The difference between blackstone-like error ratios and probabilistic standards of proof

Law and Social Inquiry

Volumn 21, Issue 1, 1996, Pages 95-132

  DeKay, Michael L ^a,b,c  

^a VETERANS AFFAIRS MEDICAL CENTER   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030551829     PISSN: 08976546     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1747-4469.1996.tb00013.x     Document Type: Article

References (167)

1. John Fortescue, De Laudibus Legum Angliæ 62 (London: Companie of Stationers, 1616).
2. 2 Matthew Hale, The History of the Pleas of the Crown 289 (In the Savoy: E. & R. Nutt, & R. Gosling, 1736).
3. 4 William Blackstone, Commentaries on the Laws of England 352 (Oxford, Eng.: Clarendon Press, 1769).
4. J. Wilder May, "Some Rules of Evidence," 10 Am. L. Rev. 642, 651-64 (1876).
5. Coffin v. United States, 156 U.S. 432, 455-56 (1895).
6. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
7. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
8. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
9. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
10. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
11. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
12. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
13. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
14. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
15. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
16. Robert Birmingham, "Remarks on 'Probability' in Law: Mostly, a Casenote and a Book Review," 12 Ga. L. Rev. 535, 536-37 (1978); Alan D. Cullison, "Probability Analysis of Judicial Fact-Finding: A Preliminary Outline of the Subjective Approach," 1969 Toledo L. Rev. 538, 566-67; id., "The Model of Rules and the Logic of Decision," in Stuart S. Nagel, ed., Modeling the Criminal Justice System 225, 238, 244 n.13 (Beverly Hills, Cal.: Sage Publications, 1971) ("Cullison, 'Model of Rules'"); Ward Edwards, "Influence Diagrams, Bayesian Imperialism, and the Collins Case: An Appeal to Reason," 13 Cardozo L. Rev. 1025, 1063-64 & n.80 (1991); Bernard Grofman, "Mathematical Models of Juror and Jury Decision-Making: The State of the Art," in Bruce D. Sales, ed., The Trial Process 305, 314-15 (New York: Plenum Press, 1981) ("Grofman, 'Mathematical Models' "); Richard O. Lempert, "Modeling Relevance," 75 Mich. L. Rev. 1021, 1038 (1977); Stuart Nagel, "Bringing the Values of Jurors in Line with the Law," 63 Judicature 189, 191-92 (1979); Stuart Nagel, David Lamm, & Miriam Neef, "Decision Theory and Juror Decision-Making," in Sales, The Trial Process 353, 355-57, 359-60 n.4, 366, 376, 378, 381 ("Nagel et al., 'Decision Theory' ") (suggesting that Blackstone's conviction is perhaps the best quantitative statement of what the Constitutional framers meant by due process); Stuart S. Nagel & Miriam Neef, "Deductive Modeling to Determine an Optimum Jury Size and Fraction Required to Convict," 1975 Wash. U. L.Q. 933, 943 n.17, 945-46, 959, 963, 965 (noting the influence of Blackstone on the authors of the Constitution). In Ballew v. Georgia, 435 U.S. 223, 234 (1978), the Supreme Court referred to Nagel & Neef 's, supra, use of a 10:1 utility ratio as "perhaps not an unreasonable assumption" but made no mention of the fact that this ratio was based on Blackstone's statement. Nevertheless, Richard S. Bell, "Decision Theory and Due Process: A Critique of the Supreme Court's Law-making for Burdens of Proof," 78 J. Crim. L. & Criminology 557, 562 (1987), noted the Court's statement and suggested that "perhaps the Court has evaluated the relative disutilities of errors in criminal trials in light of Blackstone's principle." However, the Court has never explicitly paraphrased Blackstone in terms of utilities, nor has it endorsed a particular ratio of utilities. On the other hand, Justice Douglas once elevated Blackstone's ratio of error frequencies to the level of a onstitutional guarantee when writing outside the Court: "Constitutional guarantees which ensure a fair trial are not slick lawyers' tricks by which known criminals are set free. In a democratic society, the means are all important. We are a civilized people. . . . We believe that it is better for ten guilty people to be set free than for one innocent man to be unjustly imprisoned." William O. Douglas, Foreword to Jerome Frank & Barbara Frank, Not Guilty 11, 11 (Garden City, N.Y.: Doubleday, 1957). Although this last sentence was quoted in Furman v. Georgia, 408 U.S. 238, 367 n.158 (Marshall, J., concurring), the Court has never committed itself to such a ratio. In summary, the Court has entertained both ratios of error utilities and ratios of error frequencies, but it has never equated the two. See infra notes 15 and 78 and accompanying text.
17. Nagel, 63 Judicature at 191.
18. See generally Leonard J. Savage, The Foundations of Statistics (2d rev. ed., New York: Dover, 1972 [1954]).
19. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
20. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
21. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
22. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
23. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
24. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
25. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
26. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
27. John Kaplan, "Decision Theory and the Factfinding Process," 20 Stan. L. Rev. 1065, 1071-77 (1968); Cullison, 1969 Toledo L. Rev. at 564-71, and id., "Model of Rules" at 237-39; among the others, see, e.g., Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80; Michael Fried, Kalman J. Kaplan, & Katherine W. Klein, "Juror Selection: An Analysis of Voir Dire," in Rita J. Simon, ed., The Jury System in America: A Critical Overview 49, 58-64 (Beverly Hills, Cal.: Sage Publications, 1975) ("Fried et al., 'Juror Selection' "); Grofman, "Mathematical Models" at 309-15; Nagel, 63 Judicature at 191-92 & n.5; Nagel et al., "Decision Theory" at 354-60; Lawrence H. Tribe, "Trial by Mathematics: Process and Ritual in the Legal Process," 84 Harv. L. Rev. 1329, 1378-86 (1971).
28. C. M. A. McCauliff, "Burdens of Proof: Degrees of Belief, Quanta of Evidence, or Constitutional Guarantees?" 35 Vand. L. Rev. 1293, 1322 (1982).
29. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
30. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
31. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
32. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
33. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
34. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
35. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
36. Birmingham, 12 Ga. L. Rev. at 536-37; Cullison, 1969 Toledo L. Rev. at 566-67, and id., "Model of Rules" at 238; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4, 366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965.
37. United States v. Fatico, 458 F.Supp. 388, 411 (1978).
38. In re Winship, 397 U.S. 358 (1970) (Harlan, J., concurring).
39. "The Supreme Court, 1969 Term," 84 Harv. L. Rev. 1, 158 n.13 (1970) (citation omitted); see Tribe, 84 Harv. L. Rev. at 1381 n.162.
40. "The Supreme Court, 1969 Term," 84 Harv. L. Rev. 1, 158 n.13 (1970) (citation omitted); see Tribe, 84 Harv. L. Rev. at 1381 n.162.
41. In fairness to Justice Harlan, I believe "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13, and Tribe, 84 Harv. L. Rev. at 1381 n.162, misrepresented the Justice's expressed views on this point. After citing Kaplan, 20 Scan. L. Rev. at 1071-77, who clearly based his analysis on error utilities rather than error frequencies, Justice Harlan wrote: The standard of proof influences the relative frequency of these two types of erroneous outcomes. If, for example, the standard of proof for a criminal trial were a preponderance of the evidence rather than proof beyond a reasonable doubt, there would be a smaller risk of factual errors that result in freeing guilty persons, but a far greater risk of factual errors that result in convicting the innocent. Because the standard of proof affects the comparative frequency of these two types of erroneous outcomes, the choice of the standard to be applied in a particular kind of litigation should, in a rational world, reflect an assessment of the comparative social disutility of each. In re Winship, 397 U.S. 358, 371 (1970) (Harlan, J., concurring). Justice Harlan's assertion regarding the effects of the standard of proof on error frequencies was less bold than that credited to him. The Justice argued only that lowering the standard of proof will lower the ratio of erroneous acquittals to erroneous convictions, which is correct. He did not suggest that either the clear and convincing evidence standard or the reasonable doubt standard will lead to a ratio greater than one. Nor did Justice Harlan suggest, as his critics claimed, that the objective of the reasonable doubt standard is to ensure that there be many more erroneous acquittals than erroneous convictions. Although the source of misunderstanding seems to be the initial clause of Justice Harlan's final sentence, the Justice did not condition the rationality of utility-based standards in this manner elsewhere in his opinion. Id. at 370, 372; quotation infra note 78. In subsequent decisions, the Court has maintained Justice Harlan's emphasis, arguing for a balance of utilities rather than a balance of error frequencies. E.g., Mullaney v. Wilbur, 421 U.S. 684, 703-4 (1975); id. at 706 (Rehnquist, J., concurring); Patterson v. New York, 432 U.S. 197, 208 (1977); Santosky v. Kramer, 455 U.S. 744, 788 n.13 (1982) (Rehnquist, J., dissenting).
42. In fairness to Justice Harlan, I believe "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13, and Tribe, 84 Harv. L. Rev. at 1381 n.162, misrepresented the Justice's expressed views on this point. After citing Kaplan, 20 Scan. L. Rev. at 1071-77, who clearly based his analysis on error utilities rather than error frequencies, Justice Harlan wrote: The standard of proof influences the relative frequency of these two types of erroneous outcomes. If, for example, the standard of proof for a criminal trial were a preponderance of the evidence rather than proof beyond a reasonable doubt, there would be a smaller risk of factual errors that result in freeing guilty persons, but a far greater risk of factual errors that result in convicting the innocent. Because the standard of proof affects the comparative frequency of these two types of erroneous outcomes, the choice of the standard to be applied in a particular kind of litigation should, in a rational world, reflect an assessment of the comparative social disutility of each. In re Winship, 397 U.S. 358, 371 (1970) (Harlan, J., concurring). Justice Harlan's assertion regarding the effects of the standard of proof on error frequencies was less bold than that credited to him. The Justice argued only that lowering the standard of proof will lower the ratio of erroneous acquittals to erroneous convictions, which is correct. He did not suggest that either the clear and convincing evidence standard or the reasonable doubt standard will lead to a ratio greater than one. Nor did Justice Harlan suggest, as his critics claimed, that the objective of the reasonable doubt standard is to ensure that there be many more erroneous acquittals than erroneous convictions. Although the source of misunderstanding seems to be the initial clause of Justice Harlan's final sentence, the Justice did not condition the rationality of utility-based standards in this manner elsewhere in his opinion. Id. at 370, 372; quotation infra note 78. In subsequent decisions, the Court has maintained Justice Harlan's emphasis, arguing for a balance of utilities rather than a balance of error frequencies. E.g., Mullaney v. Wilbur, 421 U.S. 684, 703-4 (1975); id. at 706 (Rehnquist, J., concurring); Patterson v. New York, 432 U.S. 197, 208 (1977); Santosky v. Kramer, 455 U.S. 744, 788 n.13 (1982) (Rehnquist, J., dissenting).
43. In fairness to Justice Harlan, I believe "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13, and Tribe, 84 Harv. L. Rev. at 1381 n.162, misrepresented the Justice's expressed views on this point. After citing Kaplan, 20 Scan. L. Rev. at 1071-77, who clearly based his analysis on error utilities rather than error frequencies, Justice Harlan wrote: The standard of proof influences the relative frequency of these two types of erroneous outcomes. If, for example, the standard of proof for a criminal trial were a preponderance of the evidence rather than proof beyond a reasonable doubt, there would be a smaller risk of factual errors that result in freeing guilty persons, but a far greater risk of factual errors that result in convicting the innocent. Because the standard of proof affects the comparative frequency of these two types of erroneous outcomes, the choice of the standard to be applied in a particular kind of litigation should, in a rational world, reflect an assessment of the comparative social disutility of each. In re Winship, 397 U.S. 358, 371 (1970) (Harlan, J., concurring). Justice Harlan's assertion regarding the effects of the standard of proof on error frequencies was less bold than that credited to him. The Justice argued only that lowering the standard of proof will lower the ratio of erroneous acquittals to erroneous convictions, which is correct. He did not suggest that either the clear and convincing evidence standard or the reasonable doubt standard will lead to a ratio greater than one. Nor did Justice Harlan suggest, as his critics claimed, that the objective of the reasonable doubt standard is to ensure that there be many more erroneous acquittals than erroneous convictions. Although the source of misunderstanding seems to be the initial clause of Justice Harlan's final sentence, the Justice did not condition the rationality of utility-based standards in this manner elsewhere in his opinion. Id. at 370, 372; quotation infra note 78. In subsequent decisions, the Court has maintained Justice Harlan's emphasis, arguing for a balance of utilities rather than a balance of error frequencies. E.g., Mullaney v. Wilbur, 421 U.S. 684, 703-4 (1975); id. at 706 (Rehnquist, J., concurring); Patterson v. New York, 432 U.S. 197, 208 (1977); Santosky v. Kramer, 455 U.S. 744, 788 n.13 (1982) (Rehnquist, J., dissenting).
44. See generally David M. Green & John A. Swets, Signal Detection Theory and Psychophysics (Los Altos, Cal.: Peninsula, 1988 [1966]) ("Green & Swets, Signal Detection Theory"); Neil A. Macmillan & C. Douglas Creelman, Detection Theory: A User's Guide (New York: Cambridge University Press, 1991) ("Macmillan & Creelman, Detection Theory"); Clyde C. Coombs, Robyn M. Dawes, & Amos Tversky, Mathematical Psychology: An Elementary Introduction 165-201 (Englewood Cliffs, N.J.: Prentice Hall, 1970) ("Coombs et al., Mathematical Psychology").
45. See generally David M. Green & John A. Swets, Signal Detection Theory and Psychophysics (Los Altos, Cal.: Peninsula, 1988 [1966]) ("Green & Swets, Signal Detection Theory"); Neil A. Macmillan & C. Douglas Creelman, Detection Theory: A User's Guide (New York: Cambridge University Press, 1991) ("Macmillan & Creelman, Detection Theory"); Clyde C. Coombs, Robyn M. Dawes, & Amos Tversky, Mathematical Psychology: An Elementary Introduction 165-201 (Englewood Cliffs, N.J.: Prentice Hall, 1970) ("Coombs et al., Mathematical Psychology").
46. See generally David M. Green & John A. Swets, Signal Detection Theory and Psychophysics (Los Altos, Cal.: Peninsula, 1988 [1966]) ("Green & Swets, Signal Detection Theory"); Neil A. Macmillan & C. Douglas Creelman, Detection Theory: A User's Guide (New York: Cambridge University Press, 1991) ("Macmillan & Creelman, Detection Theory"); Clyde C. Coombs, Robyn M. Dawes, & Amos Tversky, Mathematical Psychology: An Elementary Introduction 165-201 (Englewood Cliffs, N.J.: Prentice Hall, 1970) ("Coombs et al., Mathematical Psychology").
47. E.g., Grofman, "Mathematical Models" at 307-17; Norbert Kerr, "Stochastic Models of Jury Decision Making," in Reid Hastie, ed., Inside the Juror: The Psychology of Juror Decision Making 116 (New York: Cambridge University Press, 1993) ("Hastie, Inside the Juror"); Robert D. Sorkin & Huanping Dai, "Signal Detection Analysis of the Ideal Group," 60 Organizational Behav. & Hum. Decision Processes 1 (1994); Ewart A. C. Thomas & Anthony Hogue, "Apparent Weight of Evidence, Decision Criteria, and Confidence Ratings in Juror Decision Making," 83 Psychol. Rev. 442 (1976); Barbara D. Underwood, "The Thumb on the Scales of Justice: Burdens of Proof of Persuasion in Criminal Cases," 86 Yale L.J. 1299, 1331 n.93 (1977).
48. E.g., Grofman, "Mathematical Models" at 307-17; Norbert Kerr, "Stochastic Models of Jury Decision Making," in Reid Hastie, ed., Inside the Juror: The Psychology of Juror Decision Making 116 (New York: Cambridge University Press, 1993) ("Hastie, Inside the Juror"); Robert D. Sorkin & Huanping Dai, "Signal Detection Analysis of the Ideal Group," 60 Organizational Behav. & Hum. Decision Processes 1 (1994); Ewart A. C. Thomas & Anthony Hogue, "Apparent Weight of Evidence, Decision Criteria, and Confidence Ratings in Juror Decision Making," 83 Psychol. Rev. 442 (1976); Barbara D. Underwood, "The Thumb on the Scales of Justice: Burdens of Proof of Persuasion in Criminal Cases," 86 Yale L.J. 1299, 1331 n.93 (1977).
49. E.g., Grofman, "Mathematical Models" at 307-17; Norbert Kerr, "Stochastic Models of Jury Decision Making," in Reid Hastie, ed., Inside the Juror: The Psychology of Juror Decision Making 116 (New York: Cambridge University Press, 1993) ("Hastie, Inside the Juror"); Robert D. Sorkin & Huanping Dai, "Signal Detection Analysis of the Ideal Group," 60 Organizational Behav. & Hum. Decision Processes 1 (1994); Ewart A. C. Thomas & Anthony Hogue, "Apparent Weight of Evidence, Decision Criteria, and Confidence Ratings in Juror Decision Making," 83 Psychol. Rev. 442 (1976); Barbara D. Underwood, "The Thumb on the Scales of Justice: Burdens of Proof of Persuasion in Criminal Cases," 86 Yale L.J. 1299, 1331 n.93 (1977).
50. E.g., Grofman, "Mathematical Models" at 307-17; Norbert Kerr, "Stochastic Models of Jury Decision Making," in Reid Hastie, ed., Inside the Juror: The Psychology of Juror Decision Making 116 (New York: Cambridge University Press, 1993) ("Hastie, Inside the Juror"); Robert D. Sorkin & Huanping Dai, "Signal Detection Analysis of the Ideal Group," 60 Organizational Behav. & Hum. Decision Processes 1 (1994); Ewart A. C. Thomas & Anthony Hogue, "Apparent Weight of Evidence, Decision Criteria, and Confidence Ratings in Juror Decision Making," 83 Psychol. Rev. 442 (1976); Barbara D. Underwood, "The Thumb on the Scales of Justice: Burdens of Proof of Persuasion in Criminal Cases," 86 Yale L.J. 1299, 1331 n.93 (1977).
51. E.g., Grofman, "Mathematical Models" at 307-17; Norbert Kerr, "Stochastic Models of Jury Decision Making," in Reid Hastie, ed., Inside the Juror: The Psychology of Juror Decision Making 116 (New York: Cambridge University Press, 1993) ("Hastie, Inside the Juror"); Robert D. Sorkin & Huanping Dai, "Signal Detection Analysis of the Ideal Group," 60 Organizational Behav. & Hum. Decision Processes 1 (1994); Ewart A. C. Thomas & Anthony Hogue, "Apparent Weight of Evidence, Decision Criteria, and Confidence Ratings in Juror Decision Making," 83 Psychol. Rev. 442 (1976); Barbara D. Underwood, "The Thumb on the Scales of Justice: Burdens of Proof of Persuasion in Criminal Cases," 86 Yale L.J. 1299, 1331 n.93 (1977).
52. In SDT, it is standard practice to use conditional distributions as in fig. 1. Although other authors (e.g., Grofman, "Mathematical Models" at 312) have used distributions that do reflect the relative proportions of truly innocent and truly guilty defendants, some important quantities - most notably the likelihood ratio P(x|G)/P(x|I) - cannot be read directly from such a figure.
53. For reviews, see John A. Swets, "Indices of Discrimination or Diagnostic Accuracy: Their ROCs and Implied Models," 99 Psychol. Bull. 100 (1986), and id., "Measuring the Accuracy of Diagnostic Systems," 240 Science 1285 (1988).
54. For reviews, see John A. Swets, "Indices of Discrimination or Diagnostic Accuracy: Their ROCs and Implied Models," 99 Psychol. Bull. 100 (1986), and id., "Measuring the Accuracy of Diagnostic Systems," 240 Science 1285 (1988).
55. Labels for these outcomes differ across disciplines and methodologies. For example, convictions of truly innocent defendants (CI) are equivalent to false positives in medicine, false alarms in SDT, and Type I errors in statistics. Likewise, acquittals of truly guilty defendants (AG) = false negatives = misses = Type II errors, convictions of truly guilty defendants (CG) = true positives = hits, and acquittals of truly innocent defendants (AI) = true negatives = correct rejections.
56. See, e.g., May, 10 Am. L. Rev. at 653-54 (cited in note 4).
57. Terry Connolly, "Decision Theory, Reasonable Doubt, and the Utility of Erroneous Acquittals," 11 Law & Hum. Behav. 101, 104 (1987).
58. Kenneth R. Hammond, Lewis O. Harvey, & Reid Hastie, "Making Better Use of Scientific Knowledge: Separating Truth from Justice," 3 Psychol. Sci. 80, 84 (1992).
59. Connolly, 11 Law & Hum. Behav. at 104; Hammond et al., 3 Psychol. Sci. at 84.
60. Connolly, 11 Law & Hum. Behav. at 104; Hammond et al., 3 Psychol. Sci. at 84.
61. Birmingham, 12 Ga. L. Rev. at 536-37; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4,366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965 (all cited in note 6).
62. Birmingham, 12 Ga. L. Rev. at 536-37; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4,366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965 (all cited in note 6).
63. Birmingham, 12 Ga. L. Rev. at 536-37; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4,366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965 (all cited in note 6).
64. Birmingham, 12 Ga. L. Rev. at 536-37; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4,366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965 (all cited in note 6).
65. Birmingham, 12 Ga. L. Rev. at 536-37; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4,366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965 (all cited in note 6).
66. Birmingham, 12 Ga. L. Rev. at 536-37; Grofman, "Mathematical Models" at 314-15; Lempert, 75 Mich. L. Rev. at 1038; Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 355-57, 359-60 n.4,366, 376, 378, 381; Nagel & Neef, 1975 Wash. U. L.Q. at 943 n.17, 945-46, 959, 963, 965 (all cited in note 6).
67. Of course, one may make meaningful statements about ratios of temperatures using the Kelvin scale. Because the Kelvin scale has a nonarbitrary zero point characterized by the complete absence of heat (0°K = -273.15°C = -459.67°F), it is a ratio scale. Needless to say, the prospects for discovering a similar "absolute zero" for utility are incredibly slim.
68. John von Neumann & Oskar Morgenstern, The Theory of Games and Economic Behavior 20-29, 617-28 (3d ed. New York: Wiley, 1947 [1953]) ("von Neumann & Morgenstern, Theory of Games").
69. See discussion infra p. 117.
70. Cullison, 1969 Toledo L. Rev. at 566-67 & n.42 (cited in note 6). Cf. Cullison, "Model of Rules" at 238, 244 n.13 (cited in note 6) (using identical nomenclature, but not mentioning utility differences explicitly).
71. Cullison, 1969 Toledo L. Rev. at 566-67 & n.42 (cited in note 6). Cf. Cullison, "Model of Rules" at 238, 244 n.13 (cited in note 6) (using identical nomenclature, but not mentioning utility differences explicitly).
72. Edwards, 13 Cardozo L. Rev. at 1062-65 & n.80 (cited in note 6).
73. See discussion infra p. 117.
74. Although the present article is concerned with SEU (Savage, The Foundations of Statistics (cited in note 8)), and not its predecessor, expected utility theory (von Neumann & Morgenstern, Theory of Games), the term "expected utility" is often used in place of "subjective expected utility" for convenience. The distinguishing characteristic of SEU is that probabilities are estimated by the decision maker rather than being given.
75. Although the present article is concerned with SEU (Savage, The Foundations of Statistics (cited in note 8)), and not its predecessor, expected utility theory (von Neumann & Morgenstern, Theory of Games), the term "expected utility" is often used in place of "subjective expected utility" for convenience. The distinguishing characteristic of SEU is that probabilities are estimated by the decision maker rather than being given.
76. von Neumann & Morgenstern, Theory of Games 24-29, 617-28.
77. For real-world tests of the relationship between expected utility strategies and long-run outcomes, see Richard P. Larrick, Richard E. Nisbett, & James N. Morgan, "Who Uses Cost-Benefit Rules of Choice? Implications for the Normative Status of Microeconomic Theory," 56 Organizational Behav. & Hum. Decision Processes 331 (1993).
78. Cullison, 1969 Toledo L. Rev. at 564-66, and id., "Model of Rules" at 238; Fried et ed., "Juror Selection" at 60-61 (cited in note 9).
79. Cullison, 1969 Toledo L. Rev. at 564-66, and id., "Model of Rules" at 238; Fried et ed., "Juror Selection" at 60-61 (cited in note 9).
80. Cullison, 1969 Toledo L. Rev. at 564-66, and id., "Model of Rules" at 238; Fried et ed., "Juror Selection" at 60-61 (cited in note 9).
81. Dorothy K. Kagehiro, "Defining the Standard of Proof in Jury Instructions," 1 Psychol Sci. 194 (1990); Dorothy K. Kagehiro &. W. Clark Stanton, "Legal vs. Quantified Definitions of Standards of Proof," 9 Law & Hum. Behav. 159 (1985); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
82. Dorothy K. Kagehiro, "Defining the Standard of Proof in Jury Instructions," 1 Psychol Sci. 194 (1990); Dorothy K. Kagehiro &. W. Clark Stanton, "Legal vs. Quantified Definitions of Standards of Proof," 9 Law & Hum. Behav. 159 (1985); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
83. Dorothy K. Kagehiro, "Defining the Standard of Proof in Jury Instructions," 1 Psychol Sci. 194 (1990); Dorothy K. Kagehiro &. W. Clark Stanton, "Legal vs. Quantified Definitions of Standards of Proof," 9 Law & Hum. Behav. 159 (1985); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
84. Dorothy K. Kagehiro, "Defining the Standard of Proof in Jury Instructions," 1 Psychol Sci. 194 (1990); Dorothy K. Kagehiro &. W. Clark Stanton, "Legal vs. Quantified Definitions of Standards of Proof," 9 Law & Hum. Behav. 159 (1985); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
85. Cullison, 1969 Toledo L. Rev. at 564-66,
86. and id., "Model of Rules" at 238;
87. Grofman, "Mathematical Models" at 313 (cited in note 6);
88. Edwards, 13 Cardozo L. Rev. at 1063 n.80.
89. The formulas for the threshold likelihood ratio presented in Grofman, "Mathematical Models" at 313, Green & Swets, Signal Detection Theory 23 (cited in note 16), and Coombs et ed., Mathematical Psychology 170 (cited in note 16), have pluses rather than minuses in front of the utilities for false alarms (CI here) and misses (AG here) because the authors assume that error utilities are negative. This assumption is both confusing and limiting. Moreover, the assumption of an absolute zero point is inconsistent with the interval nature of utility scales, von Neumann & Morgenstern, Theory of Games 23-29, 617-28. Equations (17)-(19), on the other hand, correctly express decision thresholds as ratios of utility differences. In these equations, any of the four outcomes may be evaluated positively or negatively. The expression in Macmillan & Creelman, Detection Theory 49 (cited in note 16), is identical to eq. (19) in this respect.
90. The formulas for the threshold likelihood ratio presented in Grofman, "Mathematical Models" at 313, Green & Swets, Signal Detection Theory 23 (cited in note 16), and Coombs et ed., Mathematical Psychology 170 (cited in note 16), have pluses rather than minuses in front of the utilities for false alarms (CI here) and misses (AG here) because the authors assume that error utilities are negative. This assumption is both confusing and limiting. Moreover, the assumption of an absolute zero point is inconsistent with the interval nature of utility scales, von Neumann & Morgenstern, Theory of Games 23-29, 617-28. Equations (17)-(19), on the other hand, correctly express decision thresholds as ratios of utility differences. In these equations, any of the four outcomes may be evaluated positively or negatively. The expression in Macmillan & Creelman, Detection Theory 49 (cited in note 16), is identical to eq. (19) in this respect.
91. The formulas for the threshold likelihood ratio presented in Grofman, "Mathematical Models" at 313, Green & Swets, Signal Detection Theory 23 (cited in note 16), and Coombs et ed., Mathematical Psychology 170 (cited in note 16), have pluses rather than minuses in front of the utilities for false alarms (CI here) and misses (AG here) because the authors assume that error utilities are negative. This assumption is both confusing and limiting. Moreover, the assumption of an absolute zero point is inconsistent with the interval nature of utility scales, von Neumann & Morgenstern, Theory of Games 23-29, 617-28. Equations (17)-(19), on the other hand, correctly express decision thresholds as ratios of utility differences. In these equations, any of the four outcomes may be evaluated positively or negatively. The expression in Macmillan & Creelman, Detection Theory 49 (cited in note 16), is identical to eq. (19) in this respect.
92. The formulas for the threshold likelihood ratio presented in Grofman, "Mathematical Models" at 313, Green & Swets, Signal Detection Theory 23 (cited in note 16), and Coombs et ed., Mathematical Psychology 170 (cited in note 16), have pluses rather than minuses in front of the utilities for false alarms (CI here) and misses (AG here) because the authors assume that error utilities are negative. This assumption is both confusing and limiting. Moreover, the assumption of an absolute zero point is inconsistent with the interval nature of utility scales, von Neumann & Morgenstern, Theory of Games 23-29, 617-28. Equations (17)-(19), on the other hand, correctly express decision thresholds as ratios of utility differences. In these equations, any of the four outcomes may be evaluated positively or negatively. The expression in Macmillan & Creelman, Detection Theory 49 (cited in note 16), is identical to eq. (19) in this respect.
93. The formulas for the threshold likelihood ratio presented in Grofman, "Mathematical Models" at 313, Green & Swets, Signal Detection Theory 23 (cited in note 16), and Coombs et ed., Mathematical Psychology 170 (cited in note 16), have pluses rather than minuses in front of the utilities for false alarms (CI here) and misses (AG here) because the authors assume that error utilities are negative. This assumption is both confusing and limiting. Moreover, the assumption of an absolute zero point is inconsistent with the interval nature of utility scales, von Neumann & Morgenstern, Theory of Games 23-29, 617-28. Equations (17)-(19), on the other hand, correctly express decision thresholds as ratios of utility differences. In these equations, any of the four outcomes may be evaluated positively or negatively. The expression in Macmillan & Creelman, Detection Theory 49 (cited in note 16), is identical to eq. (19) in this respect.
94. Grofman, "Mathematical Models" at 312. Apparently, Grofman's incorrect conclusion resulted from attempting to infer likelihood ratios from a graph that (unlike fig. 1) reflected the relative proportions of truly innocent and truly guilty defendants. See supra note 18.
95. E.g., Michael Barza & Stephen G. Pauker, "The Decision to Biopsy, Treat, or Wait in Suspected Herpes Encephalitis," 92 Ann. Internal Med. 614, 646 (1980); John C. Hershey, Randall D. Cebull, & Sankey V. Williams, "Clinical Guidelines for Using Two Dichotomous Tests," 6 Med. Decision Making 68, 71-72 (1986).
96. E.g., Michael Barza & Stephen G. Pauker, "The Decision to Biopsy, Treat, or Wait in Suspected Herpes Encephalitis," 92 Ann. Internal Med. 614, 646 (1980); John C. Hershey, Randall D. Cebull, & Sankey V. Williams, "Clinical Guidelines for Using Two Dichotomous Tests," 6 Med. Decision Making 68, 71-72 (1986).
97. A description of such a figure does appear in Nagel et al., "Decision Theory" at 357 n.2.
98. CI and CAG are associated with the costs (i.e., adverse effects) of treating nondiseased patients and the benefits of treating diseased patients. Stephen G. Pauker & Jerome P. Kassirer, "Therapeutic Decision Making: A Cost-Benefit Analysis," 293 New Eng. J. Med. 229, 230 (1975); id., "The Threshold Approach to Clinical Decision Making," 302 New Eng. J. Med. 1109, 1112, 1116 (1980); Hershey et al., 6 Med. Decision Making at 69.
99. CI and CAG are associated with the costs (i.e., adverse effects) of treating nondiseased patients and the benefits of treating diseased patients. Stephen G. Pauker & Jerome P. Kassirer, "Therapeutic Decision Making: A Cost-Benefit Analysis," 293 New Eng. J. Med. 229, 230 (1975); id., "The Threshold Approach to Clinical Decision Making," 302 New Eng. J. Med. 1109, 1112, 1116 (1980); Hershey et al., 6 Med. Decision Making at 69.
100. CI and CAG are associated with the costs (i.e., adverse effects) of treating nondiseased patients and the benefits of treating diseased patients. Stephen G. Pauker & Jerome P. Kassirer, "Therapeutic Decision Making: A Cost-Benefit Analysis," 293 New Eng. J. Med. 229, 230 (1975); id., "The Threshold Approach to Clinical Decision Making," 302 New Eng. J. Med. 1109, 1112, 1116 (1980); Hershey et al., 6 Med. Decision Making at 69.
101. CI and CAG are associated with the costs (i.e., adverse effects) of treating nondiseased patients and the benefits of treating diseased patients. Stephen G. Pauker & Jerome P. Kassirer, "Therapeutic Decision Making: A Cost-Benefit Analysis," 293 New Eng. J. Med. 229, 230 (1975); id., "The Threshold Approach to Clinical Decision Making," 302 New Eng. J. Med. 1109, 1112, 1116 (1980); Hershey et al., 6 Med. Decision Making at 69.
102. CI and CAG are associated with the costs (i.e., adverse effects) of treating nondiseased patients and the benefits of treating diseased patients. Stephen G. Pauker & Jerome P. Kassirer, "Therapeutic Decision Making: A Cost-Benefit Analysis," 293 New Eng. J. Med. 229, 230 (1975); id., "The Threshold Approach to Clinical Decision Making," 302 New Eng. J. Med. 1109, 1112, 1116 (1980); Hershey et al., 6 Med. Decision Making at 69.
103. See Hershey et al., 6 Med. Decision Making at 71.
104. E.g., Kaplan, 20 Stan. L. Rev. at 1073-76 (cited in note 9). However, rules of evidence and instructions to the jury may moderate such effects to a substantial degree. Id. at 1074-77; Lempert, 75 Mich. L. Rev. at 1035-40 & nn.41 & 53 (cited in note 6).
105. E.g., Kaplan, 20 Stan. L. Rev. at 1073-76 (cited in note 9). However, rules of evidence and instructions to the jury may moderate such effects to a substantial degree. Id. at 1074-77; Lempert, 75 Mich. L. Rev. at 1035-40 & nn.41 & 53 (cited in note 6).
106. E.g., Kaplan, 20 Stan. L. Rev. at 1073-76 (cited in note 9). However, rules of evidence and instructions to the jury may moderate such effects to a substantial degree. Id. at 1074-77; Lempert, 75 Mich. L. Rev. at 1035-40 & nn.41 & 53 (cited in note 6).
107. CG). Id.
108. CG). Id.
109. T (eq. (17)) exactly. In summary, the potential confounding of utilities and probabilities causes less severe difficulties for the SEU decision rule than might be expected.
110. This solution is not novel. Tribe, 84 Harv. L. Rev. at 1384-85, for example, wrote: "[O]ne will expect a lawmaker rather than the factfinder to use a model such as Kaplan and Cullison propose, and one will define the decision problem to be solved not as the one-shot problem of fixing a standard of proof for a particular trial with four possible outcomes, but as the much larger problem of establishing such standards for the trial system as a whole." The Supreme Court argued similarly: "[T]his court never has approved case-by-case determination of the proper standard of proof for a given proceeding. Standards of proof, like other 'procedural due process rules[,] are shaped by the risk of error inherent in the truth-finding process as applied to the generality of cases, not the rare exceptions.' Since the litigants and the factfinder must know at the outset of a proceeding how the risk of error will be allocated, the standard of proof necessarily must be calibrated in advance." Santosky v. Kramer, 455 U.S. 745, 757 (1982) (alterations in original) (citation omitted) (quoting Mathews v. Eldridge, 424 U.S. 319, 344 (1976)). Contra Santosky v. Kramer, 455 U.S. 745, 775, 787 (1982) (Rehnquist, J., dissenting) (arguing that it is necessary to consider the peculiarities of individual cases).
111. Kaplan, 20 Stan. L. Rev. at 1071, made the assumption implicitly, whereas Birmingham, "Remarks on Probability" at 536 (cited in note 6), Lempert, 75 Mich. L. Rev. at 1033, 1036 n.41, 1038, and Anne W. Martin &. David A. Schum, "Quantifying Burdens of Proof: A Likelihood Ratio Approach," 27 Jurimetrics J. 383, 398 (1987), made the assumption explicitly.
112. Kaplan, 20 Stan. L. Rev. at 1071, made the assumption implicitly, whereas Birmingham, "Remarks on Probability" at 536 (cited in note 6), Lempert, 75 Mich. L. Rev. at 1033, 1036 n.41, 1038, and Anne W. Martin &. David A. Schum, "Quantifying Burdens of Proof: A Likelihood Ratio Approach," 27 Jurimetrics J. 383, 398 (1987), made the assumption explicitly.
113. Kaplan, 20 Stan. L. Rev. at 1071, made the assumption implicitly, whereas Birmingham, "Remarks on Probability" at 536 (cited in note 6), Lempert, 75 Mich. L. Rev. at 1033, 1036 n.41, 1038, and Anne W. Martin &. David A. Schum, "Quantifying Burdens of Proof: A Likelihood Ratio Approach," 27 Jurimetrics J. 383, 398 (1987), made the assumption explicitly.
114. Kaplan, 20 Stan. L. Rev. at 1071, made the assumption implicitly, whereas Birmingham, "Remarks on Probability" at 536 (cited in note 6), Lempert, 75 Mich. L. Rev. at 1033, 1036 n.41, 1038, and Anne W. Martin &. David A. Schum, "Quantifying Burdens of Proof: A Likelihood Ratio Approach," 27 Jurimetrics J. 383, 398 (1987), made the assumption explicitly.
115. Lempert, 75 Mich. L. Rev. at 1036 n.41 (emphasis added).
116. Nagel, 63 Judicature at 192 n.5; Nagel et al., "Decision Theory" at 355-57; Grofman, "Mathematical Models" at 314 (all cited in note 6).
117. Nagel, 63 Judicature at 192 n.5; Nagel et al., "Decision Theory" at 355-57; Grofman, "Mathematical Models" at 314 (all cited in note 6).
118. Nagel, 63 Judicature at 192 n.5; Nagel et al., "Decision Theory" at 355-57; Grofman, "Mathematical Models" at 314 (all cited in note 6).
119. E.g., Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 366; Lempert, 75 Mich. L. Rev. at 1038-39; Martin F. Kaplan, "Cognitive Process in the Individual Juror," in Norbert L. Kerr & Robert M. Bray, eds., The Psychology of the Courtroom 197, 216 (New York: Academic Press, 1982).
120. E.g., Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 366; Lempert, 75 Mich. L. Rev. at 1038-39; Martin F. Kaplan, "Cognitive Process in the Individual Juror," in Norbert L. Kerr & Robert M. Bray, eds., The Psychology of the Courtroom 197, 216 (New York: Academic Press, 1982).
121. E.g., Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 366; Lempert, 75 Mich. L. Rev. at 1038-39; Martin F. Kaplan, "Cognitive Process in the Individual Juror," in Norbert L. Kerr & Robert M. Bray, eds., The Psychology of the Courtroom 197, 216 (New York: Academic Press, 1982).
122. E.g., Nagel, 63 Judicature at 191-92; Nagel et al., "Decision Theory" at 366; Lempert, 75 Mich. L. Rev. at 1038-39; Martin F. Kaplan, "Cognitive Process in the Individual Juror," in Norbert L. Kerr & Robert M. Bray, eds., The Psychology of the Courtroom 197, 216 (New York: Academic Press, 1982).
123. Rita J. Simon & Linda Mahan, "Quantifying Burdens of Proof: A View from the Bench, the Jury, and the Classroom," 5 Law & Soc'y Rev. 319 (1971).
124. Lempert, 75 Mich. L. Rev. at 1038-39.
125. Id. at 1039.
126. Tribe, 84 Harv. L. Rev. at 1379-80.
127. Patricia G. Milanich, "Decision Theory and Standards of Proof," 5 Law & Hum. Behav. 87, 93 (1981); id. at 90-91.
128. Patricia G. Milanich, "Decision Theory and Standards of Proof," 5 Law & Hum. Behav. 87, 93 (1981); id. at 90-91.
129. Connolly, 11 Law & Hum. Behav. at 109 (cited in note 22).
130. von Neumann & Morgenstern, Theory of Games 23-29, 617-28 (cited in note 27). See discussion supra p. 108.
131. Ronald J. Allen, "The Restoration of In re Winship: A Comment on Burdens of Persuasion in Criminal Cases after Patterson v. New York," 76 Mich. L. Rev. 30, 47 n.65 (1977).
132. Michael O. Finkelstein, Quantitative Methods in Law: Studies in the Application of Mathematical Probability and Statistics to Legal Problems 65-78 (New York: Free Press, 1978) ("Finkelstein, Quantitative Methods").
133. Bell, 78 J. Crim. L. & Criminology at 570-72, 579 (cited in note 6).
134. Id. at 573-74, 579-83.
135. Alan E. Gelfand & Herbert Soloman, "Modeling Jury Verdicts in the American Legal System," 69 J. Am. Stat. Ass'n 32, 35-36 (1974).
136. Robert D. Sorkin, personal communication, 7 Sept. 1994.
137. Nagel, 63 Judicature, and Nagel et al., "Decision Theory" at 368-69, 376-81 (both cited in note 6).
138. Nagel, 63 Judicature, and Nagel et al., "Decision Theory" at 368-69, 376-81 (both cited in note 6).
139. Reid Hastie, "Algebraic Models of Juror Decision Processes," in Hastie, Inside the Juror 84, 102-5 (cited in note 17).
140. See discussion supra pp. 97-98 and note 15.
141. E.g., Ronald J. Allen, "A Reconceptualization of Civil Trials," 66 B.U. L. Rev. 401, 410 n.28 (1986).
142. Connolly, 11 Law & Hum. Behav. at 104-5 (cited in note 22).
143. Id. at 105.
144. Id.
145. Alan E. Gelfand & Herbert Soloman, "A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials," 68 J. Am. Stat. Ass'n 271, 278 (1973); id., 69 J. Am. Stat. Ass'n at 35-36.
146. Alan E. Gelfand & Herbert Soloman, "A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials," 68 J. Am. Stat. Ass'n 271, 278 (1973); id., 69 J. Am. Stat. Ass'n at 35-36.
147. Harry Kalven, Jr., & Hans Zeisel, The American jury 488 (Boston: Little, Brown & Co., 1966).
148. Sorkin & Dai, 60 Organizational Behav. & Hum. Decision Processes (cited in note 17).
149. Robert D. Sorkin, personal communication, 7 Sept. 1994.
150. May, 10 Am. L. Rev. at 653-54 (cited in note 4).
151. Bell, 78 J. Crim. L. & Criminology at 558 (cited in note 6), suggested that "[t]he intellectual origin of the Court's due process doctrine for burdens of proof is Kaplan's article, Decision Theory and the Factfinding Process." Indeed, Justice Harlan's concurring opinion in In re Winship appears to have been influenced by Kaplan's analysis: [E]ven though the labels for the alternative standards of proof are vague and not a very sure guide to decisionmaking, the choice of the standard for a particular variety of adjudication does, I think, reflect a very fundamental assessment of the comparative social costs of erroneous factual determinations. . . . . . . . . . . I view the requirement of proof beyond a reasonable doubt in a criminal case as bottomed on a fundamental value determination of our society that it is far worse to convict an innocent man than to let a guilty man go free. In re Winship, 397 U.S. 358, 369-70, 372 (1970) (Harlan, J., concurring) (citing Kaplan). Mullaney v. Wilbur, 421 U.S. 684, 703-4 (1975); id. at 706 (Rehnquist, J., concurring); Patterson v. New York, 432 U.S. 197, 208 (1977); Santosky v. Kramer, 455 U.S. 744, 788 n.13 (1982) (Rehnquist, J., dissenting). See discussion supra note 15 and accompanying text.
152. Kagehiro, 1 Psychol Sci. 194, and Kagehiro & Stanton, 9 Law & Hum. Behav. 159 (both cited in note 36); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
153. Kagehiro, 1 Psychol Sci. 194, and Kagehiro & Stanton, 9 Law & Hum. Behav. 159 (both cited in note 36); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
154. Kagehiro, 1 Psychol Sci. 194, and Kagehiro & Stanton, 9 Law & Hum. Behav. 159 (both cited in note 36); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
155. Kagehiro, 1 Psychol Sci. 194, and Kagehiro & Stanton, 9 Law & Hum. Behav. 159 (both cited in note 36); Nagel, 63 Judicature at 194-95, and Nagel et ed., "Decision Theory" at 377-78 (both cited in note 6).
156. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
157. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
158. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
159. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
160. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
161. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
162. "[B]urdens of proof are founded on considerations of policy. These considerations are explicated by the policy for factfinders' erroneous decisions as a wanted ratio of errors. . . . A burden of proof is inconsistent with due process only if it apportions factfinding errors in an impermissible way." Bell, 78 J. Crim. L. & Criminology at 583 (emphasis added) (footnote omitted); id. at 563, 573-74, 580-81; "If the burden of errors is deemed to be the same for both parties, the aim should be equal rates of errors for both parties." Finkelstein, Quantitative Methods 67 (cited in note 60) (emphasis added); "[T]he reasonable doubt standard seeks to assure that erroneous acquittals of the guilty are far more common than the erroneous convictions of the innocent." "The Supreme Court, 1969 Term," 84 Harv. L. Rev. at 158 n.13 (cited in note 15) (emphasis added); "A demanding burden of proof is imposed on the prosecution in order to assure that men are wrongly convicted much less often than they are wrongly acquitted. . . . [T]he objective [is to assure] that erroneous acquittals of the guilty occur with greater frequency than erroneous convictions of the innocent." Tribe, 84 Harv. L. Rev. at 1381 n.162 (cited in note 9) (emphasis added); see discussion supra pp. 97-98 and note 15. Cf. Finkelstein, Quantitative Methods 69 (suggesting that different goals might apply in different situations). But see David Kaye, "Naked Statistical Evidence," 89 Yale L.J. 601, 605-8 (1980) (book review) (criticizing Finkelstein's preference for standards based on ratios of errors).
163. Bell, 78 J. Crim. L. & Criminology at 580 (emphasis added). But cf. supra notes 6, 15, and 78 and accompanying text (arguing that the Court has favored a utility-based approach and has not adopted Blackstone's ratio).
164. Connolly, 11 Law & Hum. Behav. at 104-5 (cited in note 22).
165. Finkelstein, Quantitative Methods 73. Cf. quotation, supra note 80 (advocating an error-equalizing rule).
166. Connolly, 11 Law & Hum. Behav. at 104.
167. Deborah Frisch & Robert T. Clemen, "Beyond Expected Utility Theory: Rethinking Behavioral Decision Research," 116 Psychol. Bull. 46, 49-50 (1994).