# Why random selection of political leadership is not chaotic but remarkably stable

This article explores selecting legislative leadership by random selection, otherwise known as sortition. Sortition is sometimes criticized for being “too random”. To be charitable, I take this criticism to mean that sortition produces chaotic results due to random chance. However contrary to intuition, when sortition is used to selected hundreds of people at a time to form a legislature, sortition results in remarkable stability.

# Unlikelihood of Extremist Domination

A typical argument against sortition goes like this: because of random chance, it’s possible that a crazy group of extremists will be selected into an assembly. Well, exactly how likely is this scenario? Fortunately statistics can be used to estimate the likelihood using a binomial distribution.

Let’s assume a huge percentage of a country believes in Nazi extremist ideology. In the Weimar Republic for example, the Nazi party achieved 33% of the vote under free elections (in subsequent elections, political opponents were harassed and killed). In such an environment, what is the likelihood that Nazis would dominate a sortition assembly? We can calculate the likelihood using this chart shown below. In this chart, the y-axis shows the percentage of extremists in a population from 5% to 50%. On the x-axis, the size of the sortition assembly is varied from 30 to 1000. For each of these parameters, the probability that the extremist faction obtains a majority in the assembly (and therefore achieves domination) is calculated.

For an assembly of 100 people, if the number of extremists in the population is 35%, the likelihood of domination by extremists is only 0.15%, or 1 in 667 lotteries. For an assembly of 500 people, the likelihood of extremist domination is 4.4x10^-10, or 1 in 227 *billion *lotteries. In other words, you’re far more likely to win the megamillions lottery several times over than for the Nazis to take over, even in the worst case scenario where electoral support is at its peak in 1932 Weimar Germany.

# Preference Stability

You might respond, it’s interesting that sortition is able to prevent extremist domination, and you’ve set the bar too low! How can we be sure that the decisions made by one assembly will resemble the decisions made by another, when random chance is involved?

Well, exactly how chaotic would the preferences of a sortition assembly be? Preferences can be approximately modeled using a 1-dimensional, spatial preferences of a Gaussian or normal probability distribution. In such a model, the median member of the assembly would control all decision making by forming a majority coalition. How would the median member change after simulations of 1 million lotteries? We can simulate the formulation of 1 million random assemblies and observe how the median member changes from one assembly to another. Statistics for the median preference of the assembly, given assembly sizes from 30 to 1000 people, are shown in Figure 2. The median preference population density function for an assembly of 500 people is shown in Figure 3 as a histogram. This histogram plots the preference distribution of the population against the arbitrary preference axis, which has units in terms of the standard deviation of the distribution.

For a 500 member assembly, in 50% of trials, the median preference is within 3.8% of a standard deviation of the population preference. In 98% of the trials, the median preference is within 13% of a standard deviation of the population preference. At the maximum after 1 million trials, the largest observed median preference difference from the population was 26% of a standard deviation.

In other words, the preferences of the median member of a sortition assembly will be very close to the median preferences of the population for the vast, vast majority of all lotteries. And in the worst case, the median preference is about a quarter of a standard deviation. In other words, variance is small. The decisions made by a random sortition assembly will be very good at approximating the preferences of the population median.

# Concluding Remarks

Counter to intuition, a sortition assembly is not chaotic and does not produce “random” results. Instead, sortition and random selection would lead to a more stable government from one lottery to another compared to elections. This is in stark contrast to US Congress, where median political ideology swings wildly from one extreme to another after each election. In contrast to random lottery, several factors make elections wild and unpredictable:

Who decides to run for office

Who decides to fund & endorse a politician’s campaign

The number of candidates that decide to run, and their ideologies which may cause vote splitting.

Who decides to vote, and people who decide that they’re too disgusted by the whole process to bother to vote.

The chaos of the rules of primary elections, general elections, runoff elections, and instant runoff elections.

With superior ability to estimate the median preference of a population, sortition is better able to satisfy the preferences of a population compared to elections.

This is only true if those randomly drawn actually serve. For tasks that take a long time, or a lot of work, many people may decline resulting in self-selection bias. We either need quasi-mandatory service or multiple bodies with different levels of effort required. To be clear, even with some self-selection bias democratic lotteries will generate bodies that are likely to be far more representative than any elected legislature. The proposal I have made to address the problem of less-representative citizen assemblies is to use multiple bodies for different tasks. Bodies requiring longer duration or effort (agenda setting, drafting, reviewing drafts, etc.) might be smaller and somewhat less representative, with the final adopt or reject decision being made by a large, short-duration (possibly mandatory service) jury to maximize representativeness. A journal article I wrote about mult-body sortition is here:

https://delibdemjournal.org/articles/abstract/10.16997/jdd.156/

It would be great if someone with the skills and resources would create a sortition wiki that could be used to discus and develop a "constitution of sortition" so to speak, that a govt could eventually use as a guideline or adopt. This might also generate general interest and understanding of exactly what is proposed.