British Academy: The UK's National Academy for the Humanities and Social Sciences
Enquiry, Evidence and Facts: An Interdisciplinary Conference
The Subtleties of Alibi Evidence
Dr Amanda Hepler
Department of Statistical Science, University College London, Gower Street, London, WC1E 6BT
Dr David Lagnado
Department of Psychology, University College London, Gower Street, London WC1E 6BT
Dr Gianluca Biao
Department of Statistical Science, University College London, Gower Street, London WC1E 6BT
An abstract presented to the conference
‘Enquiry, Evidence and Facts: An Interdisciplinary conference’
at the British Academy, London, on 13 December 2007
Biographies
Dr Amanda Hepler
Amanda Hepler is currently working as a Research Fellow for the Evidence Programme, and is based at University College London. After obtaining her B.S. from Towson University, she earned her Masters degree and doctorate while at North Carolina State University. Trained as a forensic statistician, she specializes in the application of Bayesian network technology to aid evidence analysis. Her dissertation research explored modeling the complexities involved in DNA evidence interpretation when individuals arise from inbred populations. In addition to continuing this work, Dr. Hepler is also investigating formal models for other types of forensic evidence, including alibis, expert witness testimony and eyewitness credibility.
Dr David Lagnado
David Lagnado is a lecturer in cognitive and decision sciences in the department of psychology at UCL. He also an ELSE Research Fellow at UCL, and was a post-doctoral researcher on the Evidence project. He has a PhD in philosophy, and an MSc in cognitive science. His main research is in human learning and inference, with particular focus on models of causal and probabilistic reasoning. His work on the Evidence project includes studies on how people use evidence to make probabilistic inferences, and how this fits with normative models of inference. Of particular interest is the role of causal knowledge: how do people acquire it, and how do they use it for prediction and explanation? He is the co-author of a recent book on the psychology of decision making: ‘Straight choices: the psychology of decision making’, 2007, Psychology press.
Dr Gianluca Baio
Gianluca Baio graduated with a degree in Statistics and Economics from the University of Florence (Italy), after spending a period studying at the Sheffield Hallam University, Sheffield (UK). Subsequently, he has been a Research Fellow in the University of Siena (Italy), where he started to work on applied Bayesian statistics with particular reference to the economic evaluation of health systems. He completed his PhD in Applied Statistics at the University of Florence, after spending a period at the Program on the Pharmaceutical Industry at the MIT Sloan School of Management, Cambridge, Massachusetts, and currently is a Research Fellow at University College London (UK). His main interests are in Bayesian statistical modelling, probabilistic expert systems, and applications to decision-making problems, particularly in health care.
Abstract
This work presents a genuinely interdisciplinary collaboration between researchers in statistics and psychology. It stems from distinctive issues that arise when trying to understand and model the nature of alibi evidence. Formal models exist assessing the impact of a witness' testimony on the hypothesis of guilt for the suspect. These models, proposed by Schum, take into account various characteristics of the witness, i.e. credibility, competence, and character. However, subtle nuances exist in alibi testimony which demands a novel modelling approach.
By definition, an alibi involves additional dependencies not typically evident in witness models. Specifically, a suspect's testimony depends on whether or not they committed the crime. This is not typically the case for testimony from an impartial witness. To illustrate, consider the Bayesian network representing witness testimony appearing in Figure 1.
Figure 1. Impartial Witness Model.
Each node in the graph represents either a hypothesis or an event. In this example, H denotes the hypothesis of interest ‘Did the suspect commit the crime?’ E denotes an event for which we have testimony, denoted by E*. When we have testimony as to the whereabouts of the suspect, E represents whether or not the suspect was at the scene of the crime. Dependencies between nodes are represented by arrows. The first arrow flows from the hypothesis to the event. This indicates that the suspect being at the scene of the crime depends on whether or not the suspect actually committed the crime. The second arrow indicates that testimony about E depends on whether or not E actually occurred.
When the testimony E* represents alibi testimony taken from the suspect, an additional dependence must be made explicit. In words, if the suspect actually committed the crime, they are more likely to claim not to be at the scene of the crime. In terms of conditional probabilities, this implies the probability of E* must be conditioned not only on E, but also on H. The corresponding Bayesian network appears in Figure 2.
Figure 2. Suspect Alibi Model.
An interesting subtlety is laid bare once the model is correctly specified. As discussed by Schum in an earlier report, we have a situation where information about the source of evidence might be at least as valuable as knowing the fact for certain. In the context of our example, knowing the suspect lied about being at the scene increases our probability of guilt, over and above the probability of guilt if we only knew they were at the scene. This is more clearly stated in symbols: Pr(H|E, E*) > Pr(H|E).
The model appearing in Figure 2 may also apply to testimonies from individuals other than the suspect. For example, if the alibi evidence is provided by the suspect’s partner, they may have knowledge as to whether or not the suspect committed the crime; therefore this knowledge will influence their testimony. There is another scenario that must also be considered: perhaps the suspect’s partner is not aware that the suspect committed the crime, however strives to provide evidence which will cast their partner in the best light. This scenario leads to the next model, where motivation to deceive is explicitly represented in the model.
Figure 3. Deception Model.
This more robust model can apply to all of the aforementioned scenarios, by modifying the conditional probability statements regarding D and E*.
Scenario 1: Impartial witness provides alibi
Regardless of whether or not the suspect committed the crime, the probability of deception is low. When D is not true, the probability of E* is just what it would have been if the witness was not aware of H. Thus, the model from Figure 3 reverts back to the original model of Figure 1.Scenario 2: Suspect provides alibi
If H is true, the suspect will have a much higher probability of deception than if HC is true. If D is true, the probability E* matches E is very small. If D is false, the model reverts to the original model. The need for a direct link between H and E* is removed, or ‘screened off’ by the hypothesis of deception.Scenario 3: Partial witness provides alibi
The witness may know H and then the Scenario 2 description remains in place. If the witness does not know H, and we have other evidence suggesting the witness has motivation to deceive, (e.g. the testimony of a close friend or relative of the suspect) then the probability of deception will be high whether or not H is true.
The difference between the suspect alibi model and the impartial witness model has also been studied experimentally (Lagnado, this volume). Mock jurors were given simplified crime cases, and had to judge the probability that a suspect was guilty on the basis of sequentially presented items of evidence. They were given either witness or alibi testimonies, and these were subsequently discredited (through the discovery of deception). In the witness case people’s final judgments simply returned to their baseline judgments of guilt (before the testimony had been presented). In contrast, in the alibi case people’s judgments rose much higher than their previous baseline judgments. They took the fact that the alibi was fabricated as additional evidence for the guilt of the suspect, as predicted by the formal models.
We intend to run additional experiments to investigate mock jurors’ sensitivity to the different scenarios addressed by our formal models.. These experiments will manipulate the status of the alibi provider (suspect, relative of suspect or stranger), and their knowledge of the suspect’s guilt (H). On the basis of the formal models, we predict that when the alibi is provided by a suspect or relative, mock jurors will adopt the model in Figure 2, and judge the probability of H given E & E* as higher than the probability of H given just E. In other words, mock jurors will take the fact that the alibi was fabricated as additional evidence for the guilt of the suspect. In contrast, we predict that when the alibi is provided by a stranger, mock jurors will adopt the model in Figure 1, and judge the probability of H given E & E* as equal to the probability of H given just E.
The results of these experiments will help us to develop a better psychological model of how mock jurors process alibi evidence. They will also inform possible extensions of the formal models.