"Allowed" is not an applicable concept, since the few laws regulating juror conduct pertain to corrupt behavior (such as bribery). Instead, there are standards for juror conduct that the legal profession wishes to be adhered to, and the only way that impression is conveyed to jurors is through the judge's instructions (or lack therein). It is held in Sparf and Hansen v. United States 156 U.S. 51 that
In the courts of the United States, it is the duty of the jury, in
criminal cases, to receive the law from the court, and to apply it as
given by the court, subject to the condition that, by a general
verdict, a jury of necessity determines both law and fact as
compounded in the issue submitted to them in the particular case.
In criminal cases, it is competent for the court to instruct the jury
as to the legal presumptions arising from a given state of facts, but
it may not, by a peremptory instruction, require the jury to find the
accused guilty of the offense charged, nor of any offense less than
One of the "technical" rights of a jury is the right to judge the law itself (jury nullification). This arises in part from the Zenger trial and similar colonial events, and (in terms of legal precedent) from a famous instruction by Jay in Georgia v. Brailsford, 3 U.S. 1:
It may not be amiss, here, Gentlemen, to remind you of the good old
rule, that on questions of fact, it is the province of the jury, on
questions of law, it is the province of the court to decide. But it
must be observed that by the same law, which recognizes this
reasonable distribution of jurisdiction, you have nevertheless a right
to take upon yourselves to judge of both, and to determine the law as
well as the fact in controversy. On this, and on every other occasion,
however, we have no doubt, you will pay that respect, which is due to
the opinion of the court: For, as on the one hand, it is presumed,
that juries are the best judges of facts; it is, on the other hand,
presumable, that the court are the best judges of the law. But still
both objects are lawfully, within your power of decision.
Sparf v. US however finds that a judge is under no obligation to inform jurors of that right, and jury instructions say things like "you must apply the law as I give it to you, even if you disagree with the law". For examples, instruction 101 in the California criminal instructions manual says that trials are
conducted in open court with the parties presenting evidence and the
judge deciding the law that applies to the case. It is unfair to the
parties if you receive additional information from any other source
because that information may be unreliable or irrelevant and the
parties will not have had the opportunity to examine and respond to
it. Your verdict must be based only on the evidence presented during
trial in this court and the law as I provide it to you.
This is not an enforceable law, for instance if a juror (esp. an attorney) argues one way based on his version of the law, that is not a punishable offense, nor is it a punishable offense if a juror (who is an engineer) argues that some expert testimony on an engineering matter is factually wrong. Jurors are not supposed to do either thing, but there are no legal consequences if they do.
Since the legal ideal is that a jury will evaluate the (allowed) testimony in court and applies the law as given by the judge, and attorneys have an ethical obligation to uphold the law, they thus have an ethical obligation to not restate the law and especially to not do so under the guise of being an attorney (who has expert knowledge of the law). This is basically an unenforceable principle. There was an instruction in California saying that:
should . . . any juror refuse to deliberate or express an
intention to disregard the law or to decide the case based on penalty
or punishment, or any other improper basis, it is the obligation of
the other jurors to immediately advise the Court of the situation
but People v. Engelman 28 cal 4th 436 nixed that instruction. That case says that
jurors have no right to refuse to deliberate or to disregard the law
in reaching their decision
Directing the jury immediately before deliberations begin that jurors
are expected to police the reasoning and arguments of their fellow
jurors during deliberations, and immediately advise the court if it
appears that a fellow juror is deciding the case upon an "improper
basis," may curtail or distort deliberations.
This does not mean that in the rare instance that a lawyer is on a jury, he must suppress his conclusions, even when they are professionally informed. This article recounts a lawyer's experience on a jury and identifies a point of law (and how the issue was handled). In that case, the question is what to make of a statement that something is "not at issue". The non-;awyers interpreted that to mean "we aren’t supposed to award her anything for back and neck injuries". The lawyer said:
I was pretty sure this was wrong. While it was true that the lawyers
had said the back and neck injuries were “not at issue,” that was a
phrase that I could recall uttering in court, too. When I said it, I
meant that both sides agreed on a certain fact or point of law. I did
not mean that the fact or point of law was not material to the case.
No other juror interpreted the lawyers’ statements my way, and when we
checked, we found that the jury instructions were silent on the issue.
So, we wrote the judge a question. Turns out, “the lawyer” was right.
The judge instructed us to consider any injury from the collision,
whether it was an injury to the plaintiff’s back, to her neck, to her
shoulder, or elsewhere. The lesson for attorneys: explain to the jury
exactly what you mean. Don’t assume they understand your shorthand
terms, like “not at issue.”
In other words, the judge still determines what the law is, though in this case it looks like it took the expert knowledge of an attorney to figure out that the jury needed to ask the judge what "not at issue" means.