A jury is supposed to rely only on the evidence presented at trial and ruled admissible, no matter how obvious or compelling other evidence might seem. The only exceptions are for fundamental matters of common sense, like the fact that the sun does not shine brightly at night or that gravity usually causes things to fall down rather up or sideways.
Any kind of external research by a juror is right out - that's like bringing in additional testimony after the trial has taken place, and undermines a defendant's right to cross-examine and dispute the evidence. If an attorney's omission of some information seems like a glaring oversight, that's not the jury's problem. Maybe the client has an incompetent attorney (lots of cases involving that) or maybe the two sides agreed to a partial deal before the trial which included staying off that topic...there's no 'right to know' and juror's are not allowed to introduce any new information to others in the jury room. Any personal background knowledge which gives a juror extra insight, he is supposed to keep to himself. Usually that is considered juror misconduct.
Now here you're only looking at putting pieces of evidence into a matrix and scoring them, which seems totally neutral - but unless it's a very simple case and you can fit all the evidentiary arguments on there verbatim, then the losing side would probably claim the presentation of evidence in such simplistic fashion gave rise to bias.
A recent appeal of a murder conviction examined the use of software by a juror in depth. Although the judge concluded it was acceptable, it was only because the juror used the software alone and it simply served a note-taking function, rather than letting him manipulate or explore the paramaters in any novel way: http://scholar.google.com/scholar_case?case=1103407335837753... Scroll down to section B2 for the software use challenge.
I think it will be a long time before any kind of data-organizing tool will be allowed. I am a bit skeptical about allowing even the frame-by-frame video playback in the second case, because not all video codecs are created equal and it's possible that artifacts in the display of a video image might distort it enough to sway a person's mind about whether it resembled a defendant (cf http://en.wikipedia.org/wiki/Pareidolia). IANAL, mind.
Usually a judge will err on the side of caution if any technological innovations are proposed, since being reversed for not conducting the rial properly is bad for one's future career. Please note, IANAL and this is an amateur opinion.
I do think there are some judges who would like to use tools like this for their own analysis of a complex case, without a jury. Richard Posner springs to mind, he's very much into Bayesian reasoning and formal methods.
Software aside, wouldn't the output of the software simply stand on its own as particularly insightful reasoning? What's to prevent a juror from using it privately and then mentioning the output to the rest of the jurors, who, if rational, would be hard pressed not to agree.
I think that would be OK for an individual, no different from using a notebook to organize one's thoughts. You'd still have the benefit of the systematic circumstance/condition comparison, although you'd lose the benefit of the voting aspects.
California criminal jury instructions say jurors can take notes, but cautions that they are only for individual use.
