Many of the attacks on mathematical analysis of evidential inference were misdirected; many of them – probably the vast majority of them – rested on basic misunderstandings about the nature and possible uses of mathematics. (Some critics seemed to assume that numbers are only good for counting. Other observers seemed to assume that all mathematical expressions amount to recipes for solving problems.) But some of the attacks on mathematical argument about evidence and inference harbored, even if not always distinctly, intuitions that seem to have considerable substance.
One such intuition is that it makes little sense to ask people such as jurors to use a method of analysis or argument – such as Bayesianism – that is beyond their “common,” or “ordinary,” understanding.
Another important intuition is that the nuances and complexities of real-world evidence and inference are too great to be captured by any type of formal analysis.
Both of these intuitions involve assumptions about the cognitive capacities of human beings and the human brain. One reason I am interested in visualization of evidence and inference is that I suspect and hope that visualization of evidence and inference can make the logic of formal analytical methods such as Bayesianism more readily intelligible to so-called ordinary people – to people such as judges, jurors, law teachers, and law students, to people such as me.
I am interested in visualization for another reason: I also suspect that visualization may help to remedy or ameliorate certain cognitive limitations that afflict even very extraordinary people, even people with extensive training in logic and mathematics, for example.
These two conjectures of mine can be stated in the following deliberately-suggestive way: I suspect that visualization can make it possible for the extraordinary computational capacity of the ordinary brain to do a better job of taking advantage of whatever assistance explicit formal argument about evidence is capable of providing.
Whether some complexities and nuances of real-world evidence and inference in legal proceedings are beyond the limits of formal analysis is still an open question. But I have a theoretical prejudice that bears on the question of how complex inference should be managed and addressed: I suspect that the people who tend to believe that the solution to the problem of complexity is generally to wash out some details – I suspect that the people who think we need simple and simplifying heuristics are on the wrong track. I suspect that the devil is generally in the details and I suspect that washing out detail generally degrades rather than enhances inferential performance. If I am right about this, every effort should be made to develop tools that makes it possible for human decision makers to increase (rather than decrease) the number of evidential premises and evidential inferences that decision makers should try to consider when they address uncertain factual hypotheses.
Having said that attention to detail is important, I hasten to say that large amounts of detail do present a serious problem, particularly for the enterprise of developing and deploying formal argument about evidence and inference. I take it as gospel that assessment of the sort of evidence ordinarily found in real-world litigation (and in many other decision making situations) usually involves numerous evidential premises and numerous evidential inferences. An abundance of evidentiary and inferential detail presents a serious difficulty for the dream of explicit and comprehensive formal analysis of evidence in legal proceedings. As the number of items of evidence increases and as the number of pertinent possible inferences increases, the resources required to consider the inferences suggested or supported by a body of evidence increases exponentially. If a human actor who uses a formal method of analysis (such as Bayesianism) must allocate even a very small increment of time – one or two or three seconds, let us say – to each premise and to each step in a complex evidential argument, it becomes hard to imagine how a comprehensive explicit formal analysis of even a relatively small amount of evidence presented in a legal proceeding can ever be done by any real human being. Furthermore, the difficulty of just keeping in mind all of the necessary or important parts of an inferential argument (including its evidential premises) seems to increase enormously as the number of evidential premises and inferential links increases; the task is akin to trying to play n-dimensional chess blindfolded.
That’s the way I see things, and that’s why I hoped that a conference on “graphic and visual representations of evidence in legal settings” (http://tillers.net/conference.html) would shed light on how or whether visualization can contribute to the solution of two possible problems: (i) the possible problem of the unintelligibility of complex formal argument about evidence and inference; and (ii) the possible problem of the impracticability of explicit formal analysis of evidence and inference in legal proceedings.
The full introduction -- Visualizing Evidence in Legal Settings -- is available here