Tech Breakfast
2023-10-05
For more than two thousand years, until the 18th century, democracy was seen as the rule of the people, when political institutions emerge directly from the people largely by lot(tery).
Es gilt z. B. für demokratisch, daß die Staatsämter durchs Los, für oligarchisch, daß sie durch Wahl besetzt werden“
– Aristoteles: Πολιτικά (Politik), 345 bis 325 v. Chr.
Eligible for public offices:
Deputies, judges and most senior officals were determined by lot.
The random distribution of this office was an essential pillar of democracy:
I judge my neighbour and he judges me.
– Franziska Weise
N rows and M columns of slots (e.g. N=50, M=5 (but also M=11))
The first significant examination of Athenian allotment procedures was Headlam-Morley (1891): On Election by Lot at Athens
General mistrust against too powerful persons and groups
This method was also adopted in Orvieto, Siena, Pistoia, Perugia and Lucca
This lottery procedure “is more likely to promote good life, sound administration and government in the towns and cities than the orders which, conversely, are based on election. They are more united and equal, more peaceful and free from passions”.
– King Ferdiand II
“The suffrage by lot is natural to democracy; as that by choice is to aristocracy.” „Die Entscheidung durch das Los entspricht dem Wesen der Demokratie, die Entscheidung durch Wahl dem der Aristokratie.“
–- Baron de Montesquieu: De l’esprit des loix (Vom Geist der Gesetze), 1748
But:
French Revolution: Hereditary nobility replaced by elected nobility
French Republic, not French Democracy!
Democracy is possible only if the decision-makers are a representative sample of the people concerned.
– John Burnheim (1985): Is Democracy Possible?
If you have cooked a large pan of soup, you do not need to eat it all to find out if it needs more seasoning. You can just taste a spoonful, provided you have given it a good stir.
– George Gallup
How many samples \(n\) from a total of \(N\) items do we need, so that our sample is representative?
The formula for computing the sample size \(n\) of a finite population \(N\) \[ n = \frac{n_\infty}{1 + \frac{n_\infty - 1}{N}} \] where the sample size for an infinite population \(n_\infty\) is given as \[ n_\infty = \frac{z^2 p(1-p)}{e^2} \] with the the z-score \(z\) for a specific confidence level, the margin of error \(e\) of your sampling results and \(p\) being the proportion of the population picking a specific choice (\(p=50%\) generates maximal sample sizes).
If you want to be confident that in 95% of the decisions the parliament represents the will of the people within an error margin of 5%, the sample size formula suggest a parliament size of 384 people (for a population > 1 million)
If the European Parliament with 751 seats would be selected by lot in 95% of the cases the will of the european people would be represented with a margin of error of about 3.5 %.
For a village with 1000 persons, we need 440 in the “Gemeinderat” for the same margin of error.
=> Sortition/Selection by lot is much more efficient for bigger population sizes
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Dr. Andreas Maier
Senior Data Scientist
andreas.maier@um-orange.com