Decision Trees -- a tool for better decision-making Rebecca A. Bowman, Esq., P.E.
Why is litigation  decision-making difficult? <ul><li>Complexity </li></ul><ul><li>Uncertainty </li></ul>
Complexity <ul><li>Facts </li></ul><ul><ul><li>What actually happened? </li></ul></ul><ul><ul><li>What evidence is there? ...
Complexity <ul><li>The Law </li></ul><ul><ul><li>Statutes </li></ul></ul><ul><ul><li>Best precedents </li></ul></ul><ul><l...
Complexity <ul><li>Damages </li></ul><ul><ul><li>What types of damages? </li></ul></ul><ul><ul><li>What evidence/documenta...
Complexity <ul><li>Other factors – almost all  involve uncertainty </li></ul><ul><ul><li>Direct cost </li></ul></ul><ul><u...
Complexity <ul><li>Other factors – almost all involve uncertainty </li></ul><ul><ul><li>Time to judgment </li></ul></ul><u...
Intuition <ul><li>Uncertainty and complexity usually dealt with intuition </li></ul><ul><li>Intuition includes bias </li><...
Systematic Approach <ul><li>Deal with complexity  </li></ul><ul><li>Understand factors  of uncertainty </li></ul><ul><li>E...
Estimating probability <ul><li>Min Max </li></ul><ul><li>“ Very likely” _____ _____ </li></ul><ul><li>“ Probably” _____ __...
Disclosure of  unasserted claims <ul><li>Possible claim – no disclosure </li></ul><ul><li>Probable claim – disclosure </li...
Probability <ul><li>Expert subjective judgment </li></ul><ul><ul><li>Based on experience and information </li></ul></ul><u...
Judgment <ul><li>If you judge by outcomes, </li></ul><ul><ul><li>Decisions will be made </li></ul></ul><ul><ul><li>to purs...
A Good Decision <ul><li>Logically consistent </li></ul><ul><li>with knowledge </li></ul><ul><li>and preferences </li></ul>
Logic for Decisions <ul><li>Alternatives “What can I do?” </li></ul><ul><li>Information “What do I know?” </li></ul><ul><l...
Value Considerations <ul><li>Dominated by  litigation uncertainties  and monetary outcomes </li></ul><ul><li>Only obvious ...
Logic for quantification <ul><li>Break problem in simple pieces </li></ul><ul><li>Delete unimportant factors </li></ul><ul...
Risk Management Process <ul><li>Structure the problem </li></ul><ul><li>Assess probabilities </li></ul><ul><li>Assess outc...
Case I:  Assembler v. Parts <ul><li>Assembler is suing Parts </li></ul><ul><li>Alleged defective components  from Parts </...
Case I:  Assembler v. Parts <ul><li>Finding of no liability means  no consequentials </li></ul><ul><li>Negative outcome wo...
Objective <ul><li>Projection of net present value  of trial outcome. </li></ul><ul><li>What would you ask a  fortune-telle...
Step 1  Establish a discount rate <ul><li>For our case study, we’ll use 10% </li></ul><ul><li>$1 paid out in is = X$ today...
Step 2 Identify significant factors  of uncertainty <ul><li>Finding of direct liability </li></ul><ul><li>Finding of conse...
Step 3 Build a decision tree Decision  Direct  Consequential  Business Loss    Liability  Liability ($3M)  ($1M) ($1M)  Ye...
Step 4 Assign probabilities Decision  Direct  Consequential  Business Loss Liability  Liability ($3M)  ($1M) ($1M)  Yes Ye...
Step 5 List net outcomes Decision  Direct  Consequential  Business Loss  Outcomes Liability  Liability ($3M)  ($1M) ($1M) ...
Step 6:  Evaluate from the left  the left to get expected values Decision  Direct  Consequential  Business Loss  Outcomes ...
Step 7:  Evaluate from the left to obtain probability distribution Decision  Direct  Consequential  Business Loss  Outcome...
Step 8:  Plot sensitivity to find  impact of critical factors 25%  50%  75%  Probability  Value -0.4M -0.8M -1.2M -1.6M -2...
Step 8:  Plot sensitivity to find  impact of critical factors 25%  50%  75%  Probability  Value -0.4M -0.8M -1.2M -1.6M -2...
Case 2:  Driver v. Machine <ul><li>Driver is suing Machine  for personal injury </li></ul><ul><li>Machine failed to  provi...
Step 1  Establish a discount rate <ul><li>For our case study, we’ll use 10% </li></ul><ul><li>$1 paid out in is = X$ today...
Step 2 Identify significant factors  of uncertainty <ul><li>Finding of direct liability </li></ul><ul><li>Amount of damage...
Step 3 Build a decision tree Decision  Liability  Damages  Hi   ($5M) Yes  Med ($4M)  Lo  ($2M)  Litigate  No Settle ($1.5M)
Step 4 Assign probabilities Decision  Liability  Damages  Hi   ($5M) .2  Yes  Med .6  .5  ($4M)  Lo  .3  ($2M)  Litigate  ...
Step 5 List net outcomes Decision  Liability  Damages  Hi  Outcomes   ($5M)  $5M .2  Yes  Med $4M .6  .5  ($4M)  Lo  .3  (...
Step 6 Evaluate from the right to get expected values Decision  Liability  Damages  Hi  Outcomes   ($5M)  $5M .2x$5M=$1M  ...
Step 7 Evaluate from the left to obtain probability distribution Decision  Liability  Damages  Hi  Outcomes  Probability  ...
Step 8:  Plot sensitivity to find  impact of critical factors 25%  50%  75%  Probability  Value -0.4M -0.8M -1.2M -1.6M -2...
Step 8:  Plot sensitivity to find  impact of critical factors 25%  50%  75%  Probability  Value -$1M -$2M -$3M Settlement ...
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Decision Trees - a tool for better decision-making

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Uploaded on behalf of Rebecca A. Bowman. Presented at the ABA Annual Meeting, Toronto, on August 4, 2011

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Decision Trees - a tool for better decision-making

  1. 1. Decision Trees -- a tool for better decision-making Rebecca A. Bowman, Esq., P.E.
  2. 2. Why is litigation decision-making difficult? <ul><li>Complexity </li></ul><ul><li>Uncertainty </li></ul>
  3. 3. Complexity <ul><li>Facts </li></ul><ul><ul><li>What actually happened? </li></ul></ul><ul><ul><li>What evidence is there? </li></ul></ul><ul><ul><li>Can evidence be acquired? </li></ul></ul><ul><ul><li>Is the evidence admissible? </li></ul></ul><ul><ul><li>Is the evidence believable? </li></ul></ul>
  4. 4. Complexity <ul><li>The Law </li></ul><ul><ul><li>Statutes </li></ul></ul><ul><ul><li>Best precedents </li></ul></ul><ul><li>Liability </li></ul><ul><ul><li>Will there be liability? </li></ul></ul><ul><ul><li>Under which statutes? </li></ul></ul>
  5. 5. Complexity <ul><li>Damages </li></ul><ul><ul><li>What types of damages? </li></ul></ul><ul><ul><li>What evidence/documentation is available? </li></ul></ul><ul><ul><li>Is the evidence/documentation persuasive? </li></ul></ul><ul><ul><li>Punitives? </li></ul></ul>
  6. 6. Complexity <ul><li>Other factors – almost all involve uncertainty </li></ul><ul><ul><li>Direct cost </li></ul></ul><ul><ul><li>Impact of the trial on business </li></ul></ul><ul><ul><li>Impact of outcome on business </li></ul></ul><ul><ul><li>Value of injunction </li></ul></ul><ul><ul><li>Importance as precedence </li></ul></ul>
  7. 7. Complexity <ul><li>Other factors – almost all involve uncertainty </li></ul><ul><ul><li>Time to judgment </li></ul></ul><ul><ul><li>Time to end of appeals </li></ul></ul><ul><ul><li>Time value of money </li></ul></ul><ul><ul><li>Attitude toward risk </li></ul></ul>
  8. 8. Intuition <ul><li>Uncertainty and complexity usually dealt with intuition </li></ul><ul><li>Intuition includes bias </li></ul><ul><li>Intuition may not suggest alternatives/answers </li></ul><ul><li>Can’t document/assess/audit </li></ul>
  9. 9. Systematic Approach <ul><li>Deal with complexity </li></ul><ul><li>Understand factors of uncertainty </li></ul><ul><li>Explicitly account for uncertainty </li></ul><ul><li>Language to deal with uncertainty - probability </li></ul>
  10. 10. Estimating probability <ul><li>Min Max </li></ul><ul><li>“ Very likely” _____ _____ </li></ul><ul><li>“ Probably” _____ _____ </li></ul><ul><li>“ Almost certain” _____ _____ </li></ul><ul><li>“ Likely” _____ _____ </li></ul>
  11. 11. Disclosure of unasserted claims <ul><li>Possible claim – no disclosure </li></ul><ul><li>Probable claim – disclosure </li></ul><ul><ul><li>Reasonably certain </li></ul></ul><ul><ul><li>Extrinsic evidence strong enough to establish presumption </li></ul></ul><ul><ul><li>Prospect of non-assertion slight </li></ul></ul>
  12. 12. Probability <ul><li>Expert subjective judgment </li></ul><ul><ul><li>Based on experience and information </li></ul></ul><ul><ul><li>Don’t know? 50-50 </li></ul></ul><ul><li>Expected value – not precision </li></ul><ul><ul><li>Characteristics of alternatives </li></ul></ul><ul><ul><li>Potential outcomes </li></ul></ul><ul><ul><li>Likelihood of outcomes </li></ul></ul><ul><li>Value of uncertainty </li></ul><ul><ul><li>Attitude toward risk-taking </li></ul></ul>
  13. 13. Judgment <ul><li>If you judge by outcomes, </li></ul><ul><ul><li>Decisions will be made </li></ul></ul><ul><ul><li>to pursue lowest probability </li></ul></ul><ul><ul><li>of bad outcome </li></ul></ul>
  14. 14. A Good Decision <ul><li>Logically consistent </li></ul><ul><li>with knowledge </li></ul><ul><li>and preferences </li></ul>
  15. 15. Logic for Decisions <ul><li>Alternatives “What can I do?” </li></ul><ul><li>Information “What do I know?” </li></ul><ul><li>Values “What do I want?” </li></ul>
  16. 16. Value Considerations <ul><li>Dominated by litigation uncertainties and monetary outcomes </li></ul><ul><li>Only obvious when quantified explicitly </li></ul><ul><ul><li>i.e. impact on sales from negative publicity </li></ul></ul><ul><li>Which outcome do I really prefer? </li></ul><ul><li>How much do I prefer that outcome? </li></ul>
  17. 17. Logic for quantification <ul><li>Break problem in simple pieces </li></ul><ul><li>Delete unimportant factors </li></ul><ul><ul><li>Use judgment </li></ul></ul><ul><ul><li>Use sensitivity analysis </li></ul></ul><ul><li>Focus on the few, critical issues </li></ul>
  18. 18. Risk Management Process <ul><li>Structure the problem </li></ul><ul><li>Assess probabilities </li></ul><ul><li>Assess outcomes </li></ul><ul><li>Analyze the structure </li></ul><ul><li>Evaluate the probabilities </li></ul><ul><li>Iterate if necessary </li></ul><ul><li>Decide </li></ul>
  19. 19. Case I: Assembler v. Parts <ul><li>Assembler is suing Parts </li></ul><ul><li>Alleged defective components from Parts </li></ul><ul><li>Caused high return rate of Assembler’s products </li></ul><ul><li>Direct damages (value of parts) = $1M </li></ul><ul><li>Consequential damages (returns, repairs, damage to reputation) = $3M </li></ul>
  20. 20. Case I: Assembler v. Parts <ul><li>Finding of no liability means no consequentials </li></ul><ul><li>Negative outcome would have adverse publicity which would cost Parts a pending contract worth $1M of profit </li></ul>
  21. 21. Objective <ul><li>Projection of net present value of trial outcome. </li></ul><ul><li>What would you ask a fortune-teller if you could? </li></ul>
  22. 22. Step 1 Establish a discount rate <ul><li>For our case study, we’ll use 10% </li></ul><ul><li>$1 paid out in is = X$ today </li></ul><ul><li>1 year $.91 </li></ul><ul><li>2 years $.83 </li></ul><ul><li>3 years $.75 </li></ul><ul><li>4 years $.68 </li></ul><ul><li>5 years $.62 </li></ul>
  23. 23. Step 2 Identify significant factors of uncertainty <ul><li>Finding of direct liability </li></ul><ul><li>Finding of consequential liability </li></ul><ul><li>Business losses </li></ul><ul><li>Litigate or settle </li></ul>
  24. 24. Step 3 Build a decision tree Decision Direct Consequential Business Loss Liability Liability ($3M) ($1M) ($1M) Yes Yes No Yes Yes Litigate No No No Settle
  25. 25. Step 4 Assign probabilities Decision Direct Consequential Business Loss Liability Liability ($3M) ($1M) ($1M) Yes Yes .6 .6 .4 No Yes Yes .6 .6 Litigate .4 No .4 No .4 No Settle
  26. 26. Step 5 List 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 .6 Litigate .4 No .4 No $1M .4 No $0 Settle ?
  27. 27. Step 6: Evaluate from the left the left to get expected values Decision 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 $1.6M Litigate =2.04M =$0.64M .4 x $1M=$.4M $1M $2.04M .4 x $0 = $0 No $0 Settle <$2.04M
  28. 28. 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
  29. 29. 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
  30. 30. 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
  31. 31. Case 2: Driver v. Machine <ul><li>Driver is suing Machine for personal injury </li></ul><ul><li>Machine failed to provide safety guard </li></ul><ul><li>Workers’ comp claim settled </li></ul><ul><li>Settlement offer of $1.5M </li></ul><ul><li>Low liability estimate of $2M </li></ul><ul><li>High liability estimate of $5M </li></ul><ul><li>Best guess is $4M </li></ul>
  32. 32. Step 1 Establish a discount rate <ul><li>For our case study, we’ll use 10% </li></ul><ul><li>$1 paid out in is = X$ today </li></ul><ul><li>1 year $.91 </li></ul><ul><li>2 years $.83 </li></ul><ul><li>3 years $.75 </li></ul><ul><li>4 years $.68 </li></ul><ul><li>5 years $.62 </li></ul>
  33. 33. Step 2 Identify significant factors of uncertainty <ul><li>Finding of direct liability </li></ul><ul><li>Amount of damages </li></ul><ul><li>Litigate or settle </li></ul>
  34. 34. Step 3 Build a decision tree Decision Liability Damages Hi ($5M) Yes Med ($4M) Lo ($2M) Litigate No Settle ($1.5M)
  35. 35. Step 4 Assign probabilities Decision Liability Damages Hi ($5M) .2 Yes Med .6 .5 ($4M) Lo .3 ($2M) Litigate .4 No Settle ($1.5M)
  36. 36. Step 5 List 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
  37. 37. Step 6 Evaluate from the right to 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
  38. 38. Step 7 Evaluate from the left to obtain probability distribution Decision 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
  39. 39. 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
  40. 40. Step 8: Plot sensitivity to find impact of critical factors 25% 50% 75% Probability Value -$1M -$2M -$3M Settlement of $1.5M

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