Q: Can a jury system work for political elections?

A jury of 12 people returning a unanimous verdict may not directly translate to political elections. However, our proposed election by jury model reimagines the electoral process from the ground up. Instead of a unanimous legal verdict, we envision a standard election-style voting approach with carefully designed parameters to improve democratic representation.

And while there might only be 12 jurors in criminal cases, a grand jury typically consists of 16 to 23 jurors. There are two primary concerns around sample size.

1. We want a sufficiently high sample size to achieve high statistical confidence. That is, that our result matches what we’d achieve if we involved the entire population.

2. We want a sufficient size to prevent jury tampering.

Statistical confidence

We'll start with the statistical confidence aspect, because it's just straightforward statistical math. Since only serious candidates typically make it onto the ballot, we expect relatively competitive races—we rarely see blowouts of e.g. 80% to 20%. The graph shows this; it peaks in the middle, meaning close results (like 60-40) are more common than landslides (like 90-10). We use a mathematical tool called Beta(10,10) distribution to model this real-world pattern. We can explore some examples with the help of the Julia programming language. Our probability calculation script is cited here for those who would like to peruse it.

For instance, if 16 of 23 jurors from a population of 100 support X over Y, then we have a 94.5% confidence that our majority result reflects what we’d get with 100% voter turnout. With a population of 1000, that's reduced to 92%. If we then increase the yeses to 17 of 23, then we go back up to 95.8%.  If we then increase the population to 10,000, we go down to 95.6%. So we see that once we get to a pretty large margin of difference, we don't need a very big sample size regardless of the population.

But now say we hold the population constant but have a sample size of 40, and 26 of them (65%) say yes (or no, doesn't matter). Then we get 94.17%. If we boost the population to 100,000, it barely changes to 94.13%, so we don't need to increase the sample size much unless we want to be robust to closer call elections. With a population of 1,000,000, 115 yes out of 200 gives us 97.9%.

The lesson here is that population doesn't matter very much past a certain point. What matters a lot more is the lopsidedness of the outcome, and to some extent sample size. The question is, what's the ideal sample size given the odds of very close elections? After all, it might seem unjust to have even a 90% confidence, given that means there's a substantial 10% chance we elected the wrong candidate.

But before we go demanding a jury size on the order of 100 jurors, it’s crucial to consider that election by jury corrects several much larger statistical biases in the current system.

• Massive demographic disparities in voter turnout
  Voter turnout skews heavily toward older, whiter, and wealthier demographics. This means election outcomes often do not match the preferences of the entire population. Election by jury solves this by requiring all randomly selected jurors to participate, just like jurors in our current criminal justice system. This ensures that the jury composition closely mirrors our society.

• The average voter lacks a deep understanding of the issues and candidates
  Surveys show average voters are highly misinformed about basic issues. For instance, the disconnect between public perception and demographic reality is stark. Americans (on average) think that:

  • 21 percent of Americans are Transgender

  • 27 percent of Americans are Muslim

  • 30 percent of Americans are Jewish

  • 41 percent of Americans are Black

  • 30 percent of Americans live in New York City

  • 30 percent of Americans are gay or lesbian

And here are the actual numbers.

• Transgender: 1 percent

• Muslim: 1 percent

• Jewish: 2 percent

• Black: 12 percent

• Live in New York City: 2 percent

• Gay or lesbian: 3 percent

If voters are so misinformed about basic national demographics, how can we expect them to be well-informed about complex issues like economics and climate change? How can they accurately assess candidates' positions on these issues, let alone their competence and integrity? Election by jury addresses this by having jurors sit through expert testimony, cross-examination, and deliberation, allowing the strongest arguments from all parties to emerge.

• Campaign costs exacerbate the influence of money
  The average cost for a winning campaign in the House of Representatives is $2.5 million. Even the losing campaigns spend $1.2 million on average. Challengers typically spend less, with the average closer to $1.2 million. These high campaign costs create a systemic bias - only candidates who are rich, or well-connected with the rich, are capable of winning an election. It’s no surprise that about 50% to 60% of congress members have a net worth of $1 million or more.
  Even municipal elections face this issue. For instance, St Louis mayor Tishaura Jones raised half a million dollars for her successful 2021 campaign. Election by jury obviates the need by requiring jurors to listen to the best arguments put forward by all candidates, regardless of how much money they have to spend on advertising. This is not only good for candidates, but it also mitigates the corrupting influence of money in politics.

• Choose-one “plurality voting” aka first-past-the-post
  Traditional voting forces voters into a single-candidate choice, making it prone to “vote splitting” between similar candidates, leading to what’s known as the “spoiler effect”. This is why voters often choose a more electable second or third choice rather than casting a sincere vote for the long shot candidate they truly prefer. One of the advantages of election by jury should be that it allows a greater number of candidates to run, because the voting members of the jury have considerably more opportunity to research the plethora of choices and cast an informed vote even in a crowded race. But this increases the risk of vote splitting. Further, a relatively small electorate means a greatly increased risk of ties, which could complicate things.
  Using score voting—which allows voters to score candidates on a scale—can dramatically improve electoral accuracy. According to social utility efficiency calculations from voting methods researcher Marcus Ogren, even a small jury can capture remarkable results, if using an advanced voting method like score voting:
  
  - With just 24 honest voters, we capture 94.8% of the optimal obtainable social utility.
  - As few as 12 honest voters still achieve over 90% efficiency. Contrast that with something around 80% with plurality voting.
  
  Why is this relevant to election by jury? While technically orthogonal to the concept of election by jury, a potentially larger candidate pool as well as a smaller jury size are both reasons to strongly consider an advanced voting method that can mitigate the spoiler effect when there are many candidates, as well as mitigate issues with a small sample size, such as the risk of ties. There are several voting methods that are up to this task, but score voting is by far the simplest and generally best from a game theoretical perspective. While a more advanced voting method can be a logistical challenge for traditional large scale elections, the administrative overhead from both an implementation perspective as well as a voter education perspective is virtually nullified in the context of the small electorate that comprises an electoral jury.
  
  One piece of esoterica with respect to Ogren's social utility efficiency metrics is that wrong-way elections are indeed captured in these results. And this high degree of efficiency partially reflects the fact that in close elections, which are the very case where wrong-way elections are relatively likely, the negative utility caused by picking the "wrong winner" is statistically negligible. That is, if the election is especially close, then the difference in overall welfare for society is likely to be small regardless of who wins. This is admittedly a counterintuitive point to consider, but worth mentioning. We believe the predominant consideration should be that a multitude of the mundane procedural failures we've already discussed produce a significantly larger risk of inaccuracy, and given election by jurmostly neutralizes them, its upsides dominate such obscure and implausible downsides.

Any single one of these issues can lead to staggeringly high odds of electing the "wrong candidate". Thus we believe election by jury does more to enhance the accuracy of election results than any potential sampling error from a small jury size. We believe the bigger consideration with respect to jury size is in the service of mitigating jury tampering, which we now turn to.

Jury tampering

Drawing insights from long-established practices of criminal jury selection, election by jury must ensure both statistical representativeness and protection against tampering. Building on the statistical validity demonstrated earlier, larger juries further improve both sampling confidence and tamper resistance. The historical precedent of jury management in high-stakes criminal trials offers valuable lessons for creating selection mechanisms that can withstand sophisticated tampering attempts.

The fundamental challenge lies in determining how large a jury must be to make tampering economically infeasible. As population size increases, so do the resources potentially available for tampering attempts. A presidential election, for instance, involves vastly greater incentives and available resources for manipulation than a local election.

Secret balloting forms the foundation of tamper resistance, making it impossible to verify how any juror voted. However, the jury must still be large enough that bribing or coercing enough jurors to swing an election would be prohibitively expensive relative to the potential benefits. For a US House election representing roughly 550,000 voters, this suggests a jury size of several hundred members. Presidential elections, with their vastly greater stakes and available resources, require correspondingly larger juries to maintain security.

The key insight is that jury size must scale with the resources available for tampering, not with population size itself. The incentives and means for tampering grow with the power of the office and the resources it controls. A presidential election requires more jurors than a local election because the incentives and means for tampering are so much greater.

Historical jury selection practices, particularly in complex criminal trials involving organized crime, demonstrate the importance of robust selection mechanisms. Election by jury can adapt these proven strategies while accounting for the unique scale of electoral decisions. The goal is creating a system that is not just theoretically sound, but practically resistant to real-world tampering attempts.

Ultimately, we must build a system that maintains public confidence through demonstrated security. This means scaling jury size based on the resources available for tampering in each type of election, while implementing strong protections like secret ballots. The result is a carefully calibrated approach that provides both excellent statistical validity and practical security against manipulation attempts.