Decision Trees

-- a tool for better decision-making

Rebecca A. Bowman, Esq., P.E.

Why is litigation decision-making difficult?

Complexity

Uncertainty

Complexity

Facts

What actually happened?What evidence is there?Can evidence be acquired?Is the evidence admissible?Is the evidence believable?

Complexity

The LawStatutesBest precedents

LiabilityWill there be liability?Under which statutes?

Complexity

DamagesWhat types of damages?What evidence/documentation is available?Is the evidence/documentation persuasive?Punitives?

Complexity

Other factors – almost all involve uncertainty

Direct costImpact of the trial on businessImpact of outcome on businessValue of injunctionImportance as precedence

Complexity

Other factors – almost all involve uncertainty

Time to judgmentTime to end of appealsTime value of moneyAttitude toward risk

Intuition

Uncertainty and complexity usually dealt with intuitionIntuition includes biasIntuition may not suggest alternatives/answersCan’t document/assess/audit

Systematic Approach

Deal with complexity

Understand factors of uncertainty

Explicitly account for uncertainty

Language to deal with uncertainty - probability

Estimating probability

Min Max

“Very likely” _____ _____“Probably” _____ _____“Almost certain” _____ _____“Likely” _____ _____

Disclosure of unasserted claims

Possible claim – no disclosureProbable claim – disclosure

Reasonably certainExtrinsic evidence strong enough to establish presumptionProspect of non-assertion slight

ProbabilityExpert subjective judgment

Based on experience and informationDon’t know? 50-50

Expected value – not precisionCharacteristics of alternativesPotential outcomesLikelihood of outcomes

Value of uncertaintyAttitude toward risk-taking

Judgment

If you judge by outcomes,

Decisions will be made

to pursue lowest probability

of bad outcome

A Good Decision

Logically consistent

with knowledge

and preferences

Logic for Decisions

Alternatives “What can I do?”

Information “What do I know?”

Values “What do I want?”

Value ConsiderationsDominated by litigation uncertainties and monetary outcomesOnly obvious when quantified explicitly

i.e. impact on sales from negative publicity

Which outcome do I really prefer?How much do I prefer that outcome?

Logic for quantification

Break problem in simple pieces

Delete unimportant factorsUse judgment Use sensitivity analysis

Focus on the few, critical issues

Risk Management Process

Structure the problemAssess probabilitiesAssess outcomesAnalyze the structureEvaluate the probabilitiesIterate if necessaryDecide

Case I: Assembler v. Parts

Assembler is suing PartsAlleged defective components from PartsCaused high return rate of Assembler’s productsDirect damages (value of parts) = $1MConsequential damages (returns, repairs, damage to reputation) = $3M

Case I: Assembler v. Parts

Finding of no liability means no consequentialsNegative outcome would have adverse publicity which would cost Parts a pending contract worth $1M of profit

Objective

Projection of net present value of trial outcome.

What would you ask a fortune-teller if you could?

Step 1 Establish a discount rateFor our case study, we’ll use 10%

$1 paid out in is = X$ today 1 year $.91 2 years $.83 3 years $.75 4 years $.68 5 years $.62

Step 2Identify significant factors

of uncertainty

Finding of direct liabilityFinding of consequential liabilityBusiness lossesLitigate or settle

Step 3Build a decision tree

Decision Direct Consequential Business Loss Liability Liability ($3M) ($1M)

($1M) Yes Yes

No Yes Yes

Litigate No

No

No

Settle

Step 4Assign probabilities

Decision Direct Consequential Business Loss Liability Liability ($3M) ($1M) ($1M) Yes Yes .6

.6 .4 No Yes Yes .6 .6Litigate .4 No

.4 No

.4 No

Settle

Step 5List net outcomes

Decision Direct Consequential Business Loss Outcomes Liability Liability ($3M) ($1M) ($1M) Yes $5M Yes .6

.6 .4 No $4M Yes Yes $2M .6 .6Litigate .4 No

.4 No $1M

.4 No $0

Settle ?

Step 6: Evaluate from the left

the left to get expected valuesDecision Direct Consequential Business Loss Outcomes

Liability Liability ($3M) ($1M) ($1M) Yes $5M Yes .6 x $5M=$3M

.6 x $4.6M =$2.76M .4 x $4M=$1.6M $4M Yes Yes $2M .6 x $2M=$1.2M .6 x $3.4M .4 x $1.6MLitigate =2.04M =$0.64M

.4 x $1M=$.4M $1M$2.04M .4 x $0 = $0 No $0

Settle <$2.04M

Step 7: Evaluate from the left to obtain probability distribution

Decision Direct Consequential Business Loss Outcomes Probability Liability Liability ($3M) ($1M) ($1M) Yes $5M .6x.6x.6 Yes .6 x $5M=$3M =.216

.6 x $4.6M .6x.6x.4 =$2.76M .4 x $4M=$1.6M $4M =.144 Yes Yes $2M .6x.4x.6 .6 x $2M=$1.2M =.144 .6 x $3.4M .4 x $1.6M Litigate =2.04M =$0.64M

.4 x $1M=$.4M $1M .6x.4x.4$2.04M =.096 .4 x $0 = $0 No $0 =.400

Settle <$2.04M

Step 8: Plot sensitivity to find impact of critical factors

25% 50% 75% Probability Value

-0.4M

-0.8M

-1.2M

-1.6M

-2.0M

Step 8: Plot sensitivity to find impact of critical factors

25% 50% 75% Probability Value

-0.4M

-0.8M

-1.2M

-1.6M

-2.0M

Settlement of $.8M

Settlement of $1.4M

Case 2: Driver v. MachineDriver is suing Machine for personal injuryMachine failed to provide safety guardWorkers’ comp claim settledSettlement offer of $1.5MLow liability estimate of $2MHigh liability estimate of $5MBest guess is $4M

Step 1 Establish a discount rateFor our case study, we’ll use 10%

$1 paid out in is = X$ today 1 year $.91 2 years $.83 3 years $.75 4 years $.68 5 years $.62

Step 2Identify significant factors

of uncertainty

Finding of direct liability

Amount of damages

Litigate or settle

Step 3Build a decision tree

Decision Liability Damages Hi ($5M) Yes Med ($4M) Lo ($2M) Litigate

No

Settle ($1.5M)

Step 4Assign probabilities

Decision Liability Damages Hi ($5M) .2 Yes Med .6 .5 ($4M) Lo .3 ($2M) Litigate

.4 No

Settle ($1.5M)

Step 5List net outcomes

Decision Liability Damages Hi Outcomes ($5M) $5M .2 Yes Med $4M .6 .5 ($4M) Lo .3 ($2M) $2M Litigate

.4 $0 No

Settle ($1.5M) $1.5M

Step 6Evaluate from the rightto get expected values

Decision Liability Damages Hi Outcomes ($5M) $5M .2x$5M=$1M Yes Med $4M .6x$3.6M .5x$4M=$2M ($4M) =$2.16M Lo .3x$2M=$.6M ($2M) $2M Litigate

.4x$0=0 $0 No

Settle ($1.5M) $1.5M

Step 7Evaluate from the left to

obtain probability distributionDecision Liability Damages Hi Outcomes Probability ($5M) $5M .6x.2=.12 .2x$5M=$1M Yes Med $4M .6x.5=.30 .6x$3.6M .5x$4M=$2M ($4M) =$2.16M Lo .3x$2M=$.6M ($2M) $2M .6x.3=.18 Litigate

.4x$0=0 $0 .4 No

Settle ($1.5M) $1.5M

Step 8: Plot sensitivity to find impact of critical factors

25% 50% 75% Probability Value

-0.4M

-0.8M

-1.2M

-1.6M

-2.0M

Step 8: Plot sensitivity to find impact of critical factors

25% 50% 75% Probability Value

-$1M

-$2M

-$3M

Settlement of $1.5M