canada
Jurors have an obligation to not consider evidence they have been instructed to disregard
Jurors are expressly instructed to not consider evidence that was not admitted in the trial. They must comply with this instruction. This is a legal obligation and they are presumed to follow it.
The principle of juror secrecy will almost always prevent evidence of non-compliance with the above obligation
Were a juror to not comply with this obligation, evidence of that non-compliance will never properly come to the court's awareness, unless the improper information came to the jury from outside.
The common law rule, applicable in Canada, is that evidence about what occurs among the jurors in the jury room is inadmissible. This is traceable back to a judgment of Lord Mansfield, Vaise v. Delaval (1785), 1 T.R. 11, 99 E.R. 944 (K.B.).
For example, evidence that a jury foreperson told other jurors of an accused's previous convictions (even though evidence about previous convictions would be almost always be inadmissible in the trial) was inadmissible as evidence of an improper verdict. See R. v. Pan; R. v. Sawyer, 2001 SCC 42, para. 56.
The rule is this (para. 77):
statements made, opinions expressed, arguments advanced and votes cast by members of a jury in the course of their deliberations are inadmissible in any legal proceedings. In particular, jurors may not testify about the effect of anything on their or other jurors’ minds, emotions or ultimate decision. On the other hand, the common law rule does not render inadmissible evidence of facts, statements or events extrinsic to the deliberation process, whether originating from a juror or from a third party, that may have tainted the verdict.
This category of "extrinsic" interference includes things such as: the fact that a prosecutor entered the jury room and erased the blackboard (R. v. Mercier et al. (1973), 12 C.C.C. (2d) (Qc. C.A.)); the fact of improper communications between a juror and one of the parties (R. v. Mehl, 2021 BCCA 264); etc. What matters is if the information or influence comes from "outside the jury."
If the information is in the juror's head, because of their own experiences, especially the experience of being in the very trial that they observed, the fact that they shared that information with other jurors and the effect it might have had on deliberations is inadmissible.
As just one example of the dividing line, the Supreme Court of Canada wrote (para. 62):
For example, if a juror shares with his fellow jurors his detailed familiarity with the location where the crime was alleged to have been committed, this may be viewed as an intrinsic matter protected by the secrecy rule. If the same juror, however, went on a visit to the site, took photographs and brought them back to the jury room to support his interpretation of the facts at issue, this may be extrinsic, outside information that falls outside the secrecy rule.
Comparison to nullification
For the same reason, jury nullification is seen as a de facto power of a jury, even though it is contrary to the law.
juries have a de facto power to disregard the law as stated to the jury by the judge. We cannot enter the jury room.
Some comparative law
The High Court of Australia, while agreeing that the general jury secrecy rule applies in Australia, said the rule does not operate to preserve the secrecy of criminal conduct ([2014] HCA 3). The evidence in question was a note from a juror that said they had been "physically coerced by a fellow juror to change [their] plea."
