Saturday, October 27, 2007

One More Advance Paper on Visualization of Evidence and Inference

This paper happens to be mine. See Peter Tillers, Introduction: visualizing evidence and inference in legal settings Law, Probability and Risk Advance Access published on October 27, 2007. doi:10.1093/lpr/mgm006 (But the diagram that appears above is just for show; it does not appear in this paper.)

The above link will expire when the hard copy of the paper appears. If you don't have a subscription to the journal Law, Probability and Risk, your employer or your law library may have a group license.

The paper will be available in about 12 months via WESTLAW.

Finally, a draft of the paper (substantially the same as the final version) is available at SSRN. Here are a few extracts (sans footnotes) from an earlier draft of this short paper:

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.


I am trying to lead graph theorists down a particular garden path. I have noticed (and I suspect that many other people have noticed) that when graph theorists try to explain themselves, they often use visual images as well as mathematical expressions and equations to describe their reasoning. I imagine (but I don’t really know) that some graph theorists would explain their use of visual images as an unfortunate but necessary concession to the intellectual limitations and weaknesses of dunces such as P. Tillers, who often have trouble following lengthy arguments made only with mathematical expressions. But I wonder if this sort of condescending (though entirely accurate) response offers backhanded support for the conjecture that visual images are sometimes excellent vehicles for getting ordinary human brains to work the way we want them to work – and the way we think that our brains, if properly assisted, can work.

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