Conjunction and Aggregation

Michigan Law Review

Volumn 99, Issue 4, 2001, Pages 753-755

  Levmore, Saul ^a  

^a NONE

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EID: 0345893999     PISSN: 00262234     EISSN: None     Source Type: Journal    
DOI: 10.2307/1290534     Document Type: Article

References (90)

1. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
2. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
3. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
4. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
5. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
6. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
7. EDWARD J. DEVITT ET AL., 3 FEDERAL JURY PRACTICE AND INSTRUCTIONS, CIVIL § 80.17 (4th ed. 1987). Nearly identical language is used in actual cases. See, e.g., Folks v. Kirby Forest Ind. Inc., 10 F.3d 1173, 1176 n.4 (5th Cir. 1994) (noting language used by district court below while reversing and remanding on other grounds). There is some variety across states, as the elements of a tort claim might be described as two or three or even one in number. Thus, in Alabama: The plaintiff claims the defendant was negligent and that his negligence proximately caused certain injuries suffered by the plaintiff. . . . This presents for your determination the following. Was the defendant negligent as claimed by the plaintiff? If so, was such negligence of the defendant the proximate cause of any injury sustained by the plaintiff as claimed? If you find both of the above issues in favor of the plaintiff and against the defendant what sum of money will fairly and reasonably compensate him for the injury so sustained? ALABAMA PATTERN JURY INSTRUCTIONS - CIVIL 21.01 (1974). But in Colorado: For the plaintiff to recover from the defendant on his claim of negligence, you must find that all of the following have been proved by a preponderance of the evidence: 1. The plaintiff had injuries; 2. The defendant was negligent; and 3. The defendant's negligence was a cause of the plaintiff's injuries. If you find that any one or more of these [three] statements has not been proved, then your verdict must be for the defendant. On the other hand, if you find that all of these [three] statements have been proved, then your verdict must be for the plaintiff. COLORADO JURY INSTRUCTIONS - CIVIL 9.1 (4th ed.). Oregon expresses the ideas of negligence and causation almost as if these were a single element: "To recover, the plaintiff must prove by a preponderance of the evidence that the defendant was negligent in at least one respect charged in plaintiff's complaint which was a cause of damage to the plaintiff." OREGON JURY INSTRUCTIONS FOR CIVIL CASES 10.01 (1984). Some states are more ambiguous in their treatment of the conjunction issue. For example, Florida's standard jury instructions read: The issues for your determination on the claim of (claimant) against (defendant) are: whether (defendant) was negligent in (describe negligence); and, if so, whether such negligence was a legal cause of injury sustained by claimant. If the greater weight of the evidence does not support the claim of (claimant), then your verdict should be for (defendant). FLORIDA STANDARD JURY INSTRUCTIONS IN CIVIL CASES 3.5, at 1c - 2, 3.6, 3.7 (1967). Although this instruction is somewhat ambiguous on whether the weight of the evidence must support the entire claim or individual issues, Florida and other states with similar jury instructions seem to suppress the product rule as well. Instructions might also be given regarding the meaning of the preponderance standard, of negligence, and so forth. Even where judges are inclined to roll everything they wish to communicate into one (ambiguous) sentence, the jury may return with questions as to how to combine its findings. As will become clear, there are many ways to try and avoid the conjunction problem, but I prefer in this Article to show that the apparent illogic of the law may actually be clever in light of aggregation problems. Other commentators have of course noted and argued about the law's ambiguity and the correct approach to multiple requirements. See, e.g., Ronald J. Allen, A Reconceptualization of Civil Trials, 66 B.U. L. REV. 401, 405-08 (1986) (arguing that the conventional but misguided view of trials is what makes the conventional view of probability as applied to law seem erratic and irrational); Dale A. Nance, A Comment on the Supposed Paradoxes of a Mathematical Interpretation of the Logic of Trials, 66 B.U. L. REV. 947 (1986) (noting math-law divide and emphasizing ambiguity of jury instructions). As a descriptive matter, there is some dispute as to what courts actually do, and as a normative matter there is no agreement on what they ought to do. I weigh in with my own descriptive and normative views, but the more important point here is to show the possibility of a connection between conjunction and aggregation, and in turn the possibility of seeing prevailing practices, both as to conjunction (or not) and as to supermajority votes, in a new and fairly optimistic light.
8. LEWIS A. GROSSMAN & ROBERT G. VAUGHN, A DOCUMENTARY COMPANION TO A CIVIL ACTION 626 (1999) (quoting jury instruction regarding circumstantial proof).
9. There are several ways to interpret these numbers. Our factfinder might reason that if he or she observed evidence of this sort ten times, it would be the case that the defendant was negligent seven times and not negligent three times.
10. The "product" or multiplication rule applies whenever two events are independent. Thus, there is a .25 chance of seeing two heads in a row when a fair coin is tossed, because for each coin the probability of a head is .5 and (.5)(.5) = .25. Independence, prior probabilities, and other nuances are taken up presently.
11. The product rule is but one strategy for dealing with the conjunction issue, but in order to avoid repetition I will use the terms in a way that approaches interchangeability. Law avoids the conjunction issue; a reasonable and nearly universal approach (outside of law) to this issue is to deploy the product rule; law therefore can be said to suppress the product rule.
12. In the torts setting the idea is that absent defendant's misstep, the chance that plaintiff would have been injured is very low. "[T]he more serious the breach of duty and the less the amount of unavoidable accident, the less proof that should be required of the plaintiff on the cause in fact issue." MARK F. GRADY, CASES AND MATERIALS ON TORTS 567 (1994).
13. For evidence to this effect, see infra Section I.B.5 and accompanying notes.
14. Thus, if a jury thinks that defendant was negligent, it is sensible for it to ask whether given defendant's negligence and given plaintiff's injury, it is more likely than not that defendant's negligence caused plaintiff's injury. This sort of argument is developed in A.P. Dawid, The Difficulty About Conjunction, 36 THE STATISTICIAN 91 (1987).
15. See, e.g., Laurence H. Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 HARV. L. REV. 1329 passim (1971).
16. See People v. Collins, 438 P.2d 33, 36 (Cal. 1968) (concluding that defendant should not have had his guilt determined "by the odds," where prosecutor misapplied the product rule in remarkable fashion). The case is discussed in Maya Bar-Hillel, Probabilistic Analysis in Legal Factfinding, 56 ACTA PSYCHOLOGICA 267, 268-70 (1984), and Tribe, supra note 9, at 1341-42 & n.40.
17. See People v. Collins, 438 P.2d 33, 36 (Cal. 1968) (concluding that defendant should not have had his guilt determined "by the odds," where prosecutor misapplied the product rule in remarkable fashion). The case is discussed in Maya Bar-Hillel, Probabilistic Analysis in Legal Factfinding, 56 ACTA PSYCHOLOGICA 267, 268-70 (1984), and Tribe, supra note 9, at 1341-42 & n.40.
18. Of course, the product rule could often be used in favor of plaintiffs, but courts and litigants have not recognized the necessary arguments. Imagine, for example, a plaintiff in a products liability suit who should win if she can show that defendant's product was defectively designed (D), defectively manufactured (M), or sold with an inadequate warning (W). Here, the multiple requirements are not to be conjoined because they are alternative routes to success. If plaintiff can show only that each claim is but .4 likely to be true, the lawyer expects plaintiff to lose - but the product rule suggests that plaintiff should win. There is, after all, a .6 chance that defendant did not produce a defective design, D, and similarly a .6 chance of not-M. If D and M are independent, then there is a .36 chance that defendant was well-behaved with respect to both design and manufacture. The possibility of W, a third route for plaintiff, further reduces the likelihood (to .216) that defendant should be absolved; with three such routes, it is quite likely that we err by requiring plaintiff to satisfy the preponderance standard for at least one alternative on its own. In this example, conjunction issues arise where there are not multiple requirements but alternative routes for a decision; the plaintiff's alternatives amount to the presence of multiple requirements (and conjunction) for defendant to succeed. Unfortunately, the court that has come closest to recognizing this issue of reverse conjunction failed to grasp the full power of the pro-plaintiff argument. See Cheshire Med. Ctr. v. W.R. Grace & Co., 49 F.3d 26, 31-32 (1st Cir. 1995) (acknowledging the product rule issue but, by focusing on plaintiff's burden rather than the conjoined likelihood of defendant's avoiding all alternative claims, missing the applicability of the product rule). I will return to this "reverse conjunction" problem below. It presents no special difficulty for the theory advanced here.
19. We ask factfinders to overcome their math anxieties with respect to things other than damages. Thus, some jurisdictions impose market share liability where there are "recurring cases," and some give recovery for "lost chances." See Saul Levmore, Probabilistic Recoveries, Restitution, and Recurring Wrongs, 19 J. LEGAL STUD. 691 (1990).
20. Following the framing strategy advanced by Gerd Gigerenzer, The Psychology of Good Judgment: Frequency Formats and Simple Algorithms, 16 MED. DECISION MAKING 273 (1996) (discussing the use and accuracy of "fast and frugal algorithms" that help people perceive statistical or probabilistic relationships). See also Gerd Gigerenzer & Ulrich Hoffrage, How to Improve Bayesian Reasoning Without Instruction: Frequency Formats, 102 PSYCHOL. REV. 684 (1995).
21. Following the framing strategy advanced by Gerd Gigerenzer, The Psychology of Good Judgment: Frequency Formats and Simple Algorithms, 16 MED. DECISION MAKING 273 (1996) (discussing the use and accuracy of "fast and frugal algorithms" that help people perceive statistical or probabilistic relationships). See also Gerd Gigerenzer & Ulrich Hoffrage, How to Improve Bayesian Reasoning Without Instruction: Frequency Formats, 102 PSYCHOL. REV. 684 (1995).
22. We do not want to ask the jury to imagine 100 cases in which there are injuries of the sort experienced here, followed by the question of how often defendant was negligent (and then how often in this subset defendant caused the injury) because this encourages hindsight bias of a sort.
23. This is an important condition because without it jurors will feel encouraged to expand the number of voters on their own through consultation and the like. We might encourage jurors to see themselves as representatives of a large group, but one that is constrained to work with certain information.
24. See Allen, supra note 1.
25. See Mark F. Grady, Untaken Precautions, 18 J. LEGAL STUD. 139 (1989).
26. Thus, when told a story about "Bill" (an "intelligent, but unimaginative" thirty-four-year-old), subjects in a psychology experiment regularly assessed the likelihood that Bill was an accountant who also played jazz as greater than the likelihood that Bill was an accountant or jazz hobbyist. It appears that the compound story of Bill as an accountant who plays jazz for a hobby is more appealing, if that is the right word, than the story of Bill as a mere accountant or jazz hobbyist, even though, as a mathematical proposition, the likelihood of the conjunctive event (accountant and jazz hobbyist) is, of course, less likely than the single event (accountant). In these studies, subjects were not asked to generate numerical assessments but rather to rank the likelihood of various stories or characteristics (including both compound and single ones), so that we do not know whether the conjoining error they made involved underestimates of the likelihood of the single characteristic or overestimates of the compound characteristics. It is difficult, therefore, to take from these studies any easy conclusions about law. It is possible that factfinders seriously overestimate conjoined events, because the entire story is somehow more appealing, and that law does nothing to offset this either because lawmakers suffer from the same psychological bias or because lawmakers think there is no point in fighting human nature. But it is also possible that factfinders generate reasonable assessments of multiple events and simply underestimate single events that are not embedded in complete and appealing stories. See Amos Tversky & Daniel Kahneman, Judgments of and by Representativeness, in JUDGMENT UNDER UNCERTAINTY: HEURISTICS AND BIASES 91-96 (Daniel Kahneman et al. eds., 1982).
27. In criminal law, the defense is given some latitude. It is conventional for the defense to remind the jury of all the small doubts that have been raised and to imply that they combine to leave more than a reasonable doubt. Unfortunately, the law (once again) suppresses the nature of this combinatorial process. It is not surprising that in criminal law we are especially disinclined to attach real numbers to standards. The product rule suggests that the jury engage in some multiplication; lay (statistically unsophisticated) intuitions suggest addition; a third, reasonable view might require that at least one of these doubts on its own needs to be substantial enough to meet the reasonable doubt standard. After all, if reasonable doub means that one has a reason for the doubt, then perhaps a check on this reason is that it not be trivial. On the other hand, it can be uniquely held. A jury can acquit even when each juror points to a different reasonable doubt, but there are other elements that jurors might need to agree upon. See Richardson v. United States, 526 U.S. 813 (1999) (holding that, in a continuing criminal enterprise case under 21 U.S.C. § 848, jurors are required to agree unanimously not only that accused committed continuing series of violations, but also as to which specific violations made up the continuing series). I do not pursue these puzzling rules here.
28. For the claim that suppression can (somehow) offset the lack of a partial liability rule, see Alex Stein, Of Two Wrongs That Make a Right: Two Paradoxes of the Evidence Law and Their Combined Economic Justification, 79 TEX. L. REV. _ (forthcoming 2001).
29. As far as I can tell, no state encourages simple majority verdicts. See infra note 33.
30. Condorcet's 1785 work is discussed in DENNIS C. MUELLER, CONSTITUTIONAL DEMOCRACY 158-59 (1996). The theorem assumes that there is a "right" answer to the question at hand, that each voter is equally likely to know the right answer, or at least that each is more likely than not to discern the correct answer, and that we have no way of identifying those who are most likely to be right or even likely to benefit from deliberation. On some issues an expert will obviously do better than a large well-meaning group of voters, although adding in enough additional voters, each of whom is more likely to be right than wrong, will eventually improve the stew. It is where a non-expert is more likely to be wrong than right, or where a non-expert does no better than guess, that we most need experts. Thus, if only to date this Article, the audience in the television program "Who Wants to be a Millionaire" offers a remarkably reliable "lifeline" for contestants. When this audience agrees on an answer it is rarely wrong. In the program, there is a "right" answer, there is no way of discerning experts except that the contestant knows his own doubts and non-expertise, there is no incentive for the jurors to vote strategically, and the nature of the questions and audience suggests that indeed each member is more likely than not to be right.
31. 5p), where p is, once again, the chance that each voter is correct.) But of course these numbers should appeal only to the purist, as they are misleading. In reality, when supermajority or unanimity rules are in place, and especially when they are symmetrical as between the parties, the voters are encouraged to deliberate and to reach a verdict. It is hardly the case that 99 out of 100 twelve-person juries generate mistrials when bound by a unanimity rule. Without some excellent theory and evidence as to how such compromise verdicts (if they are that) are reached, it will be impossible to assess our confidence in the correctness of the results. Finally, note that the discussion sets aside such things as the possibility that six jurors would pay more attention to the evidence than would the fifty because of a kind of collective action problem. But this sort of claim takes aim at the basic assumptions of the Jury Theorem, because it raises the possibility that each member of a small group is significantly more likely to be right than each member of a large group.
32. 5p), where p is, once again, the chance that each voter is correct.) But of course these numbers should appeal only to the purist, as they are misleading. In reality, when supermajority or unanimity rules are in place, and especially when they are symmetrical as between the parties, the voters are encouraged to deliberate and to reach a verdict. It is hardly the case that 99 out of 100 twelve-person juries generate mistrials when bound by a unanimity rule. Without some excellent theory and evidence as to how such compromise verdicts (if they are that) are reached, it will be impossible to assess our confidence in the correctness of the results. Finally, note that the discussion sets aside such things as the possibility that six jurors would pay more attention to the evidence than would the fifty because of a kind of collective action problem. But this sort of claim takes aim at the basic assumptions of the Jury Theorem, because it raises the possibility that each member of a small group is significantly more likely to be right than each member of a large group.
33. I hesitate to say that the probability approaches 1.0 because of the problem, see Grofman & Owen, supra note 23, that in reality this unanimous group may have compromised or impatiently emerged with a unanimous decision. In any event, the text avoids some nuances that are not central to the argument. Thus, I ignore the possibility that voters know when to abstain; it is possible that an advantage of large-group decisionmaking is that those who know that they are clueless abstain, while the remaining voters do better because they are more expert. I also avoid questions that are not posed in binary form. We can ask as many jurors as we like to add .25 and .6, and the fact that most if not all give answers of .85 does not make the right answer 1.0. The Jury Theorem is best framed as dealing with binary questions, such as guilt (under some standard) or not, liability or not, and so forth. If we ask jurors whether the sum of .25 and .6 is more likely to be .85 or 1.0. and each is more likely than not to get such an addition problem right, then with a likelihood approaching 1.0 the group will vote for .85. Still, framing can turn many questions into binary form. If we want an assessment of negligence, we can ask a jury whether a defendant is more than .5 likely to have behaved negligently. If there is an affirmative answer we can then ask whether it is more than .6 likely, and so forth. But for the most part we avoid confusion if we are careful with the part of the Jury Theorem that requires that each voter be more likely than not to get the question right. Still, framing can make the Theorem's applicability a slippery question. Imagine that the evidence suggests that A was negligent in injuring B, but that one witness thought that B has a preexisting condition such that it was possible, perhaps 10% or 20 % likely that A did not cause B's injury. If this witness was perfectly credible, all the jurors might simply share the view that A was negligent and that A probably caused B's harm. Additional jurors or voters will simply confirm the reaction to the defense witness but it will not raise the probability of getting it all right to 1.0. For the purpose of this Article, however, I think it more than sufficient to say that large juries or large supermajorities can often raise our confidence level above what any one juror thinks. I will be careful not to insist that this increase is to the limit - but I do think it is fair to say that without the benefit of the Condorcet Jury Theorem we would underestimate the power of group decisionmaking.
34. It is possible that thinking of this sort is at the root of the argument in Neil Cohen, Confidence in Probability: Burdens of Persuasion in a World of Imperfect Knowledge, 60 N.Y.U. L. REV. 385, 399 (1985) - that subjective assessments of probabilities by factfinders are more properly analogized to probabilities from sample data rather than complete information. One claim is that: Not only must factfinders determine that their best estimate of the probability in question exceeds the threshold level - 0.5 for the preponderance of the evidence standard - based on the evidence presented, but they also must have a certain level of confidence that the true probability, based on all possible evidence, exceeds that threshold. Id. But Cohen says nothing about the number of factfinders, and indeed the argument might be about a single assessor.
35. Though it should be noted that statutes or constitutions permitting plebiscites, referenda, or other exercises in direct democracy sometimes limit the problem by imposing a single-subject requirement on these popular votes. See generally James D. Gordon III & David B. Magleby, Pre-Election Judicial Review of Initiatives and Referendums, 64 NOTRE DAME L. REV. 298, 303 (1989).
36. See Matthew Rabin & Joel L. Schrag, First Impressions Matter: A Model of Confirmatory Bias, 114 Q.J. ECON. 37 (1999).
37. And it is unlikely that the overconfidence bias would generate a corresponding need in the opposite direction.
38. More generally, it would be useful to know more about the relative strength of the confirmatory and self-confidence biases. It would be interesting to see how juries reacted to hearing first from one side or the other (because the confirmatory bias suggests that there is an advantage in going first) and to hearing warnings about the bias itself. But these topics are beyond the scope of this Article. I aim to make discrete points about the Jury Theorem, the likely views of inframarginal jurors (especially where there are supermajority requirements), and the product rule. I refer to these perception biases in order to remind readers and author alike that there is much more going on than what is discussed in this Article.
39. A different approch would be to work in reverse and to be more interested in the selection of a voting rule than in the suppression of the product rule. The same set of observations can be used to explain the location of supermajority voting rules. We might eliminate uses of supermajoritarianism that appear to take the place of bicameralism, other confederating devices, or "brakes" on faction-supported government intervention, and then ask whether other instances of supermajority requirments can be linked to multiple requirements and hence the (suppression of the) product rule. On the relationship among these tools, see Saul Levmore, Bicameralism: When are Two Decisions Better than One?, 12 INT'L REV. L. & ECON. 145 (1992). We might be able to explain the disinclination to assess things more directly (and calculate their product) with our observations about strategic voting. This is obviously not the place for such an exhaustive exercise, but it may be useful to point out that we virtually never find a supermajority requirements in committees. Closer to home, law faculties often work with supermajority requirements for personnel matters, and often not. These supermajorities can be explained, I think, but not in ways that have much to do with the product rule. In my own experience in academic settings, simple majority voting has been associated with a wonderful and remarkably low level of strategic voting. Participants seemed to act as if they understood the genius of the July Theorem. Some of the most respected faculty members were often, as far as I could tell, perfectly content to "lose" and to abide happily by the majority. My other, shorter experience has been with serious supermajoritarianism. It too functions remarkably well. I might explain the rule as amounting to fairly explicit deference to experts - in keeping with the Jury Theorem after all. Alternatively, every faculty personnel matter can be seen as a difficult question of agenda-setting because one does not know what future appointment is foreclosed by a current appointment. A large and enthusiastic supermajority makes it quite likely that the future candidate will not be preferred to the present one.
40. Strategic behavior problems are discussed infra Section II.C.5.
41. Put differently, simultaneous - as opposed to sequential - decisionmaking can lead to interesting anomalies. See infra Section III.B.
42. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
43. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury
44. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
45. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
46. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
47. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
48. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
49. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three-fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
50. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
51. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
52. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60-248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
53. Roughly speaking, more than a third of the states require unanimity in civil cases, see, e.g., CONN. SUPER. CT. R. 16-30; S.C. R. Civ. P. 48. (South Carolina). States sometimes relax the unanimity requirement, however, once juries have deliberated for some hours. See e.g., MINN. STAT. ANN. § 546.17 (1999); IOWA R. CIV. P. 203. Moreover, in many states the parties can opt out of the unanimity rule by agreeing on another decision rule. Among the states that do not require unanimity, about half call for an 80% supermajority (by requiring agreement of either ten of twelve or five of six jurors, depending on the jury size), many ask for a three-quarters supermajority, and a few permit two-thirds supermajorities. See, e.g., N.Y. C.P.L.R. § 4113 (2001) (five of six); WIS. STAT. § 805.09 (1999) (five of six); CAL. CIV. P. CODE § 618 (2000) (three-fourths rule); TEX. CONST. art. V, § 13 (three- fourths rule); MONT. CODE ANN. § 25-7-403 (West 2000) (two-thirds rule); MO. CONST. art. 1, § 22(a) (two-thirds rule in courts not of record). There is some variety as to jury size, so that a greater percentage might be required for a smaller jury. See KAN. STAT. ANN. § 60- 248(g) (West 1999); LA. CODE CIV. P. ANN. art. 1797 (West 2000). The supermajority character of the argument offered here is emphasized in the next Section of the text.
54. For expository purposes, I set aside the question of whether the presiding judge permits the jury to convey this information.
55. The language in the text reflects the fact that apart from rare (and perhaps nonexistent) cases with special verdicts as to the jury's precise judgment, we have not received a .51 response but rather an affirmative answer to the question of whether each requirement is met by the POE standard, which is to say is more than .5 likely. More generally, it should be noted that special verdicts of the kind observed do not much affect the analysis here. Juries simply tell us that multiple requirements are met (one at a time); they are not encouraged to take the products of probabilities. Nor, of course, does the discussion here suggest that they ought to be so encouraged.
56. The argument here is largely unaffected by the question of whether the majority on one question is different from that supporting the other. Strategic problems aside (for now), it should matter little.
57. I do not mean to hazard a guess as to the distribution of assessments. But given that unanimity and 80% supermajority requirements are so common, a calculation of the sort sketched here is quite defensible.
58. Perhaps I should say "more intense assessments" because the jury's report will, in like fashion, suppress information that would have suggested a lower numerical assessment when the jury finds that a requirement is less likely than not to be present. The math-law divide, however, is only an issue where multiple requirements are all (individually) assessed as satisfying the standard for liability. Note that the explanation offered here does not depend on the Jury Theorem and therefore, unlike the argument advanced in Section II.B, it is not open to claims that the assumptions of that theorem are absent.
59. The only saving grace of the law's suppression of the product rule (as I will continue to call it) comes from the Jury Theorem. If nine million jurors thought .51 and three million thought 0.0, then following the Condorcet Jury Theorem we might be quite confident in the .51. Certainly if the supermajority multitude thought .7 and the minority thought 0.0, we would be comfortable with liability (even though (.7)(.7) is less than .5). But I am trying to set aside this argument from the Jury Theorem against the simple application of the product rule in part because we can do better and in part because we do not deploy juries of huge populations.
60. In some situations we might choose to discard outliers, but again we would do so at both ends of the spectrum. Apart from problems associated with asking jurors for specific assessments (rather than yes or no responses to the POE question), see infra Section II.C.5, an added problem here is that jurors may be strategic in their attempts not to be dismissed as outliers. The discussion in this Section sets aside the Jury Theorem's insight that multiple judgments in sync with one another, are better than one. Put slightly differently, although the Jury Theorem itself might be the reason why we abide by majorities, there is no reason to throw out the information provided by the putative minority, so long as the question is neither binary nor one that commands an absolute majority for a single position (but rather is the kind of question considered here, where we really want a point estimate).
61. There seems to be little relationship between the size and decision rule of a state's juries and the degree to which the product rule is suppressed. Thus, New Hampshire requires a unanimous verdict from a twelve-person jury, but its sample jury instructions are rather ambiguous regarding the product rule: "The plaintiff claims: [State essential elements of the claim, making reference to time, place and circumstances] . . . These are the issues which are to be determined by you based on the facts as you find them to be and by applying the law as the court instructs you." N.H. CIV. JURY INSTRUCTIONS § 1.1 (1999). Michigan permits a verdict from five out of six jurors, but the product rule is suppressed in the sample jury instructions: "The plaintiff has the burden of proof on each of the following propositions: a. that the plaintiff [was injured / sustained damage]; b. that the defendant was negligent in one or more of the ways claimed by the plaintiff, as stated to you in these instructions; c. that the negligence of the defendant was a proximate cause of the [injuries / damages] to the plaintiff." MICH. STD. CIV. JURY INSTRUCTIONS 16.02 (1998).
62. There seems to be little relationship between the size and decision rule of a state's juries and the degree to which the product rule is suppressed. Thus, New Hampshire requires a unanimous verdict from a twelve-person jury, but its sample jury instructions are rather ambiguous regarding the product rule: "The plaintiff claims: [State essential elements of the claim, making reference to time, place and circumstances] . . . These are the issues which are to be determined by you based on the facts as you find them to be and by applying the law as the court instructs you." N.H. CIV. JURY INSTRUCTIONS § 1.1 (1999). Michigan permits a verdict from five out of six jurors, but the product rule is suppressed in the sample jury instructions: "The plaintiff has the burden of proof on each of the following propositions: a. that the plaintiff [was injured / sustained damage]; b. that the defendant was negligent in one or more of the ways claimed by the plaintiff, as stated to you in these instructions; c. that the negligence of the defendant was a proximate cause of the [injuries / damages] to the plaintiff." MICH. STD. CIV. JURY INSTRUCTIONS 16.02 (1998).
63. Similarly, if we had imagined agreement on .25, then (.75)(.75)(.75)=.422.
64. See supra note 11, where D, M, and W are given concrete form.
65. See Levmore, supra 12.
66. See Saul Levmore, More Than Mere Majorities, 2000 UTAH L. REV. 759 (forthcoming 2001) (manuscript at 13-16, on file with author).
67. Deliberation might also explain a supermajority rule quite generally, but then aggregation considerations are needed to understand the math-law divide.
68. Unfortunately, it is difficult to quantify this conjecture. In a large fraction of jury-verdict cases, reasonable people might disagree as to whether the jury had been asked one or multiple independent questions. There is difficulty in assessing whether a jury deliberated and voted on multiple requirements (or a single one) and there is also difficulty in assessing whether these multiple questions would (or should) have been regarded as independent. A random sample of jury verdicts reported in Jury Verdicts Weekly (Jan.-Mar. 1996), for example, suggests that, in about 30% of cases, jurors must decide on two or more independent, contested elements. In another 20% of the cases, it is clear that jurors are only asked to decide one issue, either because one or more issues are stipulated or not seriously contested or because the case involved but one issue. But in the remaining 50% of the sample cases, it is not clear whether the jury is deciding one issue or more. These cases ostensibly involve multiple elements, but often they are interdependent, as when multiple issues depend on the credibility of a single witness.
69. The blending of views into a single number is a useful reminder of the sort of process explored here. If a supermajority agrees on liability but the jurors then discovered, for example, that their damage assessments differ and range from one hundred thousand dollars to one million dollars, I think we would be startled to hear that they could not come to agree on a "unanimous" verdict if required to do so. And it would seem unlikely that our best guess as to their compromise or unanimous verdict would be one hundred thousand dollars. We expect verdicts to reflect the mean or median voter, more or less - and for strategic behavior reasons we are unlikely to wish it were otherwise - and that is why supermajority verdicts (especially) might not require much in the way of application of the product rule.
70. See supra Section I.B.5; infra Section II.C.5.
71. Note that I am not claiming that this strategic behavior leads to perverse results, by which I mean results that are contrary to what the majority itself prefers. For some development of this theory, see Saul Levmore, Voting with Intensity, 53 STAN. L. REV. 111, 149-58 (2000), where there is a claim that most legal and political systems prefer schemes that do not lend themselves to strategic behavior that can lead to perverse results - which is to say ex post "dissatisfied majorities." For example, if we allowed people to buy and sell votes, we might easily find ourselves with a winning candidate that a majority did not wish for (even in a two candidate election) and that even most intense voters did not prefer. This winner may have emerged because voters misestimated the likely vote or the likely price of votes. In contrast, if half a jury assesses negligence (and causation, to make the example quicker) at .6 and half at .9, we know that the wisdom of the group favors liability, even with the product rule applied. But some of the .6 assessors may see that when they apply the product rule to their own assessments, the defendant is free of liability. Fearful that other voters will come up with higher numbers, they might respond with 0 or .1 when polled. But at least they will be pleased if there is no liability.
72. I do not discuss deliberation here, but it is hard to see why we should prefer to take these votes without or prior to deliberation. Among other things, deliberation can serve to bring out "expert" knowledge and assessments which (even) the Jury Theorem bows to.
73. In an important sense, this argument is a close relative of one considered in the matter of "issue" versus "outcome" voting on judicial panels. See Lewis A. Kornhauser & Lawrence G. Sager, The One and the Many: Adjudication in Collegial Courts, 81 CAL. L. REV. 1, 55-56 (1993).
74. Unless the problem is that a juror may think that the deterrence or expressive function of law is too far in one direction or the other. In that case, a juror will be extreme and little influenced by the facts of the particular case.
75. The plan gives up on the Condorcet Jury Theorem, in a manner of speaking.
76. If I were not trying to set the Jury Theorem aside, I might say that with numerous jurors (perhaps twelve), we ought to be satisfied with asking whether their assessments exceeded .6 or even some lower assessment.
77. One reason it is hard to accept the idea that strategic voting may be against self-interest in some settings, is that we do not experience these settings in everyday life. Thus, in law schools, law firms, and congressional committees, voting is often about matters that relate to one's preferences - rather than to something that has a "right" answer (and regarding which we are unlikely to be expert). But if the Jury Theorem is useful in some domain, and if actual jury decisions as deployed by courts are included in this domain, then strategic behavior "should" be less of an issue than is normally thought.
78. Or at least so they might think. In fact, it might be hard to choose between the supermajority requirement and the single judge.
79. In American jurisdictions we can look to see whether judges acting alone implicitly apply the product rule where there are multiple requirements. In most non-American jurisdictions judges generally operate without juries - but then sometimes in panels - so that comparisons are likely to be especially interesting. But I should warn the reader that I am not holding back any striking evidence in favor of the broad application of the thesis advanced here. I know of no jurisdiction that explicitly applies the product rule.
80. There would also be opportunity to see a subtle effect when panel decisions were unanimous. Thus, if a three-judge panel is unanimous in finding two elements of liability, we might anticipate more subtle suppression of the product rule than if the panel had been divided.
81. See supra text accompanying note 26.
82. Nor is this symmetrical. The judge who "should" assess at .4 thinks that the requirement is less likely than not to be present. The judge will find against liability - and if the judge is overconfident and subsequently revises the estimate to .1, the outcome will be the same.
83. Indeed, if a comparative inquiry suggested that European or Japanese judges, operating without juries, suppressed the product rule in a manner different from their American counterparts, we might connect this observation to the norm of shorter and much less expensive trials.
84. See Evan H. Caminker, Sincere and Strategic Voting Norms on Multimember Courts, 97 MICH. L. REV. 2297 (1999); Maxwell L. Stearns, Should Justices Ever Switch Votes?: Miller v. Albright in Social Choice Perspective, 7 SUP. CT. ECON. REV. 87 (1999).
85. See Evan H. Caminker, Sincere and Strategic Voting Norms on Multimember Courts, 97 MICH. L. REV. 2297 (1999); Maxwell L. Stearns, Should Justices Ever Switch Votes?: Miller v. Albright in Social Choice Perspective, 7 SUP. CT. ECON. REV. 87 (1999).
86. See articles cited supra note 63.
87. Although we could presumably ask whether the judge's confidence exceeded some level or not. See supra Section II.C.5.
88. The same might be true with strategic voting if judges internalize the product rule.
89. Imagine, for example, that we need two issues decided for plaintiff on appeal in order to uphold a finding of liability against the defendant. If we denote a decision on an issue for plaintiff with a "1" and a decision against plaintiff with a "0," then a judge working alone whose assessment is (0,1) or (1,0) should decide against plaintiff, while one who finds on both issues for plaintiff, denoted as (1,1), will find for plaintiff. Imagine now that Panel A consists of three judges whose assessments are (0,1), (1,0), and (1,1), and that Panel B in a different case has assessments of (1,1), (1,1), and (0,0). Panel A's issue voting yields a win for plaintiff, but two of the three judges would with outcome voting decide against plaintiff. Panel B decides for plaintiff by a 2-1 vote either way. With numerous panelists, issue voting seems superior. There are, after all, two affirmative (and, by hypothesis, independent) assessments for each issue on the two panels. But on a small panel the argument for outcome voting is that we may mimic what the product rule would have done with precisely recorded assessments. Panel B's outcome demonstrates, of course, that outcome voting is not a perfect substitute for precise assessments plus the product rule.
90. If we set aside the aggregation and product rule issues discussed here, a decent argument for outcome voting is that it removes the temptation to vote strategically. The more we ask for outcomes, the less room there is for strategic voting. My concern in this Article is not so much with issue and outcome voting on their own but rather on explanations for the suppression (or recognition) of the product rule. If one kind of voting substitutes for the product rule, and there is reason not to apply the product rule directly, then there is a good argument for that voting procedure. Vote trading might be defended if we thought judges felt most intensely when they were also most expert or even most confident. On the other hand, judges might recognize subject matter expertise in their fellow judges, and defer accordingly. It seems more likely that trading would elevate judges' preferences, which in turn threatens to diminish the (Jury Theorem style) advantage of using more than one judge - offset, however, by the increased chance of bowing to real judicial expertise.