We are all talking about the time after the evidence period is over. I would like to point out that the same problem can be found when deciding what evidence is admissible during an appeal. There, again, we have the problem that the loosing party can introduce evidence that would change the outcome of the appeal that all jurors from the lower instance could not possibly have been aware of. This is even more problematic than when just looking at a single round since this allows a bad faith actor to trick the opposing party into spending unnecessary money on fees for the appeal. Some way has to be found to prevent this which means that there must be some requirements for evidence to be admissible.
Disabling evidence is an option that I would not recommend. First, it does not solve the problem for appeals and second it prevents discussions on issues of law. I consider the latter to be quite important since I believe that jurors should have some time to discuss issues of law once the evidence period is over and they know all the facts.
As a base rule therefore I recommend that evidence regarding matters of fact should be inadmissible after the evidence period in the first round of appeals ends.
Now let’s talk about the exceptions.
This point requires some discussion in my opinion. It states that a fair ruling requires that the court knows what happened. And I agree with that statement almost entirely. However, we must acknowledge that the parties naturally know most about the case and can therefore provide (or withhold) most of the relevant evidence and direct the attention of the court to certain aspects of the case. This power of the parties, in my opinion, needs to be sanctioned when they misuse it. With my general rule stated above I presume that the power is misused once the evidence period is over and a party still submits facts. The question is, when this presumption can be proven wrong.
I suggest that this presumption is wrong when the parties can show that it was impossible for them to submit the evidence before the end of the evidence period. Knowing the facts is a prerequisite for justice and giving them to the court in a timely manner is a duty of the parties.
Jurors who inform themselves from public sources should then decide whether they share their sources with the jurors - if they perform research on an aspect that was not yet thoroughly discussed - or if they consider that the research is such an obvious step in evaluating the facts that all other jurors will consult them as well. Jurors should not be incentivised to search for information that is not easily available if the parties do not point towards it since they cannot be sure that the other jurors will find them as well and because they know that the information will be deemed inadmissible if it is introduced by the parties later on.
By the way, jurors should, as marijn pointed out, rule on the state of the world at the time the evidence period ended. So changes that happended after that may not be considered.
My approach comes close to 3). Yet, I want to allow evidence that was not held back in bad faith. The difference between my concept and 3) eventually comes down to the question of who bears the risk of new evidence emerging. Is it a party who risks loosing a case it should have won just because a timer ran out? Or are it the jurors who already voted and who evaluated the evidence as good as they could and, without it being their fault, reached a wrong conclusion? 1) and 2) would shift the risk entirely to the parties. 3) and my proposal would shift it primarily to the jurors but seeks to strike a fair balance. I believe that my solution leaves a margin of appreciation towards the jurors when deciding what evidence they let in. Furthermore, that way the courts can develop some case law to cover all different scenarios.
This being said, I propose the following rule:
(1) Jurors shall disregard evidence on matters of fact that were submitted after the evidence period of the first round has ended.
(2) Submissions after that can be considered by the court if the submitting party can show that it was unable to submit the evidence in advance.
and - optionally
(3) Even when the conditions of paragraph 2 are met the court can reject an application if it would unfairly affect the outcome of the trial.