Center for Blue Democracy Explainer

Why Use Simulated Annealing?

Imagine you’re a metalsmith crafting a perfect sword. You heat the metal until it’s glowing hot (but not melting), then gradually cool it down according to a precise schedule. This controlled cooling process – called annealing – makes the metal stronger and more durable by allowing its internal structure to settle into its optimal state.

Similarly, simulated annealing is a method for selecting members of citizens’ assemblies that starts with a lot of freedom to explore different possible group compositions (like the hot, energetic metal), and then gradually becomes more selective (like the cooling metal) to find the optimal arrangement. Just as the careful cooling helps atoms find their best positions in the metal, this digital cooling process helps find the best possible match between the assembly’s composition and the community’s demographic profile.

Prioritizing accuracy in random selection

The primary aim in selecting members of the citizens’ assembly is to create a group that accurately reflects the demographic makeup of the community. Accuracy means that the number of assembly members from each demographic category (such as age groups, gender, education level, etc.) matches the proportions of these groups in the broader population. For example, if young people constitute 30% of the population, then ideally, 30% of assembly members should be young people. This accuracy is essential because the assembly is meant to be a true microcosm of society.

The power of precision: understanding accuracy and closeness

Simulated annealing uses two important measures to ensure the selected group truly represents the community:

The Accuracy Index

Think of the Accuracy Index as a scorecard that counts how many “mismatches” there are between the ideal demographic composition and what we actually achieve.

Let’s look at a simple example – suppose in your city:
– 50% are women (so in a 40-person assembly, you want 20 women)
– 30% are under 35 (ideally 12 people)
– 20% have a university degree (ideally 8 people)

If your selected group has 19 women (off by 1), 11 young people (off by 1), and 9 university graduates (off by 1), your Accuracy Index would be 3 – the sum of all deviations. The lower the number, the better. The Accuracy Index 0 indicates that the perfect composition of the assembly has been achieved (there are no mismatches).

The Closeness Index

The Closeness Index is like the more sophisticated cousin of the Accuracy Index. It considers not just the number of mismatches but also the magnitude of each mismatch (this is accomplished by raising the mismatch to the power of 1.6). A group that is off by one person in three categories, as in the example above, would score better than a group that is off by three people in one category. It helps ensure that no single demographic group is severely under- or overrepresented. The lower the number, the better, with 0 indicating the perfect composition.

Equality considerations

Equality is built into simulated annealing through its probabilistic nature. When the algorithm explores different possible combinations of assembly members, it does so through a series of random steps. Each step has a chance of being accepted or rejected based on how well it helps achieve the desired demographic composition. This element of randomness means that every volunteer has a chance of being selected.

Equality in terms of the chances for being selected is closely related to the desired composition of the assembly and the individual characteristics of all volunteers. The method’s effectiveness in this regard was confirmed through statistical indicators:
– The standard deviation scores show that selection chances are well distributed (provided the target makeup of the assembly and individual characteristics of volunteers allow for it)
– The Gini Index demonstrates that the method achieves satisfactory results in terms of equality of selection

Key benefits of simulated annealing

1. Highest accuracy: The method achieves the best possible demographic representation given the available pool of volunteers. In real-world testing, it achieved perfect composition in every case where it was mathematically possible, and in the remaining cases – where perfect composition wasn’t achievable due to the demographic makeup of the volunteer pool – it still found the optimal solution.

2. Transparency: The entire process can be verified and explained. The code is open-source, and the results can be verified using clear metrics.

3. Accuracy with democratic fairness: The method is inherently fair because it uses probability in the selection process – everyone who volunteers has a chance to be selected. At the same time, it prioritizes what matters most: creating a genuinely representative group that can make decisions on behalf of the whole community.

4. Flexibility: The method can handle complex demographic criteria and special requirements, making it adaptable to different community needs.

Concluding remarks

The effectiveness of simulated annealing has been demonstrated in practice – from achieving perfect demographic matches to maintaining transparency in the selection process. Just as careful annealing transforms metal into its optimal state, this method helps create citizens’ assemblies that accurately reflect the communities they serve.

The fully functional script that uses simulated annealing for the random selection of citizens’ assemblies is available for download here.