Here's some language from a 9th Circuit case for you all to chew on in the other thread.
United States v. Symington, 195 F.3d 1080 (9th Cir. 1999)
 A trial judge faces special challenges when attempting to determine whether a problem between or among deliberating jurors stems from disagreement on the merits of the case.  
“[A] court may not delve deeply into a juror's motivations because it may not intrude on the secrecy of the jury's deliberations.”  Brown, 823 F.2d at 596;  see Thomas, 116 F.3d at 619.   There are important reasons why a trial judge must not compromise the secrecy of jury deliberations.   First, if trial judges were permitted to inquire into the reasoning behind jurors' views of pending cases, “it would invite trial judges to second-guess and influence the work of the jury.”  Thomas, 116 F.3d at 620.   Second, a trial judge's examination of juror deliberations risks exposing those deliberations to public scrutiny.   Such exposure, in turn, would jeopardize the integrity of the deliberative process.   See id. at 618-19.   As Justice Cardozo put it, “Freedom of debate might be stifled and independence of thought checked if jurors were made to feel that their arguments and ballots were to be freely published to the world.”  Clark v. United States, 289 U.S. 1, 13, 53 S.Ct. 465, 77 L.Ed. 993 (1933);  see Frank A. Bacelli, Note, United States v. Thomas:  When the Preservation of Juror Secrecy During Deliberations Outweighs the Ability to Dismiss a Juror for Nullification, 48 Cath. U.L.Rev. 125, 153 n. 215 (1998) (“Commentators long have feared that the disclosure of deliberations to the general public could affect a juror's decisionmaking process during trial and could potentially undermine the public's confidence in the jury system.”
;   Benjamin S. DuVal, Jr., The Occasions of Secrecy, 47 U. Pitt. L.Rev. 579, 646 (1986) (“The secrecy of the jury room, like that of the Supreme Court conference, is designed to promote the free and candid interchange of views.”
;   Note, Public Disclosures of Jury Deliberations, 96 HARV. L. REV. 886, 889 (1983) ( “Juror privacy is a prerequisite of free debate, without which the decisionmaking process would be crippled.”
.4
In refraining from exposing the content of jury deliberations, however, a trial judge may not be able to determine conclusively whether or not a juror's alleged inability or unwillingness to deliberate is simply a reflection of the juror's opinion on the merits of the case, an opinion that may be at odds with those of her fellow jurors.   Thus, in the rare case where a request for juror dismissal focuses on the quality of the juror's thoughts about the case and her ability to communicate those thoughts to the rest of the jury, “the court will likely prove unable to establish conclusively the reasons underlying” the request for dismissal.  Brown, 823 F.2d at 596.  
In such cases a trial court lacks the investigative power that, in the typical case, puts it in the “best position to evaluate the jury's ability to deliberate.”  Beard, 161 F.3d at 1194.
The Second and D.C. Circuits have recognized this dilemma.   See Thomas, 116 F.3d at 620-23;  Brown, 823 F.2d at 595-97.   Those cases both involved allegations that a juror was unwilling or unable to apply the law as instructed by the judge.   In Brown a juror informed the judge that he was “unable to discharge [his] duties as a member of th[e] jury.”   823 F.2d at 594.   In Thomas, the jury complained that one juror had a “predisposed disposition” and that he was unwilling to decide the case under the law as instructed by the judge.  116 F.3d at 611.   The Second and D.C. Circuits recognized that
the trial judges in those cases could not have plumbed the depths of the problem without delving into the juror's views on the merits of the case.   Thus, those courts held that “if the record evidence discloses any possibility that the request to discharge stems from the juror's view of the sufficiency of the government's evidence, the court must deny the request.”  Brown, 823 F.2d at 596;  Thomas, 116 F.3d at 621-22 (quoting Brown 
.
 We hold that if the record evidence discloses
any reasonable possibility that the impetus for a juror's dismissal stems from the juror's views on the merits of the case,
the court must not dismiss the juror.5  Under such circumstances, the trial judge has only two options:  send the jury back to continue deliberating or declare a mistrial.   See Brown, 823 F.2d at 596.   This rule is attentive to the twin imperatives of preserving jury secrecy and safeguarding the defendant's right to a unanimous verdict from an impartial jury.   We are confident that “[g]iven the necessary limitations on a court's investigatory authority in cases involving a juror's alleged refusal [or inability] to follow the law, a lower evidentiary standard could lead to the removal of jurors on the basis of their view of the sufficiency of the prosecution's evidence.”  Thomas, 116 F.3d at 622.6
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