Investigation

As an investigator, you are responsible to your supervisors, clients, or peers to make accurate decisions, organize and document your information, and justify your conclusions. FactLogic allows you to do this. Additionally, FactLogic allows you to provide them with a remarkable product: An organized, documented case from which your supervisors, clients, or peers can independently judge evidence and reach their own conclusions. Analysis is possible only because judgments have been quantified and FactLogic has reduced each judgment to a single number.

FactLogic is also an excellent tool for exploring and reevaluating cold and unsolved cases. It provides a fresh and more accurate evaluation of situations, suspects, facts, and probabilities. It allows you to use multiple fact finders to obtain more accurate probabilities.

The purpose of an investigation is to evaluate evidence and determine a probability of responsibility (i.e., called guilt in a criminal proceeding and liability in a civil proceeding). The probability of responsibility can be either determined by one fact finder (Sections 1) or estimated by a number of fact finders (Section 2).¹

Types of Evidence. Evidence can be inculpatory (i.e., incriminating) or exculpatory:

• Inculpatory Evidence. Inculpatory facts are those that tend to prove guilt or liability.
• Exculpatory Evidence. Exculpatory facts are those that tend to prove innocence or nonliability.

FactLogic combines both types of evidence. An fact could be judged to be both inculpatory and exculpatory, although this would be rare.

Included Evidence. Facts can be included or excluded for purposes such as the following:

• Acceptability of an Fact is Uncertain. You might be unsure whether an fact will be or should be considered by others.
• Analyze the Effect of an Fact. You might want to determine the influence of a single fact upon the overall probability of responsibility. Include all facts that you want to evaluate. You can easily omit an fact: Either enter 0 or leave blank the "Probability Fact is True." In all cases, facts must be independent. (See Independence.) Analysis is more accurate as more facts are included, as long as well-reasoned probabilities are provided.

Probabilities. Each fact is evaluated by assigning a probability that it is true and a probability that it is either inculpatory or exculpatory, given that it is true. Different probabilities can be assigned to facts in order to observe their effects on the resulting probability of responsibility.

1. Single Fact Finder

The most common application of FactLogic is to determine the probability of responsibility for a single suspect, but it is needed even more to compare multiple suspects.

1.1 Single Suspect

Example. Harry Stamp claims to have severe back pain due to slipping and falling in a hallway at the postal station where he worked. A witness said she saw him slip and he claims the fall has rendered him incapable of continuing his job as a postal worker and unable to contribute to his family responsibilities such as home repairs and to interact with his children. An insurance investigator saw and filmed Mr. Stamp playing basketball with his son in a neighborhood park two weeks after his claim was approved. A co-worker is willing to testify that one month prior to the accident, Mr. Stamp told him that he "hated his job and his supervisor" and had an early retirement plan that would guarantee his financial future. X-rays show no bone damage and physicians found no swelling or bruising. Determine the probability that Mr. Stamp is guilty of fraud by filing a claim stating that he is unable to work due severe back pain from his accident.

Solution. The judgments of a single fact finder are listed in Table 1. FactLogic computes the probability of guilt from his judgments to be 69.028%. This probability is greater than probable cause as considered by most but less than reasonable certainty as considered by most.²

1.2 Multiple Suspects

Often a case involves a number of suspects. FactLogic can determine the probability of responsibility of each suspect so they can be compared. When FactLogic is used to compare suspects, the probabilities labeled "Probability Fact is True" are the same for each suspect because these probabilities depend upon the evidence, not the suspect. The other probabilities, however, are generally not the same because they depend upon the suspect.

Example. Possible evidence from the Jon Benet Ramsey case provides an example from which to compare two suspects, an intruder and an unspecified family member. A single fact finder judges both suspects. Determine the probability of guilt for each suspect.

Solution (Intruder). Table 2 lists the facts, the probabilities for the evidence (i.e., "Probability Fact is True"), and the probabilities for an intruder. FactLogic computes the probability of guilt for an intruder to be 70.444%.

2. More Than One Fact Finder

A focus group can use FactLogic to evaluate evidence and reach conclusions that are especially trustworthy.

Independent Evaluations. Usually members of the focus group should evaluate the evidence independently (i.e., without communication). However, whether independence is desired depends upon the objective:

• Accurate Evaluation. If the objective is to evaluate the evidence accurately, members should evaluate the evidence without communicating (i.e., independently).
• Prediction. If the objective is to emulate the target group (e.g., a jury), members should evaluate the evidence by communicating as will members of the target group (i.e., dependently). If evaluations are dependent and positively correlated, the variation of estimates tends to be smaller than if evaluations are independent.

Statistical analysis is appropriate for investigations because investigators need to know how accurately they have estimated the probability of responsibility, and they need either to compare the probability of responsibility to other probabilities such as a standard of proof or to compare the probabilities of responsibility of two suspects. Statistical analysis can help you reach an accurate decision in any of three ways:

Carefully Define the Probability of Responsibility. FactLogic carefully defines the probability of responsibility by computing the average and computing an interval on both sides of the average within which you can be 95% confident that the true probability of responsibility exists.

Compare the Probability of Responsibility to the Standard of Proof. FactLogic determines the probability that is exceeded, with 95% certainty, by the mean probability of responsibility. Compare this probability to the standard of proof.

Compare the Probabilities of Responsibility of Two Suspects or Defendants. FactLogic determines if the mean probability of responsibility of one suspect or defendant is greater, with 95% certainty, than the mean of the other suspect or defendant.

2.1 Example of Analysis for a Single Suspect

Example (Carefully Define the Probability of Guilt and Compare the Probability of Guilt to Probable Cause). Mark Allen is investigating a robbery. He entered his subjective probabilities for three independent facts with FactLogic. FactLogic determines that the probability of guilt for this suspect is 92.591%. He wants the corroboration of others so he can be more confident of his decision and he can justify his decision in court. He asked four other investigators to independently (i.e., without communication) evaluate the evidence. They evaluated the evidence, and the resulting probabilities of guilt were 79.226%, 95.828%, 77.913%, and 89.053%.

• Carefully define the probability of guilt.
• Compare the probability of guilt to probable cause.

Solution (Carefully Define the Probability of Guilt). The average probability of guilt from the five investigators is 86.922%. Analysis shows that Mark Allen can be 95% confident that the probability of guilt is between 76.968% and 96.876%.

Solution (Compare the Probability of Guilt to Probable Cause). Analysis shows that Mark Allen can be 95% confident that the probability of guilt exceeds 89.296%, a probability that far exceeds probable cause.

2.2 Two Examples of Analyses for Multiple Suspects

Example (Carefully Define the Probability of Guilt and Compare the Probabilities of Guilt of the Two Suspects). Twelve detectives evaluated 13 fictitious facts from the Jon Benet Ramsey case and determined the probabilities of guilt for two suspects, an intruder and an unspecified family member.³ Carefully define the probability of guilt for each suspect.

Solution (Carefully Define the Probabilities of Guilt). The average probability of guilt for the intruder is 91.042%. The detectives can be 95% confident that the probability of guilt for the intruder is between 85.085% and 96.998%. Similarly, the average probability of guilt for the family member is 72.247%. Analysis shows that the detectives can be 95% confident that the probability of guilt for the family member is between 60.305% and 84.189%.

Example (Compare Probabilities of Guilt of an Intruder to the Family Member). The two principle suspects are an intruder and a family member, and the 12 fact finders judged probabilities of guilt for each. The average probability of guilt for the intruder is 91.042%, and the average probability of guilt for the family member is 72.247%. The probabilities of guilt, 12 for each suspect, could be distributed in such a way that it is not obvious that the intruder is "significantly more likely to be guilty" than is the family member. Compare the probabilities of guilt of the intruder to the probability of guilt of the family member.

Solution (Compare Probabilities of Guilt of an Intruder to the Family Member). Analysis shows that the detectives can believe that the probability of guilt for an intruder exceeds the probability of guilt for the family member, and the probability that they are wrong is less than 5%.

Summary

A single investigator can use FactLogic to evaluate evidence for a single suspect or to evaluate evidence for multiple suspects and compare them. A number of investigators can use FactLogic to evaluate evidence for a single suspect or to evaluate evidence for multiple suspects and compare them. When a number of investigators use FactLogic, analyses provide unusually trustworthy results.

Footnotes

¹A special verdict is a finding of the facts of a case, often of the percentages of fault in personal injury and wrongful death cases. Percentages of fault have increased in importance with the advent of the apportionment rule among tortfeasors and the rule of comparative negligence. Never have the percentages of fault been more accurately determinable than with FactLogic!

²Reasonable certainty is the complement of reasonable doubt. For example, a reasonable certainty of 85% is equivalent to a reasonable doubt of 15%.

³The 12 probabilities of guilt for an intruder are: 93.991, 88.042, 91.730, 89.135, 74.753, 97.942, 99.511, 90.714, 97.909, 97.553, 85.044, and 70.162%. The average is 91.042%. The 12 probabilities of guilt for a family member are: 60.042, 88.143, 26.158, 81.912, 74.334, 79.129, 68.801, 60.914, 61.423, 89.113, 97.129, and 79.866%. The average is 72.247%.