# The mathematics of jury size: Statistical model shows several interesting properties of US jury configurations

##### March 26, 2012 By Chris Gorski

Could different jury sizes improve the quality of justice? The answers are not clear, but mathematicians are analyzing juries to identify potential improvements.

Nowhere in the U.S. Constitution does it say that juries in criminal cases must include 12 people, or that their decisions must be unanimous. In fact, some states use juries of different sizes.

One primary reason why today's juries tend to have 12 people is that the Welsh king Morgan of Gla-Morgan, who established trials in 725 A.D., decided upon the number, linking the judge and jury to Jesus and his Twelve Apostles.

The has ruled that smaller juries can be permitted. States such as Florida, Connecticut and others have used -- or considered -- smaller juries of six or nine people. In Louisiana, super-majority verdicts of nine jurors out of 12 are allowed.

However, in 1978 the Supreme Court ruled that a five-person jury is not allowed, after Georgia attempted to assign five-person juries to certain criminal trials.

To mathematicians and , this offers a clear division between acceptable and not acceptable, and therefore an opportunity for analysis.

"What seems to be apparent reading the literature on this is that the Supreme Court is making these decisions basically on an intuitive basis," said Jeff Suzuki, a mathematician at Brooklyn College in New York. "It's their sense of how big a jury should be to ensure proper ."

At a mathematics conference earlier this year, Suzuki presented research comparing the likelihood of conviction of a hypothetical defendant with the same likelihood of guilt but different jury conditions.

Building on a well-established line of research, which began with 18th-century French philosopher and mathematician Nicolas de Condorcet, of juries has continued over the years, beginning from Condorcet's idea that each juror has some probability of coming to the correct conclusion about the defendant's guilt or innocence.

Suzuki used three different probabilities to calculate the likely decision of a jury, including the probability that the defendant is actually guilty, the probability that a juror will make the correct decision if the defendant is guilty, and the probability that a juror will make the correct decision if the defendant is not guilty.

Suzuki's model suggests that smaller juries are more likely than larger juries to convict when the defendant appears less certain to be guilty. All the juries he modeled are very likely to convict when the evidence suggests that a defendant is almost certainly guilty. But for slightly less certain cases, differences become clear.

If it appears that there's an 80 percent likelihood that the defendant is guilty, then Suzuki's model suggests that less than 10 percent of the time a 12-person jury would unanimously vote to convict, but a 6-person jury would unanimously vote to convict over 25 percent of the time -- and a Louisiana-style jury that can convict with nine out of 12 votes would convict in roughly 60 percent of such trials.

Suzuki admits that the models may not be capturing the complete picture. Even if states that use fewer than 12 jurors had higher conviction rates than other states, that wouldn't mean smaller juries convict greater numbers of innocent defendants, he said.

One potential problem with translating this research to real world trials is that it leaves out the interaction between jurors, which Suzuki admitted is a problem.

"We don't have a good model for how jurors interact with each other," he said. "The real challenge is that the data doesn't really exist."

In addition to the issue of juror interaction, the [Suzuki’s] models leave out other factors important to finding the correct verdict, such as the possibility that testimony or evidence could deceive the jury, said Bruce Spencer, a professor of statistics at Northwestern University in Evanston, Ill., who did not work with Suzuki.

"If the evidence is very misleading, it's going to tend to mislead all of [the ]," said Spencer.

In a separate study, Spencer analyzed surveys completed by judges just before juries delivered their verdict and compared what the judges thought to the juries' decisions, finding that the verdicts agreed about 80 percent of the time. He found that in about one in every five trials in his study sample, the judge and the jury came to different conclusions.

Real data on the true guilt or innocence of a defendant on trial is simply not available. The jury's decision is only half the story of a verdict's accuracy. Many factors in jury decisions cannot be captured quantitatively.

"If you're coming up with a measure of the speed of light or a standard kilogram, you like to have some assessment of uncertainty," said Spencer. "I think it is difficult to assess the uncertainty of our estimates."

Although Spencer knows either the judge or jury must have been wrong in the 20 percent of cases in his study when the two disagreed, there was not enough information to know which was correct in a given case. Using statistical modeling, he found that overall the judges and juries were about equally accurate, but cautioned about drawing conclusions based on the limited number of cases in his study.

Suzuki is trying to figure out more about verdict accuracy with his research. He said that he can build estimates of false conviction rates by counting how many verdicts are later overturned. The estimates are imperfect, he said, especially given that new technology such as DNA testing was not available when some of the original verdicts were given.

But Suzuki feels that his research can at least examine some of the important details of jury trials. Making better models helps to draw general conclusions, despite the uniqueness of each trial.

"You can use probabilistic methods to model human behavior, provided that you understand what the statistics are and are not telling you," said Suzuki.

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##### Moebius
4.3 / 5 (3) Mar 26, 2012
The stats imply that a larger jury is more likely to come to a correct decision. This has implications for the supreme court. It implies what the record shows, they are less likely to come to a correct decision because there aren't enough people. 9 is too few to decide the fate of everyone, let alone a single defendant. Most decisions are 5-4 which by itself proves their decisions are borderline at best. Couple that with the fact they are political appointees and not appointed by their peers and we not only have the recipe for disaster, we have the finished product.
##### antialias_physorg
3.8 / 5 (4) Mar 26, 2012
This has implications for the supreme court.

I'm not sure it does:
The supreme court does not judge guilt or innocence - only whether something is constitutional or not. For such a case it always has the complete facts (i.e. it does not need to contend with people lying to protect themselves). The supreme court can and does decide on abstract problems.

As political appointees one can argue that the judges on the supreme court will use any leeway to judge in favor of their political persuasion. But such interpretations are not a case of making a 'right' or 'wrong' decision.
##### that_guy
not rated yet Mar 26, 2012
I commend the authors of the study and article for taking the time to register the fact that they necessarily have imperfect information, and that there is some for interpretation.

@mobius - few states allow a 9 person jury to convict with only 5 votes. Generally that's considered "reasonable" doubt. The article states clearly that they prefer a supermajority of at least 6 out of nine, which is fairly substantial.

@anti-alias. The constitution includes trials and laws, and the concept of reasonable doubt.

Choice, composition, and jury size are all important to the supreme court, as they are given broad interpretation rights by the constitution to ensure that Citizens are given a fair trial and convictions are beyond reasonable doubts. So yes, if the case comes to the supreme court, I believe that they will find the concept important.
##### antialias_physorg
not rated yet Mar 26, 2012
The constitution includes trials and laws, and the concept of reasonable doubt.

Yes, but the supreme court is there to interpret the constitution - not administer law.

The supreme court CANNOT judge on whether someon is guilty or not innocent (e.g. of murder). It can only judge on whether an act (e.g. a law or treaty or even an act of an individual) is constitutional or not.

The power to administer (criminal) law (via the courts) is only held by the states. The supreme court cannot sentence anyone to prison.
##### that_guy
not rated yet Mar 26, 2012
But the supreme court can determine that a trial with too few jurors is unconstitutional and give a person a new trial.

This does have implications for the supreme court - as determining what constitutes a fair trial very much concerns them. If a case lands there, predicated on this type of issue, this kind of research would help determine how the supreme court rules.

Even though the states and federal government administer their own respective justice systems - if a case is brought up to the supreme court that concerns how they run those judicial systems (Where someone has an 'unfair' trial), the supreme court does absolutely have the power to tell them what to do and what not to do with their entire judicial system, as it pertains to what caused the injustice.

The entire country provides you with defense if needed. No municipality or state convenes a jury of less than 6 people. Miranda rights. Etc. These are all factors specifically laid out by the supreme court.
##### that_guy
not rated yet Mar 26, 2012
It concerns the supreme court as to how they would rule on a potential case concerning justice and constitutionality of someone's conviction.

It does not concern the supreme court as to their specific setup, because the supreme court does not do jury trials.
##### antialias_physorg
not rated yet Mar 27, 2012
But the supreme court can determine that a trial with too few jurors is unconstitutional and give a person a new trial.

Sure - but that has nothing to do with the case being tried. Only with how it is being conducted (and whether it has to be repeated)

the supreme court does absolutely have the power to tell them what to do and what not to do with their entire judicial system,

Only if the can find a clause in the constitution that pertains to that specific item. I'm not sure that there is one for this case (it only says "jury of their peers" - but doesn't specify a number...so anything down to two could not be unconstitutional...unless one could make a case that this somehow constitutes an 'unfair trial' EVERY time.

(And if the supreme court actually did manipulate a trail in such an indirect way then that itself would be unconstitutional. It's "Catch 22" in that case)
##### that_guy
not rated yet Mar 27, 2012
the supreme court does absolutely have the power to tell them what to do and what not to do with their entire judicial system,

Only if the can find a clause in the constitution that pertains to that specific item.

as I said directly, as it pertains to directly to what cause the injustice, and other places referenced the points about the constitution.

Look, I've already addressed the points you're bringing up. This research or information may not be pertinent in most trials, but it is information that could affect a supreme court decision if the applicable case came up.
##### Bigbobswinden
not rated yet Mar 27, 2012
This is a very difficult field. I served on a jury and it came down to who's word you believed. As a salesman of my acquaintance said "its all down to sincerity, when you can fake that the world your oyster." I have never been sure we got it right.
##### Ooo O
not rated yet Mar 27, 2012
The problem with something like this is that they do not take into account the intelligence of jurors. I would not trust most people I come in contact with to understand things like 'Reasonable Doubt' when they are being force fed specific chains of events that may or may not be true on both sides of the trial.

I would fear greatly if I were put on trial for murder or something even if I did not do anything. If you think I'm paranoid watch Investigation Discovery sometime.

Heck even getting a jury of my peers would be impossible. What are they going to get a whole jury with 150 give or take IQ? The judges would most likely fall short of 150 in their own right. Let alone lawyers and the jury.
##### RazorsEdge
not rated yet Apr 03, 2012
Suzuki's work is a waste of time. Without any consideration of the facts the probability that a defendant is guilty is 50%. Any other figure postulated is a statement that the observer has made an analysis of the evidence.
I've been a juror on two criminal cases. The probability that we reached the correct decision is 100%.