09 June 2025
Jury service is an important civic duty, providing a way for people to directly participate in upholding the law and contribute to their community. But the jury service process, like much of the justice system, is designed around the needs of the system rather than the needs of the people it serves.
This article is inspired by a recent experience of being summoned for jury service. The process involved almost 100 people who attended the Court to potentially serve on one of three juries for trials scheduled to begin that week. The jury assembly area was crowded, many potential jurors were apprehensive, and there was a lot of waiting.
People make their time available to the Court, foregoing work, time with family, etc. The selection process may take up to five days, potentially plus whatever time selected jurors spend participating in a trial. The Court does provide compensation, in the form of a daily payment and reimbursement of transportation expenses. But the payment is a very modest amount, more of a token than a reasonable payment for the time commitment.
During the long periods of waiting, in between the various formal Court processes, there was plenty of opportunity to ponder the question: "Surely there is a better way that doesn't require so many people?" To answer that question, in this article we describe a simulation model of the jury selection process. The goal is to explore how the needs of the justice system can be met while also respecting the time of people who report for jury service.
Download the model
The model described in this article is built in Python.
The files are available on GitHub.
Situation
We simulate the jury selection process for criminal trials in a Court. The process involves summoning (requiring people to attend) and empanelling (where people may be chosen to serve on a jury).
The current process consists of the following key steps:
- Many people are summoned via mail to attend a Court to participate in the empanelling process. The summons is for a week that is several weeks in the future.
- Potential jurors are required to respond to the summons, indicating either that they will attend or asking to be excused (which may or may not be granted).
- On the Monday of the appointed week, the summoned people who have not been excused are required to attend the Court. Although attendance is compulsory, unless excused, a portion of the summoned people do not attend the Court (referred to as a "no show"). There is a significant fine for being a no show, though it is rarely imposed.
- Once at the Court, there are typically significant periods of waiting for various formal Court processes to occur. During part of this time, the pool of potential jurors is briefed about how the empanelling and trial processes work.
- The pool of people is randomly divided into groups, with each group considered for empanelling on a jury.
- Each group goes to a courtroom where a trial will be held. People are selected, one-by-one, at random. If a person is selected, then they proceed to the jury box. Each selected person is allowed to approach the Judge to ask if they may be excused from that trial. In addition, the prosecution and defence lawyers may challenge each person before they reach the jury box, up to a maximum number of challenges each per trial.
- If the person is not excused by the Judge or challenged by the lawyers, then they are empanelled on the jury for that trial. A person can serve on, at most, one jury for each summons. An example empanelled jury is shown in Figure 1.
- The people not chosen for a jury are returned to the pool, to wait in case they are needed for that trial or another trial. In our example, the three trials were empanelled in parallel, but that is not always so.
- Even after the required juries have been empanelled, people in the pool may be required to fill jury positions. This happened during our jury service, with 60 people asked to return for another day to select one person to replace an empanelled juror who asked to be excused after a trial had started.
- Once the Judges are satisfied with the juries, the remaining pool of people is released from jury service. This may take up to five days, though it is often less.
First all-woman jury in California, 2 November 1911
Design of simulation Model 1
Overview of the simulation process
The jury is an essential part of the Court process. It is very important that the Court successfully empanels the juries required each week. Our goal is to reduce the number of people who are summoned to Court, but not needed for a jury. This creates a trade-off: summoning many people almost guarantees that we have sufficient people (allowing for an uncertain number of no shows, challenges, and those excused), but having too many people is wasteful of their time.
To model this trade-off, we simulate the summoning and empanelling process. A simulation of the current process provides a benchmark against which we can test alternative processes to see how they perform.
As a starting point, we define as an input the number of people summoned. We also have inputs for the percentage of people who are excused (either in response to the summons or during the empanelling stage), the percentage of no shows, and the rate of challenges (up to a limit). Initial modelling indicated that having a small number of people summoned per trial can lead to an insufficient pool, so we also specify a minimum pool summon size.
In addition to modelling variations in the current process, we propose a new process in which some people are assigned directly to a jury, without going through a pool. This process still allows lawyers to challenge potential jurors, though that can be done without the person needing to attend Court or even knowing that they were considered. We still allow for the possibility that some people who are assigned to a jury will request to be excused, and some will be no shows.
Process flowchart
In designing any type of model, it is important that we have a clear conceptual representation of the situation. This helps us define exactly what the model does. For this model, Figure 2 shows a flowchart of the simulation's key steps for the jury summoning and empanelling process.
The steps in the simulation are:
- Generate trials. This is a sequence of the number of trials each week, for however many weeks we're simulating. For consistency, all scenarios use the same sequence of trials.
- Set up scenario. We define the input parameters, such as the number of people summoned per trial, for the current scenario.
- Each week. A number of weeks are simulated, ranging from one to many (see the "Mode" selection below).
- Summon pool jurors. A specified number of people are summoned to be in the jury pool.
- Summon assigned jurors. A specified number of people are assigned directly to a jury. This is a proposed change to the process. In the current situation, this number is always zero.
- Remove excused and no shows. Remove those excused and no shows from both the pool and assigned jurors, leaving only those who attend the Court.
- Attempt to empanel jurors. For each trial being held this week, attempt to create a jury. Assigned jurors who show are automatically on a jury. If additional jurors are required, then they are randomly selected from the pool. If there are no assigned jurors, then all people are selected from the pool. Those selected may ask the Judge to be excused, and they may be challenged by the lawyers.
- Jury full? Check if we empanelled the required number of people per jury (typically 12).
- Trial success. If yes, then the empanelling process was successful.
- Trial fail. If no, then the empanelling process was a failure.
- More weeks? Check if there are more weeks to simulate. If yes, then return to do another week.
- Write statistics. If no, then write statistics for the current week.
- Done? Check if all scenarios have been completed. If no, then do the next scenario. If yes, then stop.
Note that we treat the trials as being empanelled sequentially, to make maximum use of the people available.
Runtime modes
The simulation has three runtime modes:
- Mode 1. Debug mode. Runs 1 week with single values for all parameters. Prints step-by-step debugging information, which is helpful for checking that the model is working as intended, along with detailed statistics.
- Mode 2. Run a specific pair of scenarios. That is, Current and Proposed for single values for all parameters. This provides a direct comparison between the current and proposed process designs. The simulation is repeated many times, via the
NUM_WEEKSparameter. Some events are relatively rare, so a large sample size, such as 1,000,000 weeks, is necessary to produce good estimates of the detailed statistics. - Mode 3. Run a range of parameters. This allows us to do a grid search of multiple parameter values, to identify good combinations. This mode also uses a large sample size for the number of weeks. As there may be many parameter combinations, we print only a one line summary for each combination.
On our modelling PC, a scenario with 1,000,000 weeks takes around 1 minute to run. Beware of running many parameter combinations, as the total run time can grow very quickly.
Figure 3 shows some debug output from Mode 1. In this example we have two trials. For the first trial, the model assigns 20 people (numbered 1 to 20) to the jury, then removes 4 excused people and 4 no shows. For the second trial, the model assigns 20 other people to the jury (numbered 21 to 40), then removes 4 excused people and 5 no shows. It also creates a list of 14 people for the pool (numbered 41 to 54), then removes an additional 3 excused people and 2 no shows. With 8 people removed from the first trial jury, we have the 12 jurors needed, so that trial succeeds. With 9 people removed from the second trial jury, we're one person short. Therefore, we need to take one person from the pool. In attempting to do that, three people ask the Judge to be excused, and two more are challenged by the lawyers. Eventually, person 45 from the pool is added to the jury for trial 2, which now also succeeds.
INFO:root:Assigned list (20): [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
INFO:root:Assigned excused candidates removed (4): [9, 17, 14, 7]
INFO:root:Assigned no show candidates removed (4): [13, 8, 2, 1]
INFO:root:Assigned list (20): [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]
INFO:root:Assigned excused candidates removed (4): [28, 37, 23, 27]
INFO:root:Assigned no show candidates removed (5): [34, 22, 30, 31, 24]
INFO:root:Pool list (14): [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54]
INFO:root:Pool excused candidates removed (3): [42, 43, 50]
INFO:root:Pool no show candidates removed (2): [49, 52]
INFO:root:Assigned jurors ([12, 11] = 23: [[3, 4, 5, 6, 10, 11, 12, 15, 16, 18, 19, 20], [21, 25, 26, 29, 32, 33, 35, 36, 38, 39, 40]]
INFO:root:Pool show (9): [41, 44, 45, 46, 47, 48, 51, 53, 54]
INFO:root:Jury (12) [3, 4, 5, 6, 10, 11, 12, 15, 16, 18, 19, 20] Success
INFO:root:Excused by Judge [51]
INFO:root:Excused by Judge [53]
INFO:root:Excused by Judge [46]
INFO:root:Challenged [44]
INFO:root:Challenged [48]
INFO:root:Jury (12) [21, 25, 26, 29, 32, 33, 35, 36, 38, 39, 40, 45] SuccessImplementation
Python code
Simulation Model 1 is coded in Python. There are several commonly used simulation libraries available, including SimPy and salabim. In some situations, those libraries can simplify the process of creating a simulation model, especially in more complex situations. In this situation, we decided to just use native Python, without a simulation library. We explore using the SimPy library in the next article to help us build Model 2.
The implementation of Model 1 closely follows the process flowchart above. The current and proposed system designs are represented in a single model, with behaviours differing only by variations in the input parameters. For example, in the current design, the number of people assigned to a jury is zero, whereas in the proposed design that parameter has a value like 20.
Figure 4 shows a central function in the simulation: empanelling a jury. We start with any people who have been pre-assigned to this jury. Then we randomly select people one-by-one from the pool, allowing them to be excused by the Judge or challenged by the lawyers. We continue until either a full jury is achieved (a success), or the pool is empty (a failure).
def empanel_jurors(assigned, pool): # Create a jury
jury = assigned[:JURY_SIZE]
assigned_count = len(jury)
challenge_rate = CHALLENGE_RATE_POOL
challenge_max = CHALLENGE_MAX_POOL if assigned_count == 0 else CHALLENGE_MAX_MIXED
num_challenged = 0
while len(jury) < JURY_SIZE: # If jury is not full, continue selecting from pool
if not pool: # No more people in pool, so fail
return jury, False
current = random.sample(pool, 1)
pool = [c for c in pool if c not in current] # Remove current person from this trial's pool, whether or not they are enpanelled
if random.uniform(0, 1) <= EXCUSE_EMPANELLING / 100: # Excuse people from pool, if they ask the Judge
logging.info(f'Excused by Judge {current}')
continue # Don't add excused person to jury
if num_challenged < challenge_max: # Only allow challenge if less than max challenges previously
if random.uniform(0, 1) <= challenge_rate / 100: # Successful challenge
num_challenged += 1
logging.info(f'Challenged {current}')
continue # Don't add challenged person to jury
jury.extend(current) # Add person to jury if they weren't excused or challenged
return jury, TrueKey assumptions
The key assumptions in the simulation are:
- Jury size: 12 people.
- Number of trials: Each simulation is for one week. The number of trials in a week has a Poisson distribution with mean of 3, capped at 9 (the number of available courtrooms in this Court).
- Pool per trial: Number of people summoned to be in the pool. Assumed to be 54 for the current design.
- Minimum pool: Lower bound on the number of people summoned to be in the pool. Size of the pool = max(Minimum pool, Pool per trial * Number of trials).
- Assigned per trial. Number of people summoned to be assigned to a jury.
- Summon excuse rate: Normally distributed with mean 25% and standard deviation 6%. Same for summoned pool and assigned jurors.
- Summon no show rate: Normally distributed with mean 20% and standard deviation 5%, of those not excused. Same for summoned pool and assigned jurors.
- Challenge rate: 25% of selected pool people are challenged during the empanelling process. Up to 8 challenges for the general pool, or up to 2 challenges when there are assigned jurors (assuming some challenges were already used when jurors were assigned). Challenges for assigned people are outside the process, with challenged people replaced by new assigned people, so challenges for assigned people do not need to be counted.
- Judge excuse. 10% of people selected during the empanelling process ask the trial Judge to be excused.
Disclaimer
We have simplified some of the real-world details, as happens in all modelling, though we've attempted to capture the essential elements. More importantly, we have only a small number of observations rather than a comprehensive set of data. For many of the assumptions, we have simply made a guess. Therefore, our modelling and results should be considered indicative only.
Examples of simulated process flow
Current design
Given our assumptions, an example of the flow of people through the current process design is shown in Figure 5. In this week we have two trials, so 2 * 54 = 108 people are summoned. Around 25% are excused and around 20% of the remainder are no shows.
We then attempt to empanel two juries, in sequence, with some people being challenged by the lawyers or excused by the Judge. At the end of the process, both juries succeed so we have 24 people empanelled on a jury. There are 40 people who were not needed for a jury this week. We call them the "Extra" people. It is the number of Extra people that we want to reduce. Of course, we need some extra people, to allow for variation in the number of people excused, challenged, or who don't show. But do we need that many extra people?
Figure 6 shows an example of the proposed process. It looks more complex, but that's mainly because some of the steps are separated by Pool, Assigned 1 (i.e., people pre-assigned to the first jury), and Assigned 2. A key difference from the current process example is that we summon fewer people – in part because challenges are done outside of this process, and in part because we can. In addition, the two trials have jurors pre-assigned, so we need a much smaller pool to cover those excused and the no shows. In this example, the number of Extra people is 11, compared with 40 for the current design. That's a reduction of 73%.
Scenarios
We consider some scenarios:
- Scenario 1: Current process. The Court summons 54 people per trial, with no minimum.
- Scenario 2: Current process with more risk of failure. If we allow a higher risk of failure, then we can summon fewer people per trial.
- Scenario 3: Current process with minimum summoned. The risk of failure is higher when there are only one or two trials in a week. This risk can be mitigated by imposing a minimum on the number of people summoned.
- Scenario 4: Proposed process, more risk. Pre-assigning people to a jury should enable us to summon fewer people to be in a pool of potential jurors.
- Scenario 5: Proposed process, less risk. Like Scenario 4, but with a risk of failure that it lower than for Scenario 1.
Results
Scenario 1: Current process
The Court system is extremely conservative. To avoid any risk of having insufficient jurors, many people are summoned for jury service. We assume that the Court summons 54 people per trial. If there are three trials in a week, then 162 people are summoned and we expect around 97 people to show (= 54 * 3 * 75% * 80%). This is consistent with the week we observed, where 96 people were present for 3 trials.
Figure 7 shows the simulation results for the current process design, with a sample size of 1,000,000 weeks. This output is generated by the model's Mode 2, including detailed statistics.
There are between 1 and 9 (inclusive) trials per week. On average there are very slightly less than 3 trials per week, because we truncate the Poisson distribution. Therefore, we have about 3,000,000 trials, for which we need about 36,000,000 jurors – or an average of 36 jurors per week.
In this run, 26 trials failed to empanel a jury, for a failure rate of 0.00087% (failure is a rare event, which is why we need a large sample size). This equates to 1 failure in 115,000 trials. With 3 trials per week in this Court, or 150 trials per year, we expect a failure of 1 trial every 750 years or so. Very conservative indeed.
In an average week, 161.8 people are summoned, 40.5 are excused, and 24.3 are no shows, so that 97.1 people show up. We empanel 36.0 people and have 61.1 extra people. That is, 63.0% (= 61.1/ 97.1) of the people who show are surplus to requirements – these are the extras we want to reduce.
Pool per trial: 54, minimum pool: 0, assigned per trial: 0
Weeks: 1,000,000
Jurors Initial Excused No show Show Empanelled Extra
-------------------------------------------------------------------------------------------------------------
Assigned 0 0 0 0 0 ( 0.0%) 0 ( 0.0%)
Pool 161,820,126 40,459,834 24,267,429 97,092,863 35,959,716 ( 37.0%) 61,133,147 ( 63.0%)
-------------------------------------------------------------------------------------------------------------
Total 161,820,126 40,459,834 24,267,429 97,092,863 35,959,716 ( 37.0%) 61,133,147 ( 63.0%)
Trials Success Failure Total
---------------------------------------------------------------------------------
1 149,935 ( 99.98266%) 26 ( 0.01734%) 149,961 ( 5.0%)
2 446,626 (100.00000%) 0 ( 0.00000%) 446,626 ( 14.9%)
3 671,469 (100.00000%) 0 ( 0.00000%) 671,469 ( 22.4%)
4 671,216 (100.00000%) 0 ( 0.00000%) 671,216 ( 22.4%)
5 505,755 (100.00000%) 0 ( 0.00000%) 505,755 ( 16.9%)
6 301,008 (100.00000%) 0 ( 0.00000%) 301,008 ( 10.0%)
7 152,131 (100.00000%) 0 ( 0.00000%) 152,131 ( 5.1%)
8 64,168 (100.00000%) 0 ( 0.00000%) 64,168 ( 2.1%)
9 34,335 (100.00000%) 0 ( 0.00000%) 34,335 ( 1.1%)
---------------------------------------------------------------------------------
Total 2,996,643 ( 99.99913%) 26 ( 0.00087%) 2,996,669 (100.0%)Scenario 2: Current process with more risk of failure
What if we keep the current process but accept a little more risk of failing to empanel a jury? The justice system is conservative, which is unlikely to change. But a risk of 1 failure every 750 years is extreme. What if we adopt a slightly less conservative position of, say, a 1 in 100 year risk of failure?
Using the model's Mode 3 we can run all values of the POOL_PER_TRIAL parameter from 1 to 54 (with 0 minimum and 0 assigned). If the pool has few people per trial, then there is a high risk of failure, especially if there is a small number of trials in a week. With fewer than about 24 people summoned per trial, the risk of failure rapidly approaches 100%. But if the pool is a reasonable size, then the risk is not large.
It turns out that we can reduce the number of people summoned to 49 per trial, with only a modest increase in risk. This solution, with detailed statistics generated by Mode 2, is shown in Figure 8. In this scenario we need to summon an average of 146.8 people (9% fewer, compared with Scenario 1). The number of extra people has reduced to an average of 52.1 per week (-15%). The risk of failure is 0.00694%, which equates to around 1 in 15,000 trials, or about 1 failed trial every 100 years.
We could reduce the number of people summoned per trial even further, but the risk increases rapidly. For example, summoning 40 people per trial reduces the number of extra people to 36.0 (-41%), but increases the risk of failure to around 1 trial every 4 years. That is unlikely to be acceptable.
Pool per trial: 49, minimum pool: 0, assigned per trial: 0
Weeks: 1,000,000
Jurors Initial Excused No show Show Empanelled Extra
-------------------------------------------------------------------------------------------------------------
Assigned 0 0 0 0 0 ( 0.0%) 0 ( 0.0%)
Pool 146,836,781 36,712,972 22,020,419 88,103,390 35,957,532 ( 40.8%) 52,145,858 ( 59.2%)
-------------------------------------------------------------------------------------------------------------
Total 146,836,781 36,712,972 22,020,419 88,103,390 35,957,532 ( 40.8%) 52,145,858 ( 59.2%)
Trials Success Failure Total
---------------------------------------------------------------------------------
1 149,753 ( 99.86130%) 208 ( 0.13870%) 149,961 ( 5.0%)
2 446,626 (100.00000%) 0 ( 0.00000%) 446,626 ( 14.9%)
3 671,469 (100.00000%) 0 ( 0.00000%) 671,469 ( 22.4%)
4 671,216 (100.00000%) 0 ( 0.00000%) 671,216 ( 22.4%)
5 505,755 (100.00000%) 0 ( 0.00000%) 505,755 ( 16.9%)
6 301,008 (100.00000%) 0 ( 0.00000%) 301,008 ( 10.0%)
7 152,131 (100.00000%) 0 ( 0.00000%) 152,131 ( 5.1%)
8 64,168 (100.00000%) 0 ( 0.00000%) 64,168 ( 2.1%)
9 34,335 (100.00000%) 0 ( 0.00000%) 34,335 ( 1.1%)
---------------------------------------------------------------------------------
Total 2,996,461 ( 99.99306%) 208 ( 0.00694%) 2,996,669 (100.0%)Scenario 3: Current process with minimum summoned
We observe that, for most parameter values, almost all the failed trials occur when there are only 1 or 2 trials in a week. That's because a small number of trials means a small pool to select from, with a corresponding higher risk of failure. Conversely, if there are many trials in a week, then there is a large pool of potential jurors, so the number of people excused initially, no shows, excused by a Judge, or challenged by lawyers is less likely to deplete the pool entirely. That is, we get a diversification effect as the number of trials per week increases.
One way to manage the pool when there are few trials in a week is to impose a minimum for the number of people summoned. This effectively increases the pool size when there are few trials.
By conducting a grid search over the POOL_PER_TRIAL and MIN_POOL parameters, we found a good compromise as shown in Figure 9. This solution summons 38 people per trial with a minimum of 57 people (which effectively applies only to the weeks that have 1 trial). In this scenario we need to summon an average of 116.7 people (28% fewer, compared with Scenario 1). The number of extra people reduces to an average of 34.1 per week (-44%). The risk of failure is 0.00657%, or about 1 failed trial every 100 years. There are many other combinations of the parameters that have similar statistics.
Pool per trial: 38, minimum pool: 57, assigned per trial: 0
Weeks: 1,000,000
Jurors Initial Excused No show Show Empanelled Extra
-------------------------------------------------------------------------------------------------------------
Assigned 0 0 0 0 0 ( 0.0%) 0 ( 0.0%)
Pool 116,722,681 29,199,555 17,502,975 70,020,151 35,957,664 ( 51.4%) 34,062,487 ( 48.6%)
-------------------------------------------------------------------------------------------------------------
Total 116,722,681 29,199,555 17,502,975 70,020,151 35,957,664 ( 51.4%) 34,062,487 ( 48.6%)
Trials Success Failure Total
---------------------------------------------------------------------------------
1 149,950 ( 99.99266%) 11 ( 0.00734%) 149,961 ( 5.0%)
2 446,458 ( 99.96238%) 168 ( 0.03762%) 446,626 ( 14.9%)
3 671,453 ( 99.99762%) 16 ( 0.00238%) 671,469 ( 22.4%)
4 671,214 ( 99.99970%) 2 ( 0.00030%) 671,216 ( 22.4%)
5 505,755 (100.00000%) 0 ( 0.00000%) 505,755 ( 16.9%)
6 301,008 (100.00000%) 0 ( 0.00000%) 301,008 ( 10.0%)
7 152,131 (100.00000%) 0 ( 0.00000%) 152,131 ( 5.1%)
8 64,168 (100.00000%) 0 ( 0.00000%) 64,168 ( 2.1%)
9 34,335 (100.00000%) 0 ( 0.00000%) 34,335 ( 1.1%)
---------------------------------------------------------------------------------
Total 2,996,472 ( 99.99343%) 197 ( 0.00657%) 2,996,669 (100.0%)Scenario 4: Proposed process, more risk
Scenarios 1 to 3 all use the current jury empanelling process. In Scenario 4 we propose an alternative process: assign some people to juries before summoning them to Court.
This proposed process has two significant advantages:
- Lawyers can challenge people without those people needing to be present in Court. Since the number of challenges is uncertain, modifying this part of the process materially reduces the number of people who need to be summoned.
- If we pre-assign most of a jury, or perhaps even more people than we need for a jury, then the number of people needed in the pool is substantially reduced. We need only a relatively small pool of people to fill any gaps that may remain in the juries.
Figure 10 shows the result for the proposed process, after a grid search to find the best parameters that produce a risk of about 1 failed trial per 100 years. The parameters are: summon 4 people per trial, with a minimum summon pool of 17 people, and summon 20 people assigned per trial.
The Court needs to summon an average of only 77.2 people each week (-52%), of whom an average of 46.3 are expected to show. Of those 46.3 people, an average of 36.0 are empanelled on a jury. That leaves an average of only 10.3 extra people per week – a substantial 83% reduction compared with Scenario 1, with only a small increase in risk (failure rate of 1 in 100 years compared with 1 in 750 years).
Pool per trial: 4, minimum pool: 17, assigned per trial: 20
Weeks: 1,000,000
Jurors Initial Excused No show Show Empanelled Extra
-------------------------------------------------------------------------------------------------------------
Assigned 59,983,100 14,995,749 8,998,473 35,988,878 34,542,677 ( 96.0%) 1,446,201 ( 4.0%)
Pool 17,244,766 4,309,561 2,587,229 10,347,976 1,444,675 ( 14.0%) 8,903,301 ( 86.0%)
-------------------------------------------------------------------------------------------------------------
Total 77,227,866 19,305,310 11,585,702 46,336,854 35,987,352 ( 77.7%) 10,349,502 ( 22.3%)
Trials Success Failure Total
---------------------------------------------------------------------------------
1 149,216 ( 99.99933%) 1 ( 0.00067%) 149,217 ( 5.0%)
2 448,354 ( 99.99777%) 10 ( 0.00223%) 448,364 ( 14.9%)
3 673,580 ( 99.99406%) 40 ( 0.00594%) 673,620 ( 22.5%)
4 671,832 ( 99.98274%) 116 ( 0.01726%) 671,948 ( 22.4%)
5 502,696 ( 99.99224%) 39 ( 0.00776%) 502,735 ( 16.8%)
6 303,303 ( 99.99901%) 3 ( 0.00099%) 303,306 ( 10.1%)
7 150,892 (100.00000%) 0 ( 0.00000%) 150,892 ( 5.0%)
8 65,224 (100.00000%) 0 ( 0.00000%) 65,224 ( 2.2%)
9 33,849 (100.00000%) 0 ( 0.00000%) 33,849 ( 1.1%)
---------------------------------------------------------------------------------
Total 2,998,946 ( 99.99303%) 209 ( 0.00697%) 2,999,155 (100.0%)Note that the key to the efficiency of this scenario is that we summon 20 people per trial to be directly assigned to a jury. Allowing for 25% being excused from the summons and a further 20% no shows, we expect around 20 * (1 - 0.25) * (1 - 0.20) = 12 people to show at Court for each jury. That is, we expect to fill each jury with assigned people, plus or minus a few people. We may have more people show at Court, but they are not needed. If we have fewer people show at court, then the likely few gaps can be filled from the small pool – even allowing for some people being excused by the Judge or challenged by the lawyers during empanelling. There is still a small risk of failure, but even a small pool is large enough to be sufficient almost all the time.
Scenario 5: Proposed process, less risk
Given that the Court is very conservative, they may not accept a risk of failure of 1 in 100 years. It turns out that there are many parameters combinations that have even lower risk than the current design, Scenario 1, with fewer extra people.
Figure 11 shows the result that has the lowest number of extra people while having near-zero risk. The parameters are: summon 5 people per trial, with a minimum summon pool of 19 people, and summon 21 people assigned per trial. Each of these parameters is slightly higher than for Scenario 4, leading to a higher expected number of extra people.
The Court needs to summon an average of only 83.0 people each week (-49%), of whom an average of 49.8 are expected to show. Of those 49.8 people, an average of 36.0 are empanelled on a jury. That leaves an average of 13.8 extra people per week – a substantial 77% reduction compared with Scenario 1. The failure rate is so small that it is difficult to estimate accurately. A rate of 0.00003% equates to a risk of failure of about 1 in 20,000 years.
Pool per trial: 5, minimum pool: 19, assigned per trial: 21
Weeks: 1,000,000
Jurors Initial Excused No show Show Empanelled Extra
-------------------------------------------------------------------------------------------------------------
Assigned 62,982,255 15,745,043 9,447,336 37,789,876 35,221,821 ( 93.2%) 2,568,055 ( 6.8%)
Pool 20,000,611 4,998,507 3,000,823 12,001,281 768,027 ( 6.4%) 11,233,254 ( 93.6%)
-------------------------------------------------------------------------------------------------------------
Total 82,982,866 20,743,550 12,448,159 49,791,157 35,989,848 ( 72.3%) 13,801,309 ( 27.7%)
Trials Success Failure Total
---------------------------------------------------------------------------------
1 149,217 (100.00000%) 0 ( 0.00000%) 149,217 ( 5.0%)
2 448,363 ( 99.99978%) 1 ( 0.00022%) 448,364 ( 14.9%)
3 673,620 (100.00000%) 0 ( 0.00000%) 673,620 ( 22.5%)
4 671,948 (100.00000%) 0 ( 0.00000%) 671,948 ( 22.4%)
5 502,735 (100.00000%) 0 ( 0.00000%) 502,735 ( 16.8%)
6 303,306 (100.00000%) 0 ( 0.00000%) 303,306 ( 10.1%)
7 150,892 (100.00000%) 0 ( 0.00000%) 150,892 ( 5.0%)
8 65,224 (100.00000%) 0 ( 0.00000%) 65,224 ( 2.2%)
9 33,849 (100.00000%) 0 ( 0.00000%) 33,849 ( 1.1%)
---------------------------------------------------------------------------------
Total 2,999,154 ( 99.99997%) 1 ( 0.00003%) 2,999,155 (100.0%)Summary of simulation results
Scenario parameters
Figure 12 shows a summary of the scenario parameters. Scenarios 1 to 3 all use the current process, with Scenarios 2 and 3 having relatively small changes to the parameters. Scenarios 4 and 5 use a new proposed process, with parameters that differ markedly from the other scenarios.
Scenario results
Figure 13 shows a summary of the scenario results for Model 1. That is:
- Scenario 1, Current. On average, the current process summons 162 people per week, of whom 97 show at Court. After 36 are empanelled on juries, there are 61 extra people. In this Court, the empanelling process is expected to fail once every 750 years.
- Scenario 2, Current, more risk. By taking on slightly more risk, with the empanelling process expected to fail once every 100 years, we can reduce the number of extra people by 15%.
- Scenario 3, Current + minimum. Imposing a minimum size on the summoned pool size, in addition to taking slightly more risk, allows the number of extra people to be almost halved.
- Scenario 4, Proposed, more risk. In this scenario we propose changing the process to assign people to juries before coming to Court, in addition to taking slightly more risk. The result is that we more than halve the number of people summoned and achieve an 83% reduction in the number of extra people who need to report for jury service.
- Scenario 5, Proposed, less risk. We almost halve the number of people summoned and achieve an 77% reduction in the number of extra people who need to report for jury service. Importantly, the risk of failure is substantially lower than the already very conservative risk in the current process.
Scenarios 4 and 5 are massive improvements in the use of people's time. With a relatively small change in the jury service process, we free around 50 people per week from appearing for jury service at a Court that averages 3 trials per week. Such a change would make the waiting area much less crowded. Scenario 4 requires the fewest people, while Scenario 5 has the least risk – the best choice depends on how much we value that trade-off.
Trade-off between risk and number of extra people
Figure 14 shows the trade-off between the number of extra people and the risk of trial failure (up to 0.1%, or about one fail every 7 years), given a range of parameter combinations:
- Scenario 1 is our starting point, representing the current process.
- The small red squares use the current process, though summoning fewer people per trial. Scenario 2 is on this curve.
- Scenario 3 shifts off the current curve. It summons fewer people in total by having a minimum number of people in the pool to cover weeks that have only one trial.
- The orange dots are thousands of combinations of parameters, with the number of people per trial between 0 and 20, minimum pool between 0 and 20, and people assigned per trial between 1 and 25. Only the combinations with risk less than 0.1% are shown. The trade-off with the lowest number of extra people, given a target of 1 in 100 year risk, is Scenario 4. The trade-off with the lowest number of extra people, given a near-zero risk, is Scenario 5.
Additional notes
We could further reduce the number of extra people using the new process. But the incremental reduction is small, and the risk rises quickly. For example, the average number of extra people per week could be reduced by another 2 per week if we accept a risk of failing once every 7 years. This trade-off is probably not worthwhile.
In the proposed process, people are assigned to a specific trial. If they are not needed for that trial, because more people show than are required, then those extra people are released from the process. If, instead, we added those extra people into the pool for other trials, then the number of people summoned for the pool could be further reduced. This variation, and possibly other variations, could potentially make the proposed process even more efficient.
Note that some of the results are quite sensitive to the assumed parameters. Therefore, more comprehensive data collection, and a detailed sensitivity analysis, would be necessary before implementing any changes to the current system.
Conclusion
In this article, we describe a simulation model of the jury summoning and empanelling process for criminal trials in a Court.
This modelling was inspired by the author participating in a jury service process. In that instance, 96 people attended the Court for empanelling of three jurors requiring 36 jurors. A much larger cohort of people had been summoned, but did not attend the Court either because they were excused or they simply didn't show. Even allowing for people being excused or challenged during the empanelling process, there was an overwhelming impression that there were many more people than was needed.
Our scenarios show that it is possible to significantly reduce the number of people summoned to Court, even without materially changing the process. If we allow a change in process, specifically to assign people to juries before they are summoned to Court, then we can reduce the number of extra people required by around 80% while also substantially reducing the risk of the empanelling process failing.
We've explored only a small range of scenarios. Many other variations in the process could be evaluated by adding more scenarios to the modelling.
Jury service is an important civic duty. But the process seems to show a lack of respect for people's time. With minor changes to the process, jury service can be made much more efficient, enabling it to meet the needs of the justice system while also respecting the time of people who participate.
In the next article, we replicate this model using the SimPy simulation library.
If you would like to know more about this model, or you want help with your own models, then please contact us.
