I could have also called this post "The Math of Jury Duty," but it would have been hard to find two things that more Americans hate more in a single title. Readers who have responded to a jury summons will know how tedious the process can be. If you take the trouble to show up to the courthouse, you could spend the entire day waiting around only to be sent home. Many people would rather find ways to avoid showing up in the first place. This leads to a problem--how many summons does the court need to send?

On the surface the problem seems relatively straightforward. Judges submit their cases weeks in advance, so the district clerk's office knows what's coming. If a case needs twelve jurors, and each side can strike up to six people during jury selection, then a total of twenty-four potential jurors are needed.

Unfortunately, the math isn't quite that easy. Some people who receive a summons are excused for hardship, as in the case of a single parent with young children at home. Others don't qualify because of criminal records. An individual receiving a summons has the option of postponing the date of service. A summons may be mailed to an incorrect address. In Harris County, the number of returned summonses runs into the double digits — Houstonians tend to move a lot in the three years since their last call to service. And, in spite of the fact it's a crime, many people simply ignore a summons when it arrives. The numbers add up. Roughly forty percent of people who are sent a summons don't respond to it.

This leads to a need for "overbooking," as airlines do with tickets. In fact, according to the post from the University of Houston's Andrew Boyd, Harris County has to send out three to four times as many summons as they need jurors. (Boyd's explanation is also available in an audio version.) But the court has the inverse problem of the airlines, since they need to have a minimum number of people whereas the airlines want the maximum number of people.

Further complicating the court's process is the fact that they cannot compensate people for showing up but not serving in the same way that airlines pay passengers to wait for the next flight. Jurors that respond in Harris County are paid $6 for their first day of service, and $28 thereafter. As commissioner Jerry Eversole said, "At $28 you can pay your parking and have lunch, and that's pretty much what the jury day consists of."

So how do the courts get the people they need?

As a rule, courts haven't reached that level of sophistication [NB: of airline overbooking], but many employ some level of statistical analysis. In Harris County, for example, it's known that people respond to jury summonses at different rates at different times of the year — something the district clerk's office takes into account when issuing summonses. And there's another big cause of uncertainty: settling a case on the courthouse steps. If last minute negotiations lead to a settlement on the day of the trial, there's no need for any jurors in that court. Even this type of uncertainty can be accounted for in mathematical models, but that's uncommon.

So the next time you find yourself sitting in the jury assembly room waiting for your number to be called, remember that the courts face a challenging engineering problem with a lot of uncertainty. And don't forget to bring a good book.