Why Sortition Algorithms?
How do you select a representative group of people — fairly?
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How do you select a representative group of people — fairly?
Citizens' assemblies, juries, and deliberative panels all start the same way: inviting people to participate. Letters go out to thousands of randomly chosen households.
Most people don't respond.
But some people do. They fill in a form online, on their phone, or by calling a number.
The assembly only has room for around 50 panellists. So from these ~400 responses, we need to choose 50 people in a way that is both representative — reflecting the wider population — and fair — giving everyone a reasonable chance of being selected. What exactly these words mean can vary by context, but both matter.
For the rest of this walkthrough, we'll use a simplified example: 16 candidates, from which we need to select 8 panellists.
Here are our 16 candidates. Each has three demographic attributes: Gender, Region, and Age.
Why is the pool skewed? Self-selection bias. Older people may have more time to respond. People in the South — perhaps a poorer area — may feel less able to participate, or less confident that the assembly will listen to them. The reasons vary, but the result is the same: the pool doesn't look like the city.
Another way to see the skew is to look at combinations of categories. Some intersections have many candidates, others have very few.
Count of candidates in each intersection
Before we try selecting anyone, let's think about what we actually want. If the panel is supposed to represent the city, what would that look like?
We might decide that some categories should precisely reflect the population. Gender in our city is roughly 50/50, and we're selecting 8 people, so we might want exactly 4 Male and 4 Female panellists. Same for age: exactly 4 Young and 4 Senior.
For other categories, exact balance may be less important than ensuring adequate representation. For Region, we might be happy with anywhere from 3 to 5 Northerners (and correspondingly 3 to 5 Southerners). This gives flexibility while still ensuring no region is shut out.
We could in principle set criteria for intersections too — like “at least 1 Young Southerner” — but the maths gets complicated fast, so in practice targets are set per category.
So, does a simple random draw meet our criteria? Let's try it a few times.
We can take our earlier ideas about representativeness and turn them into concrete targets that the panel must meet. These are set by the organisers based on census data and the assembly's purpose.
Here are our targets alongside the candidate pool. Some are comfortable to meet, others are tight — there isn't much room for manoeuvre.
It turns out that, for our 16-person example, there are many different panels of 8 that satisfy all the targets. Meeting the targets is possible — in fact, there are many ways to do it. The question is which valid panel to pick.
Here are two examples — you can check that they really do satisfy the targets.
Notice that Omar and Priya appear in both panels. That's not a coincidence…
Across all valid panels, some people appear far more often than others.
People who appear in very few valid panels might feel: “There's no point in registering — I have almost no chance anyway.” That's a problem for the legitimacy of the whole process.
There's a genuine tension here. The panel must look like the population (representativeness), but each individual should also have a fair shot at being selected (fairness). There is a third concern too: explainability. [more]
Real assemblies might have 400 candidates, 15 demographic categories, and need to select 50 panellists. The maths gets complicated fast — far beyond what a spreadsheet can handle.
The good news: mathematicians have developed algorithms that handle both representativeness and fairness. Let's see how they work.
An efficient way of selecting a panel that satisfies the targets, meaning it is representative. However, the algorithm does not address fairness.
The first part of the fairer algorithms (maximin, nash and leximin). These aim to balance both representativeness and fairness — meeting the targets while ensuring no candidate has a particularly low chance of selection.