Using RENO to Determine the Probabilities of Outcomes in a Lawsuit

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Example DT-2 - Lawsuit Outcomes

Software Used:
RENO

Problem Statement:

Consider the case of SALF vs. ACME, where SALF (Sue All Law Firm) is suing ACME (A Company Manufacturing Everything).

ACME considers offering SALF $2 million for an out of court settlement.

There is a 17% chance that SALF will accept the offer.
If not, SALF will counter with $5 million.

ACME can:

Accept the $5 million counteroffer (30%).
Go to court (30%).
- In court, there is:
  - A 10% chance of a $7 million award.
  - An 80% chance of a $5 million award.
  - A 10% chance of winning the case (no award).
Re-counter at $3 million (40%).

SALF can then:

Accept the $3 million settlement (20%).
Go to court.
- In court there is:
  - A 10% chance of a $7 million award.
  - An 80% chance of a $5 million award.
  - A 10% chance of losing the case (no award).

Compute the probabilities of each outcome.

RENO Solution:

Define a Constant to represent the total probability of ACME's initial offer (100%), which will then be broken down into the probabilities of all possible outcomes.

Offer Constant

Construct the Flowchart as follows:

Flowchart to model the problem

Step 1: Use a Standard Block to represent the probability of ACME's $2 million initial offer, defined in the Constant "Offer."

Standard Block evaluating to Offer Constant

Step 2 (Optional): Use a Summing Gate to pass the value down multiple paths. Note that since there is only one incoming path, the Summing Gate here serves a purely organizational purpose, visually marking a point where the paths split. If desired, you can simply join the starting block to the next two blocks, presented in Step 3.

Optional Summing Gate

Step 3: Use a Standard Block to represent the probability that SALF will accept the offer. This is one possible final outcome, so you may wish to alter its color using the Block Style window so that it stands out. Use another Standard Block to represent the probability that SALF will not accept the offer, but will counter with an offer of $5 million.

Standard Block representing the probability that the offer will be accepted

Standard Block representing the probability of a counter offer

The remainder of the Flowchart is constructed in the same way.

To calculate the probabilities, simulate the Flowchart. Since all events here are represented with fixed probabilities, only one simulation is necessary.

Flowchart with values displayed

Note that in the Flowchart shown here, the Show Block Values option has been selected from the Flowchart menu.

Another possible way to organize the Flowchart for this problem is shown below.

Alternate Flowchart with values displayed

Note that in this case, the rejection of SALF's $5 million counteroffer and the rejection of ACME's $3 million counteroffer lead to a single Summing Gate. Unlike the others, this Summing Gate is not optional, as it totals the probabilities of two different rejections, both of which lead to the case going to court and the possible outcomes there.

A RENO project with the solution for this example (called "Decision Tree (Fixed Probabilities).rnp") is shipped with the software and stored in the Examples\Decision (Event) Trees folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\Decision (Event) Trees\Decision Tree (Fixed Probabilities).rnp).

Questions?