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mathematics

Sortition

Sortition is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Sortition rather than just read about it. In short: In governance, sortition is the selection of public officials or jurors at random, i.e., by lottery, in order to obtain a representative sample. In ancient Athenian democracy, sortition was the traditional and primary method for appointing political officials, and its use was regarded as a principal characteristic of democracy.

Sortition — main illustration
Sortition — illustration

Key takeaways

  • Sortition belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Sortition to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Sortition from memory before moving on to harder problems.

Reference excerpt

In governance, sortition is the selection of public officials or jurors at random, i.e., by lottery, in order to obtain a representative sample. In ancient Athenian democracy, sortition was the traditional and primary method for appointing political officials, and its use was regarded as a principal characteristic of democracy. Sortition is often classified as a method for both direct democracy and deliberative democracy. Today, sortition is commonly used to select prospective jurors in common-law systems. What has changed in recent years is the increased number of citizen groups with political advisory power, along with calls for making sortition more consequential than elections, as it was in Athens, Venice, and Florence.

History

Ancient Athens

Athenian democracy developed in the 6th century BC out of what was then called isonomia (equality of law and political rights). Sortition was then the principal way of achieving this fairness. It was utilized to pick most of the magistrates for their governing committees, and for their juries (typically of 501 men).

Most Athenians believed sortition, not elections, to be democratic and used complex procedures with purpose-built allotment machines (kleroteria) to avoid the corrupt practices used by oligarchs to buy their way into office. According to the author Mogens Herman Hansen, the citizen's court was superior to the assembly because the allotted members swore an oath which ordinary citizens in the assembly did not; therefore, the court could annul the decisions of the assembly. Most Greek writers who mention democracy (including Aristotle, Plato, Herodotus, and Pericles) emphasize the role of selection by lot, or state outright that being allotted is more democratic than elections (which were seen as oligarchic). Socrates and Isocrates however questioned whether randomly-selected decision-makers had enough expertise. Past scholarship maintained that sortition had roots in the use of chance to divine the will of the gods, but this view is no longer common among scholars. In Ancient Greek mythology, Zeus, Poseidon, and Hades used sortition to determine who ruled over which domain. Zeus got the sky, Poseidon the sea, and Hades the underworld. In Athenian democracy, to be eligible to be chosen by lot, citizens self-selected into the available pool, then onto lotteries in the kleroteria machines. The magistracies assigned by lot generally had terms of service of one year. A citizen could not hold any particular magistracy more than once in his lifetime, but could hold other magistracies. All male citizens over 30 years of age, who were not disenfranchised by atimia, were eligible. Those selected through lot underwent examination called dokimasia to ensure citizenship and consider life, character, and at times, property; capacity for a post was assumed. Rarely were selected citizens discarded. Magistrates, once in place, were subjected to constant monitoring by the Assembly. Each magistrate appointed by lot was required, upon completion of his term, to render an account of his time in office, called a euthyna. Any citizen could request the suspension of a magistrate with due reason. A Kleroterion was used to allot officers and select eligible and willing citizens to serve jury duty. This bolstered the initial Athenian system of democracy by getting new and different jury members from each tribe to avoid corruption. James Wycliffe Headlam wrote that the Athenian Council, which consisted of 500 randomly selected male citizens, would commit occasional mistakes such as levying taxes that were too high. Headlam wrote that power did not tend to go to those who sought it, and deemed systematic oppression and organized fraud impossible due to widely and randomly distributed power combined with checks and balances. He stated that the Athenians largely trusted the system of random selection, regarding it as the most natural and the simplest way of appointment. Sortition was used for most positions, except for military positions such as strategos that were elected.

Lombardy and Venice – 12th to 18th century The brevia was used in the city states of Lombardy during the 12th and 13th centuries and in Venice until the late 18th century. Men, who were chosen randomly, swore an oath that they were not acting under bribes, and then they elected members of the council. Voter and candidate eligibility probably included property owners, councilors, guild members, and perhaps, at times, artisans. The Doge of Venice was determined through a complex process of nomination, voting and sortition. Lot was used in the Venetian system only in order to select members of the committees that served to nominate candidates for the Great Council. A combination of election and lot was used in this multi-stage process. Lot was not used alone to select magistrates, unlike in Florence and Athens. The use of lot to select nominators made it more difficult for political sects to exert power, and discouraged campaigning. By reducing intrigue and power moves within the Great Council, lot maintained cohesiveness among the Venetian nobility, contributing to the stability of this republic. Top magistracies generally still remained in the control of elite families.

Florence – 14th and 15th century Scrutiny was used in Florence for over a century starting in 1328. Nominations and voting together created a pool of candidates from different sectors of the city. The names of these men were deposited into a sack, and a lottery draw determined who would get to be a magistrate. The scrutiny was gradually opened up to minor guilds, reaching the greatest level of Renaissance citizen participation in 1378–1382. In Florence, lot was used to select magistrates and members of the Signoria during republican periods. Florence utilized a combination of lot and scrutiny by the people, set forth by the ordinances of 1328. In 1494, Florence founded a Great Council in the model of Venice. The nominatori were thereafter chosen by lot from among the members of the Great Council, indicating an increase in aristocratic power.

… excerpt ends here. Continue reading the full article.

Illustrations

Sortition illustration
Sortition: A kleroterion in the Ancient Agora Museum (Athens)
A kleroterion in the Ancient Agora Museum (Athens)
Sortition: USCAR Court select juries by sortition.
USCAR Court select juries by sortition.
Sortition: Drawing straws within a small group: one of four matches is broken to be shorter than the others, and the four are presented to the group to draw from, the chooser of the short match being selected
Drawing straws within a small group: one of four matches is broken to be shorter than the others, and the four are presented to the group to draw from, the chooser of the short match being selected
Sortition: A session of a German citizens' assembly in 2019. The participants sit around tables for deliberation in small groups.
A session of a German citizens' assembly in 2019. The participants sit around tables for deliberation in small groups.

Worked examples

Example 1 — a first encounter with Sortition

Start with the simplest possible case. Write down what Sortition claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Sortition before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Sortition ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Sortition

In research
Sortition appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Sortition in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Sortition is common in secondary-school and first-year university syllabi. It links to neighbouring topics Ancient Greece, Applications of randomness, Deliberative groups, so understanding it makes those chapters shorter.
In everyday life
Look for Sortition outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Sortition in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Sortition means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Sortition out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sortition in simple terms?

In governance, sortition is the selection of public officials or jurors at random, i.e., by lottery, in order to obtain a representative sample. In ancient Athenian democracy, sortition was the traditional and primary method for appointing political officials, and its use was regarded as a principa…

Why does Sortition matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Sortition?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Sortition.

Tags

  • Ancient Greece
  • Applications of randomness
  • Deliberative groups
  • Democracy
  • Democratization
  • Direct democracy
  • Elections
  • Sampling (statistics)

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