Can a judge break the law by issuing a ruling?

Quite true. You don’t even have to say you don’t think the government proved its case; you have an near-absolute privilege with regard to deliberations.

The legality of both are the same, they only differ in the degree of difficulty in proving a case.

Maybe, then (and this is a non-lawyer’s wild guess), because the prospect of a prosecutor charging jurors with a crime (i.e., nullification) because they didn’t reach the verdict he or she wanted would absolutely destroy the foundations of our criminal justice system?

“Illegal” has more than one meaning. It doesn’t just mean a crime. It can also mean a breach of the rules of procedure that legally justify the Judge to take action.

For instance, in Canada it is illegal for a lawyer to argue to a jury that it can nullify. However, if a lawyer ignored the law and urged the jury to nullify, the lawyer wouldn’t be charged with an offence. The judge would in all likelihood declare a mistrial and the process starts all over again. Telling the jury to nullify is illegal and can have a legal consequence, like a mistrial.

Similarly, if while the trial is in process, a juror sends a note to the judge that another juror has declared he thinks the law is bad and won’t convict, no matter what, that too could have legal consequences. The judge would likely remind all if the jurors if their oath to apply the law, and if the juror persists in saying he will nullify, the judge may kick him off the jury or even declare a mistrial. The attempt to nullify is illegal and can have legal consequences.

But, once the jury has given its verdict, that is final. Under Canadian law, no-one, not even the judge, can inquire into deliberations, and a juror cannot be punished (absent an extreme case if obstruction by a juror, such as taking a bribe). Nullification is not a basis to set aside a verdict, nor to inquire into deliberations.

So I would say that nullification is illegal and attempts at nullification can have legal consequences if caught at an appropriate stage, but can’t be the basis to set aside a verdict or to punish the jurors.

How about this since we’re now hijacked to Nullificationland and bearing in mind that a acquittal is not always absolute like if there is jury-tampering or you kill your roommate in Italy.
Defendant is acquitted and all twelve jurors immediately announce that they admit the person did it but nullification power to the people and victory for marrying your gay partner while smoking marijuana. USA! USA!

Can a mistrial be declared because they admitted to jury nullification?

Amanda Knox wasn’t acquitted. Her conviction was overturned on appeal (though one with a slightly different procedure than ours) and subsequently reinstated by a higher court.

When a Judge issues a ruling and parties wish to appeal for an alleged incorrect application of law, it is said the Judge “Abused his/her Discretion”, not broke the law.

Little post-post mortem here, but wasn’t there a juror in the OJ trial who her/himself announced after the the verdict that she wasn’t going lo listen to no evidence, no how, and that OJ had to go free?

Nullification post-facto?
ETA: NB my three Latinisms in this post, to suit the occasion. Or four, or five, if you count the posts.