Naive, Biased, yet Bayesian: Can Juries Interpret Selectively ...

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272 The Journal of Law, Economics, & Organtzaflon, V12 N1 and defendant is [pS-cH/p,-pS-cT/{l-p)}. The first derivatives whose roots characterize a Nash equilibrium are {-{c/p) - ((a + H)*S)/(a + b + H + T) 2 + S/(a + b + H + T), c/(-l + P) + ((a + H)*S)/{a +b + H + T) 2 }. The roots of these derivatives have an explicit solution, given in Equation (4a), which we reproduce below. {H\ r} = {-a + P 2 {\ - p)S/c, -b + 0- pfpS/c) if H* > 0 and T* > 0 (4a) That this solution is unique can be seen by examining the matrix of second partial derivatives of the payoff vector. {{(-2*S'{b + T))/(a +b + H + T) 3 , (S*(a -b + H - T))/(a +b + H + T) 3 }, [(S*(-a + b- H + T))/{a + b + H + T)\ (-2*(a + H)*S)/(a +b + H + T) 3 }}. The determinant of this matrix is equal to S 2 /(a +b + H + T) A . For H > 0, T > 0, it is seen that the principal minors alternate in sign, implying that the matrix is negative definite, which guarantees that the solution given in (4a) is unique. When the constraints, H > 0 or T > 0, are binding, we compute the Nash equilibria by first computing the reaction functions implied by the derivatives of the payoff vector: {-a - b - T + (c*p*S*(b + T)) l ' 2 /c, -a-b-H The reaction function of the nonconstrained litigant is positively sloped in the region of interest, so for p's near zero, where the plaintiff would like to produce negative amounts of evidence (sell evidence to the experts) but must produce more evidence (zero), the defendant produces more than he would like in an unconstrained equilibrium. Substituting the constraints into the appropriate reaction functions leads to the constrained equilibrium represented by Equations (4b) and (4c), which we reproduce below: {//**, 7"} = {-a- b + (\/c)(-ac(\ -p)) l/2 ,0} \fT*
Can Juries Interpret Selectively Produced Evidence? 273 Arnold, Morris S. 1980. "A Historical Inquiry into the Right to Trial by Jury in Complex Civil Litigation," 128 University of Pennsylvania Law Review 829—48. Ashenfelter, Orley, and D. E, Bloom. 1984. "Models of Arbitrator Behavior," 74 American Economic Review 111-24. Bcrsoff, Donald N., and David J. Glass. 1995. The Not So Weisman: The Supreme Court's Continuing Misuse of Social Science Research," 2 University of Chicago Law School Roundtable 279-300. Camerer, Colin. 1987. "Do Biases in Probability Judgment Matter in Markets? Experimental Evidence," 77 American Economic Review 981-97. 1995. 'Individual Decision Making," in John Kagel and Alvin Roth, eds., Handbook of Experimental Economics. Princeton, N J.: Princeton University Press. Campbell, James S. 1988. "The Current Understanding of the Seventh Amendment," 66 Washington University Law Quarterly 63-70. , and Nicholas LePoidevin. 1980. "Complex Cases and Jury Trials: A Reply to Professor Arnold," 128 University of Pennsylvania Law Review 965-85. Cecil, Joe S., Valerie P. Hans, and Elizabeth C. Wiggins. 1991. "Citizen Comprehension of Difficult Issues: Lessons from Civil Jury Trials," 40 American University Law Review 727-74. , and Thomas E. Willging. 1994a. "Court-Appointed Experts," in Federal Judicial Center, Reference Manual on Scientific Evidence. Colorado Springs, Col.: Shepard's McGraw Hill. , and 1994b. "Accepting Daubert's Invitation: Defining a Role for Court-Appointed Experts in Assessing Scientific Validity," 43 Emory Law Journal 995—1070. Claremont, Kevin M., and Theodore Eisenberg. 1992. "Trial by Jury or Judge: Transcending Empiricism," 77 Cornell Law Review 1124-77. Cooler, Robert D., and Daniel L. Rubinfeld. 1989. "An Economic Analysis of Legal Disputes and their Resolution," 27 Journal of Economic Literature 1067-97. , and 1994. "An Economic Model of Legal Discovery," 23 Journal of Legal Studies 435-64. Cornell, Bradford. 1990. "The Incentive to Sue: An Option Pricing Approach," 19 Journal of Legal Studies 173-89. Coulam, Robert, and Stephen Henberg. 1986. "The Use of Court-Appointed Statistical Experts: A Case Study," in M. H. DeGroot, S. E. Fienberg, and J. B. Kadane, eds., Statistics and the Law. New York: Wiley. Davis, Michael L. 1994. "The Value of Truth and Optimal Standard of Proof in Legal Disputes," 10 Journal of Law, Economics,
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