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Kleroterion

Kleroterion 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 Kleroterion rather than just read about it. In short: A kleroterion (Ancient Greek: κληρωτήριον, romanized: klērōtērion) was a randomization device used by the Athenian polis during the period of democracy to select citizens to the boule, to most state offices, to the nomothetai, and to court juries. The kleroterion was a slab of stone incised with rows of slots and with an attached tube.

Kleroterion — main illustration
Kleroterion — illustration

Key takeaways

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

Reference excerpt

A kleroterion (Ancient Greek: κληρωτήριον, romanized: klērōtērion) was a randomization device used by the Athenian polis during the period of democracy to select citizens to the boule, to most state offices, to the nomothetai, and to court juries. The kleroterion was a slab of stone incised with rows of slots and with an attached tube. Citizens' tokens—pinakia—were placed randomly in the slots so that every member of each of the tribes of Athens had their tokens placed in the same column. There was a pipe attached to the stone which could then be fed dice that were coloured differently (assumed to be black and white) and could be released individually by a mechanism that has not survived to posterity (but is speculated to be by two nails; one used to block the open end and another to separate the next die to fall from the rest of the dice above it, like an airlock.) When a die was released, a complete row of tokens (so, one citizen from each of the tribes of Athens) was either selected if the die was coloured one colour, or discarded if it was the alternate colour. This process continued until the requisite number of citizens was selected.

History Prior to 403 BC, the courts published a schedule and the number of dikastes required for the day. Those citizens who wanted to be dikastes queued at the entrance of the court at the beginning of the court day. Originally, the procedure was based on a "first come, first serve" basis. Beginning in 403 BC, Athenian allotment underwent a series of reforms, and from 370 BC onwards, they employed the kleroterion.

Procedure In his Constitution of the Athenians, Aristotle gives an account of the selection of jurors to the dikastra. Each deme divided their dikastes into ten sections, which split the use of two kleroteria. Candidate citizens placed their identification token (pinaka) in the section's chest. Once each citizen who wished to become judge for the day placed their pinaka in the chest, the presiding archon shook the chest and drew out tokens. The citizen whose token was first drawn became the token inserter (empektes) and also was automatically selected as a juror. The token inserter then pulled out tokens and inserted them into their corresponding sections. The kleroterion was divided into five columns, one column per tribe section (between two machines). Each row was known as a kanomides. Once the token inserter filled the kleroterion, the archon then placed a mix of black and white dice (kyboi) into the side of the kleroterion. The number of white dice was proportional to the number of jurors needed. The archon allowed the dice to fall through a tube on the side of the kleroterion and drew them one by one. If the die was white, the top row was selected as jurors. If the die was black, the archon moved on to the next row down from the top and repeated the process until all juror positions were filled for the day.

Scholarship The first significant examination of Athenian allotment procedures was James Wycliffe Headlam's Election by Lot, first published in 1891. Aristotle's Constitution of the Athenians, the text of which was first discovered in 1879 and first published as Aristotle's in 1890, became an important resource for scholars. Throughout the text, Aristotle makes references to a lottery system which was used to appoint government officials. Archaeologists first discovered kleroteria in the 1930s in the Athenian Agora, dating them to the second century BC. In Aristotle, the Kleroteria, and the Courts (1939), Sterling Dow gave an overview and analysis of the discovered machines. Contrary to previous scholars, who translated kleroterion as "allotment room," Dow reasoned that kleroterion cannot be translated to mean "room," as Aristotle writes "εἰσὶ δὲ κανονίδες [πέντε ἐ]ν ἑκάστῳ τῶν κληρωτηρίων" ("There are five kanonides in each of the kleroteria"). Dow concluded that Aristotle's fourth-century description of the kleroterion also applied to the second-century kleroterion. In 1937, Dow published a catalog of his archaeological discoveries in the Athenian agora. He lists eleven physical fragments of kleroteria:

See also Sortition Lottery machine

References Dibbell, Julian (September 1998). "Info Tech of Ancient Democracy". Alamut.com. Demont, Paul (December 2010). "Allotment and Democracy in Ancient Greece". Books and Ideas. Orlandini, Alessandro (April 2018) https://www.academia.edu/36510282/KLEROTERION._simulation_of_the_allotment_of_dikastai. simulation of the allotment.

External links Patrice Masini, Le tirage au sort démocratique, CNRS Images (2017) (a short video by French scholars) Alessandro Orlandini, https://m.youtube.com/watch?v=gt9H7nbZjAw, (2018) (video of the procedure simulation) The Machine that Selected the Citizens of Athens

Illustrations

Kleroterion: A kleroterion in the Ancient Agora Museum (Athens)
A kleroterion in the Ancient Agora Museum (Athens)
Kleroterion: A large kleroterion at the Ure Museum of Greek Archaeology in Reading, Berkshire
A large kleroterion at the Ure Museum of Greek Archaeology in Reading, Berkshire

Worked examples

Example 1 — a first encounter with Kleroterion

Start with the simplest possible case. Write down what Kleroterion 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 Kleroterion 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 Kleroterion 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 Kleroterion

In research
Kleroterion 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 Kleroterion 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
Kleroterion is common in secondary-school and first-year university syllabi. It links to neighbouring topics Ancient Greece, Athenian democracy, Democracy, so understanding it makes those chapters shorter.
In everyday life
Look for Kleroterion 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 Kleroterion in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Kleroterion 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 Kleroterion out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kleroterion in simple terms?

A kleroterion (Ancient Greek: κληρωτήριον, romanized: klērōtērion) was a randomization device used by the Athenian polis during the period of democracy to select citizens to the boule, to most state offices, to the nomothetai, and to court juries. The kleroterion was a slab of stone incised with ro…

Why does Kleroterion 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 Kleroterion?

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 Kleroterion.

Tags

  • Ancient Greece
  • Athenian democracy
  • Democracy
  • Sampling (statistics)

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