Enough in total.
One group empty.
Ten people could fill two rows of five.
But ten arrivals do not promise two people
in every letter group.
Keep the total. Exchange who turns up.
What does the shortest group decide?
A small modern attendance experiment beside
Constitution of the Athenians, 63.4 and 64.3.
A total is not a full row.
The assumptionsFive letter groups of one tribe, represented by modern tags A–E. Start with four possible people per group and a request for two per group. Keep this attendance, then exchange arrivals until every group meets the request. No person changes their group.
Slots show counts, without assigning identities to positions. Filled slots are present; dashed slots are absent. The line marks the requested count.
The total is ten, but group E is empty. Keep this example before replacing attendees.
How often does a total fill every group?
Read the exact chance at every total
Why count patterns are not equally likely
Each potential person is distinct. A pattern such as 2–2–2–2–2 represents many different individual subsets. An extreme pattern represents fewer. The table counts those subsets, instead of treating every pattern as equally probable.
Choose a pattern to construct it at the same total. The complete weighted list is included in CSV and the illustrated reading.
Read what the lots decide.
Back to the boardClose English
Loading the printed witness…
Leaf 77 and leaf 78 both print the heading LXIV. The chapter-64 page is leaf 77, where sequential numbering would give LXIII. We retain the printed heading and identify the leaf. Inspect this page at Internet Archive.
Read the edition and source record
F. G. Kenyon, Aristotelis Atheniensium Respublica, Oxford, first published 1920; the scanned imprint lists reprints through 1958. The work is late fourth century BCE and conventionally attributed to Aristotle. Square brackets retain this editor’s supplies, including supplies crossing a word boundary. English and word notes are new. All three full pages retain the critical apparatus. The row mechanism follows a material interpretation of the text, rather than treating the old translation “balloting-room” as a machine description.
Source and license notice · Retrieval and rendering record · File identities · Center for Hellenic Studies: jury selection
Keep the missing condition.
Why can the same total fail or succeed? What does παραπλησίως ἴσοι say about the registered groups, and what does it leave unknown about daily attendance?
This page does not autosave. An editable study keeps the counts, population, request, comparison and explanation.
Take this study with you.
The link includes current and kept counts, but excludes your explanation. The illustrated reading embeds the exact curve, all weighted patterns, Greek, English, full source pages, fonts and licenses.
What the total cannot tell us.
Registered groups are not daily arrivals
Chapter 63.4 describes ten approximately equal letter groups within each tribe. Chapter 64.3 describes a cube for five tickets. The ancient text does not specify how officials handled a day with too few people in one group.
A modern finite population
Five represented groups, each with four, six or eight distinct possible people. The request is the same in every group. These sizes, attendance counts and equal full-row requirement are teaching assumptions. The inserter, total jury quota and later courtroom allocation are outside this model. Historical service concerned eligible male citizens with age and status restrictions (63.3), not all Athenians.
A stated sampling assumption
The exact probabilities assume an unbiased subset of a fixed size, sampled without replacement from this small population. Real jurors might travel together or choose when to attend. The random model does not establish a historical turnout rate.
A question in scholarship
David C. Mirhady and Carl Schwarz, “Dikastic Participation” (2011), pp. 753–757, investigate turnout under an explicitly random-arrival model and discuss the unanswered question of uneven groups. This bench uses a smaller, exact modern count. The article remains an online reference; the retained ancient-text pages work offline.
Read the row-selection clause in the separate allotment workshop. That workshop starts with complete rows; this one tests whether attendance can supply them.