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  • Articles  (7,259)
  • Oxford University Press  (7,259)
  • 2010-2014  (7,259)
  • Mathematics  (7,259)
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  • Articles  (7,259)
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  • 1
    Publication Date: 2013-09-12
    Description: The tension between the meaning of causality in science and law or public policy is well-known; however, defendants in product liability cases or industries that might be affected by a government regulation may try to convince the factfinder to require evidence of a causal relationship that meets the standards of science. From the perspective of public health, however, people may be exposed unnecessarily to a health risk during the time period between the establishment of reasonably strong evidence of a causal relationship and the overwhelming evidence required for scientific causality. The Bayesian paradigm enables one to update information from epidemiologic studies as they accumulate, providing estimates of the probability that the relative risk of a particular harm from exposure exceeds a threshold value, e.g. 2.0 or 4.0 that is sufficient to meet the preponderance of the evidence standard or to support a health initiative. In order to diminish the role of the initial prior distribution, which may be quite subjective, the first case-control study or an analysis of adverse event and case reports is used to determine two prior distributions. One is the most favourable to the defendant, or industry that might be regulated, which is consistent with the previous data. The other is centred on or near the estimated relative risk from the first study. The method is applied to the studies that linked aspirin use to Reye syndrome and demonstrates that the evidence of a causal association was sufficiently strong in 1982, when the Food and Drug Administration first proposed that the public be warned of the risk, to support the regulation. Thus, lives would have been saved had the warning been given at the end of 1982 rather than in early 1985.
    Print ISSN: 1470-8396
    Electronic ISSN: 1470-840X
    Topics: Mathematics , Law
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  • 2
    Publication Date: 2013-09-12
    Description: In law, inferences of causation are sometimes made through a structured process in which multiple participants play various roles, and make decisions concerning various logical components of the overall inference (such as legal rules, policy objectives, presumptions, evidence, burdens of proof and findings of fact). This article illustrates such a process using empirical research into compensation decisions in the USA for injuries allegedly caused by vaccinations. Empirical research into actual legal processes is essential, in order to discover how various players approach their sub-tasks of decision-making. It also provides insights for areas outside of law, such as non-monotonic logic, cognitive science, sociology and artificial intelligence.
    Print ISSN: 1470-8396
    Electronic ISSN: 1470-840X
    Topics: Mathematics , Law
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  • 3
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    Oxford University Press
    Publication Date: 2013-09-12
    Description: Situations of causal factual uncertainty are relatively common in law. The problems and difficulties regarding ‘factual causation’ in law point to the need of ‘evidence’ and ‘proof’ models that are adequate and capable to accommodate the tests and methodologies used to explain and demonstrate it in a legal context. Given the configuration of the situations of causal factual uncertainty and the available ‘evidence’ and ‘proof’ models, I argue that it is justified to use an ‘argumentative-narrative’ model for ‘proving causation’ in law. However, considering that each model of ‘evidence’ and ‘proof’ reveals a different kind of ‘rationality’ that can still be viewed in different ways, I also argue that we must try to match the perspective we have on the ‘rationality’ behind the chosen model of ‘evidence’ and ‘proof’ with the ‘rationality’ underlying ‘causation’ in law.
    Print ISSN: 1470-8396
    Electronic ISSN: 1470-840X
    Topics: Mathematics , Law
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  • 4
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    Oxford University Press
    Publication Date: 2013-09-12
    Description: At least in some cases, the values confronted in legal decision-making appear to be incommensurable. Some legal theorists resist incommensurability because they fear that this presents an overwhelming obstacle to rational decision-making. By offering a close analysis of proportionality and, more particularly, measures of proportional value satisfaction, I show that this fear is unfounded. Comparative measures of proportional value satisfaction do not require the values to be commensurable. However, assuming incommensurability presents us with the problem of public significance in the proportional satisfaction of values. When two values are commensurable, this public significance is provided by the mediating effects of the overarching third value that provides the common measure of the values. However, when this common measure is removed, then the public significance of value satisfaction must be otherwise achieved. This is why I propose an equal proportional value satisfaction as the most appropriate proportionality maximand. Under equal proportional value satisfaction, the proportional satisfaction of any one value has significance for each and every other value. This kind of public significance is interpersonal rather than impersonal (or second-personal rather than third-personal). The article then shows that the legal process that is most appropriate to equal proportionality is a process that implements defeasible legal rules.
    Print ISSN: 1470-8396
    Electronic ISSN: 1470-840X
    Topics: Mathematics , Law
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  • 5
    Publication Date: 2013-09-12
    Description: In order to allocate the risk between parties in legal adjudication, we use evidentiary techniques with the main device among them being the standard of proof (SoP). The traditional view holds the grade of probability to be the parameter that shifts when moving to different standards. However, as soon as we dig slightly deeper, an incoherent picture is being revealed. In this article, I challenge the accepted view and try to show that it faces insurmountable problems concerning the rationality, the grammatical consistency and the impact of the SoP for the acceptability of verdicts. At the end of the article, I shortly discuss the theory of epistemological contextualism and propose a framework that allows rational distinctions to be drawn between different standards of proof. In the second part of this project (forthcoming), I will defend a contextualist view according to which shifting parameter is not the grade of (aleatory) probability, but instead the Set of Epistemic Defeaters in play.
    Print ISSN: 1470-8396
    Electronic ISSN: 1470-840X
    Topics: Mathematics , Law
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  • 6
    Publication Date: 2013-09-13
    Description: The aim of this paper is to study the relations between the Hausdorff dimensions of k -quasilines and the theory of extremal quasiconformal mappings. We show that there is an open and dense subset (Strebel points) of the universal Teichmüller space T (H) such that, for every [ f ] in the set, the Hausdorff dimension of the k -quasiline determined by [ f ] is strictly less than 1 + k 2 . We also show that there are some points [ f ] != [id] outside the open and dense set in the universal Teichmüller space such that the Hausdorff dimension of the quasiline determined by [ f ] is 1. Moreover, some results on the Hausdorff dimensions of the quasilines varying in the asymptotic Teichmüller space are also obtained.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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  • 7
    Publication Date: 2013-09-13
    Description: A new uniqueness result for a general n th order differential equation is obtained. We show that some previous results follow immediately from our theorem.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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  • 8
    Publication Date: 2013-09-13
    Description: Consider a discrete uniformly elliptic divergence form equation on the d ≥3 dimensional lattice Z d with random coefficients. In Conlon and Spencer [ Trans. Amer. Math. Soc. , http://www.math.lsa.umich.edu/~conlon/paper/hom10.pdf ], rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincaré inequality were obtained. Here, these results are extended to certain environments in which correlations can have arbitrarily small power law decay. These environments are simply related via a convolution to environments which do satisfy a Poincaré inequality.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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  • 9
    Publication Date: 2013-09-13
    Description: In this paper, we prove that, for any a , M N with ( a , M ) = 1, there are infinitely many Carmichael numbers m such that m a mod M .
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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  • 10
    Publication Date: 2013-09-13
    Description: We give a topological analogue for openness of a criterion for flatness that originates with Auslander. Over a normal base of dimension n , failure of openness is detected by a vertical component in the n th fibred power of the morphism.
    Print ISSN: 0024-6093
    Electronic ISSN: 1469-2120
    Topics: Mathematics
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