Abstract
In the course of legal reasoning—whether for purposes of deciding an issue, justifying a decision, predicting how an issue will be decided, or arguing for how it should be decided—one often is required to reach (and assert) conclusions based on a balance of reasons that is not straightforwardly reducible to the application of rules. Recent AI and Law work has modeled reason-balancing, both within and across cases, with set-theoretic and rule- or value-ordering approaches. This article explores a way to model balancing in quantitative terms that may yield new questions, insights, and tools.
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Notes
Note that the weight being accorded a factor is a kind of co-efficient, not to be confused with the metaphorical weight of options in the imaginary balancing process. These two different senses of ‘weight’ are often conflated and a source of confusion.
Examples of these models can be found in the references in Sect. 3.6 below.
In addition to readily handling option sets with more than two members, the approach outlined here has the advantage over the two-pan scale model of showing all assessments on a given factor in the same row, for easier comparison.
In conceptual spaces greater than two dimensions, of course, a line does not suffice to partition one area from another, and hyperplanes (of one dimension less than the ambient space) are needed. By expressing an arbitrary number of comparative ‘dimensions’ in the single mode of ‘factor,’ interestingly, the choicebox model can largely remain within an intuitive three-dimensional space for interface purposes at least.
Other work by some of these authors does introduce quantitative aspects. E.g., in Chorley and Bench-Capon (2005a) factors are held to promote values to different extents, and values are then assigned weights to give an overall score. In Bench-Capon and Prakken (2010) values are also promoted to differing degrees to accommodate the language in the decisions considered that speak of “reduced expectations” of privacy. No numbers are attached, but case facts are held to put particular situations above or below a required threshold. Bench-Capon et al. (2013) introduces argument schemes that encompass varying degrees to which values are promoted, although degree is limited to two states, strong and weak. The ‘triadic’ model proposed by Alexy (2003) incorporates ‘light,’ ‘moderate,’ and ‘serious’ degrees to which principles are satisfied.
Some weighting schemes require weights to sum to a fixed quantity, but it can be easier for users to express them in whatever relative numbers they choose, and let the system handle the associated mathematics behind the scenes. In the example here, for instance, it is easier to say that the two factors stand in an importance ratio of 5 to 2 (totaling 7), rather than having to figure out what that ratio would be against a fixed total of 10 (approximately 0.7142857–0.2857142).
Whether numbers, shapes, or other devices are used to express ratings and weightings quantitatively, in many cases results can be indifferent within ranges of quantities, and hence sensitivity analysis can be used to detect how much any particular judgments would need to change in order for the result to be different.
131 S. Ct. 1143, at 1160.
The literature on argument accrual of course reminds us that things are sometimes not so simple. Prakken (2005) for instance shows that accruals can be weaker than their accruing elements when those elements are not independent, and presents a logical formalization of argument accrual as a kind of inference. Lucero et al. (2009) turn to ‘possibilistic defeasible logic programming’ to model conflict and defeat in accrual structures.
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I am grateful to several anonymous reviewers for insightful suggestions and encouragement.
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This work is based on an earlier work: “On Balance,” in Proceedings of the Fourteenth International Conference on Artificial Intelligence and Law, © ACM (2013). http://dx.doi.org/10.1145/2514601.2514611
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Lauritsen, M. On balance. Artif Intell Law 23, 23–42 (2015). https://doi.org/10.1007/s10506-015-9163-0
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DOI: https://doi.org/10.1007/s10506-015-9163-0