanimate
objects"
¤ Yet we know it isn't
¯ But consider a two person zero sum game,
where what I win you lose.
¤ From my standpoint, your perversity is a
fact not an illusion