Center for Blue Democracy Minimum Pool Size Calculator

Introduction

When organizing a citizens’ assembly, one of your first questions will be: How many volunteers do we need to have registered to achieve the desired demographic composition of the assembly? The Minimum Pool Size Calculator helps answer this question using insights from successful random selection processes.

The calculator is created in R programming language, but you don’t need to be a programmer to use it. It comes with a clear ReadMe file that walks you through the installation process and explains step-by-step how to use the calculator. All you need to do is prepare two Excel files – one with your demographic categories and another with settings – and the calculator will do the rest.

You can download the calculator here.

The Foundation: The Lausanne Ratio

The calculator was built on an empirically validated foundation – the Lausanne citizens’ assembly. In this case, simulated annealing made something remarkable possible: perfect demographic representation using just 55 volunteers for a 20-person assembly, despite having 8 different demographic categories (including gender, age, education, income, nationality, and others) with 23 total subcategories. This showed that random selection can succeed with a ratio of only 2.7 volunteers per assembly seat (55/20 ≈ 2.7), establishing an empirical minimum baseline for achieving perfect demographic representation even with complex criteria.

However, the Lausanne case also revealed something crucial – with such precise matching requirements, there were very few possible combinations of members that would work. Out of the 55 volunteers, only 2 possible combinations achieved perfect demographic representation. This means that only some of the volunteers had a chance to be selected to the final group. This is why the calculator recommends a larger pool of volunteers, which helps ensure both good demographic representation and better chances for all volunteers to be selected.

A Safety Margin

The calculator starts with the proven Lausanne ratio but then adds a safety margin by looking at your assembly’s demographic complexity:
– How many categories you’re using (like age, gender, education, etc.)
– How many subcategories exist within each category
– How these combine to create selection requirements

A more complex demographic structure means you’ll need a larger pool of volunteers to ensure enough flexibility in selection. For example, if you’re tracking just age and gender, you need fewer volunteers than if you’re also matching education levels, income brackets, and geographic distribution.

How the Calculator Works

The calculator follows these steps:
1. Calculates your base minimum pool size using the Lausanne ratio:
– Base minimum = assembly size × 2.7

2. Assesses your demographic complexity:
– Counts your total categories (age, gender, etc.)
– Counts all subcategories within these
– Combines these into a complexity factor

3. Adds a scaled safety margin:
– Safety margin = base minimum × 0.25 × complexity factor
– This provides extra volunteers to ensure flexible selection

4. Provides your recommended minimum pool size:
– Final recommendation = base minimum + safety margin

Example in Practice

Let’s say you’re planning a 40-person assembly with:
– 2 gender categories
– 4 age brackets
– 3 education levels
– 5 geographic districts

The calculator would:
1. Calculate base minimum: 40 × 2.7 = 108 volunteers
2. Assess complexity: 4 categories with 14 total subcategories
3. Add safety margin based on this complexity
4. Provide a final recommendation that ensures enough volunteers for flexible selection

Key Takeaways

1. The Lausanne ratio (2.7 volunteers per seat) provides a proven minimum baseline
2. Your assembly’s demographic complexity determines how much extra margin you need
3. The calculator’s recommendation ensures both representation and flexibility
4. This approach helps you plan recruitment with confidence

While the calculator provides a minimum recommendation, having more volunteers is usually better. A larger pool not only helps achieve good demographic representation but also provides better chances for all volunteers to participate in the assembly.