The Constitution assumed a legal system modeled after English Common Law; it would have to be much, much, longer if it spelled out in detail all the details thereof, rather than assuming them. If a legal system requires a unanimous "guity" vote to convict and requires more than one "not guilty" for an outright acquittal, there will be an unavoidable possibility of some outcome other than conviction or acquittal. I don't know much about 18th Century Common Law practices, but I believe judges were more insistent than today that jurors deliberate until they reach a unanimous verdict. That having been said, for the Double Jeopardy provisions to really mean anything, the state's ability to declare a mistrial which would permit a retrial must be severely limited. Indeed, I would suggest that--since issues of "reasonableness" aften reset on factual matters, and since defendants have the right to have factual matters determined by jury, a defendant should have the right to have the jury at the retrial be informed of the circumstances surrounding the mistrial, and instructed that they may only convict the defendant on charges where it would appear the previous jury would not have acquitted him. In many cases, the defense would not benefit from such instruction (a jury may not look kindly on a defendant who seems to be fishing for a technicality), but in cases where such presentation and instruction would tip the jury in its favor, it should be allowed to raise it.
What ever happened to the old - think Perry Mason - way of taking verdicts one count at a time?
I.E. On the first count of .... how do you find?
On the second count of .... how do you find?
etc.......