That's an interesting thought. Imagine if you needed the same jury of twelve people who were present at the trial, to all push a button simultaneously in order to mete out whatever punishment they had decided was fair. (Anyone other than those twelve might be acting on bias or stereotype due to a lack of information about the case, after all.)

In fact, to go a bit further with this—imaging that ongoing punishment required getting this group of people back together at regular intervals and getting them all to push the button again. (For example, meting out a lifetime prison sentence one year, or one month, at a time.) It isn't meant to cause re-evaluation due to the meeting being a hassle, so maybe they could just do this online—but it should cause re-evaluation of whether each juror still feels as strongly about the person's sentence now as they did before.

One could even imagine a situation where any capitol punishment would be measured in QALYs, and then the jury each have to do that many man-years of confirming in order to apply the punishment. (Thus, applying a sentence of death to an eighteen-year-old would require decades of total work, or years per juror.) That seems about the right weight upon one's conscience. It would also mean you'd probably never be able to do jury duty more than once in your life.