Doing jury duty got me thinking about hung juries and mistrials. In the case I served on, the defense seemed to aim for a “hung jury”. In California criminal cases, all 12 jurors must agree on a verdict. If they don’t, it’s a mistrial.

I build software systems for a living. In that line of work, we think about what happens at the “edge cases”. What are the scenarios that cause a system to break. Even though the court system is run by people, not computers, the same kind of analysis still applies.

So what does edge case analysis have to do with criminal justice? Well, because of the unanimity requirement, any single juror has the power to cause a hung jury. Obviously this is an intentional feature of the system. But it provides a wedge that could be used to interfere with the system.

## Threat Model

What if some fraction of the population believed the criminal justice system was just bad, and that it should be shut down? If those people were convinced to cause a hung jury whenever called to serve, how many cases would result in mistrial?

Assume that,

- those people represent
**s%**of the population, - they’re evenly distributed throughout the population, and
- all 12 jurors are drawn randomly from that same population.

Call someone a “saboteur” if they’re in that **s%** who just want to mess things up. Then the probability of a mistrial is just the probability that 1 or more of the jurors are saboteurs.

In math,

There’s a mistrial if 1, or 2, or 3, … of the jurors are “saboteurs”. Because the only other option is that 0 of the jurors are saboteurs, you can restate this equation as,

In other words, 100% of the time, except when 0 saboteurs are on the jury. And what are the chances that 0 saboteurs are on the jury?

It’s the chance that the first juror selected is not a saboteur (**1-s**), and then that the second, third, fourth, etc… are also not saboteurs (**1-s** for each of those).

So the final probability is,

Here’s what that looks like, as **s** goes from 0% to 100%.

You can see that at 40% of the population, all cases would result in mistrial. So you can chop the graph at that point, to make things clearer.

Each block on the horizontal axis represents a 1% change in the saboteur rate. Reading numbers off the graph, it works out cleanly that it would only take,

- 1% saboteur rate to hang 10% of trials,
- 2% saboteur rate to hang 20% of trials,
- 3% saboteur rate to hang 30% of trials,
- 4% saboteur rate to hang 40% of trials, and
- 5-6% saboteur rate to hang 50% of trials.

Mistrials on this scale could easily clog the system. The case I was on took a year to come to trial, so it’s already heavily loaded. If half of trials resulted in mistrial, then the justice system would have to double in capacity just to process cases at the same rate it currently does.

## Don’t Do This at Home

Hopefully this doesn’t happen. I sincerely doubt it would be good for society. My purpose in publishing this analysis is to either 1) get people thinking about the problem and solutions, or 2) have someone find a flaw and show how there’s no problem after all.

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