Random Selection and Democracy in Athens and Asimov
The NOVA episode “Athens: Birthplace of Democracy,” which aired on Arizona PBS on July 1, 2026, stated: “For the ancient Greeks, true democracy only worked through the extensive use of random selection.”
The candidate selection process in Isaac Asimov’s classic short story “Franchise” represents the opposite extreme, with no randomness (and perhaps no human input).
Let’s look at some aspects of random selection as it relates to democracy through these examples. This post contains questions and activities that could be used for a high school or undergraduate class discussion about the “fairness” of simple random, stratified, and systematic sampling — and of nonrandom selection methods. Learning objectives include deepening understanding of these sampling methods, distinguishing between proportional and disproportional allocation, calculating sampling weights for a stratified sample, and relating advantages and disadvantages of methods for political candidate selection to statistical principles of randomization. The footnotes contain some discussion questions for an advanced undergraduate or graduate-level sampling class.
There are spoilers ahead for “Franchise” (Asimov, 1955). You may want to read the story (one of my favorites) first and then come back to this post. The story is only 14 pages and is available at https://archive.org/details/1955-08_IF and other places online, and in various Asimov anthologies.
Sortition in Ancient Athens
When a jury or council was to be chosen in Athens around 450 BCE, citizens (free adult males born to an Athenian mother and father) would assemble in front of a kleroterion (derived from the Greek word for “lot” or “chance”; see Figure 1). Each citizen would place a bronze ticket containing his name in the basket corresponding to his tribe, and a ticket-inserter would shake the basket and insert the tickets into the column for that tribe. Then a random selection mechanism was used to accept or reject each row for jury or council service.
Figure 1. Kleroterion in the Ancient Agora Museum (Athens). Source: Wikimedia Commons.
The NOVA episode “Athens: Birthplace of Democracy” shows a reenactment of the voting process. Students place their ID tickets in small boxes, and the ticket-inserters for each tribe insert the tickets in the tribe’s column of a kleroterion that has been reconstructed by a sculptor. Black and white cubes are then mixed up, poured into a tube on the side of the kleroterion, and drawn one-by-one: the entire row of students is selected if a white cube is drawn and the entire row is rejected if a black cube is drawn. If the boxes are shaken well and the tickets are of identical size, so that each ticket has an equal chance of being grabbed as the next to be inserted into the kleroterion, a column contains the tickets from that tribe in random order. If the cubes are well mixed, then the selection of rows is random as well.
The Athenians viewed sortition (selection by drawing lots) as a way to forestall corruption in politics. If the selection of citizens for a jury was done using random mechanisms, no one would know in advance who the members would be. Citizens randomly selected for the Council of 500 served one year, and no citizen could serve more than twice in his life (and not more than once per decade). All of the random selection was done transparently, in public.
Essentially, as discussed in my post “Stratified Random Sampling, Aristotle, and Democracy” (Lohr, 2019), the sortition process gives a stratified random sample of the Athenian citizens who appear that day, with tribes as the ten strata. But is this the best design to use to obtain a representative sample? Let’s look at the Athenian sortition process in the context of the three principles of sampling given in Tillé and Wilhelm (2017).
Principle 1: Randomization. Randomization “consists not only in selecting a sample at random but as random as possible. A sampling design should assign a positive probability to as many samples as possible and should tend to equalize these probabilities between the samples” (Tillé and Wilhelm, 2017, pp. 179-180). A simple random sampling design has a high degree of randomness: every subset of size n from the population of size N has an equal probability of being chosen as the sample.
A systematic sampling design has a much lower degree of randomness. To choose a systematic sample of size n = 10 from a population list of size N = 1,000, generate a random integer k between 1 and N/n =100 and select units k, k + N/n, k + 2N/n, …, k+9N/n as the sample. If k =57, the systematic sample consists of units in positions {57, 157, 257, 357, 457, 557, 657, 757, 857, 957}. Many population subsets that could be selected under simple random sampling cannot be selected under systematic sampling. For example, the population subset {1, 2, 101, 102, 201, 202, 301, 302, 401, 402} could be chosen as the sample with a simple random sampling design but not with a systematic sampling design.¹
A sampling design with a high degree of randomness, such as the stratified sampling design used in Athens, makes it difficult for someone to predict in advance which sample will be chosen. A defendant who wanted to bribe the jury members would not know who was going to be chosen to serve on his trial until the morning of the trial.
Principle 2: Overrepresentation. In simple random sampling, each population unit has the same chance of being selected for the sample. The same is true for stratified random sampling with proportional allocation, in which the same proportion of sample members is chosen from each stratum. For example, if sampling from a population of 1,000 female and 4,000 male engineers, a proportionally allocated stratified sample of size 200 has 40 women and 160 men. Each person in the sample represents 25 persons in the population (this is called a self-weighting sample, since each person’s sampling weight is the same value, 25), but if separate estimates for men and women are desired, estimates about women have less precision than estimates about men because of the smaller sample size.
To get similar precision for estimates about men and women, you might want to take a disproportionate stratified random sample of 100 women and 100 men. When estimating characteristics of the entire population of 5,000 engineers, unequal weights compensate for the unequal chances of selection. Here, the weight for each sampled woman is 10 (each woman in the sample represents 10 women in the population) and the weight for each sampled man is 40 (each man in the sample represents 40 men in the population). The total number of publications written by the population of 5,000 engineers is estimated by 10 (total number of publications by the 100 sampled women) + 40 (total number of publications by the 100 sampled men). Women are overrepresented in the sample, and thus have lower sampling weights than the sampled men.
Unequal selection probabilities are also often used when units have vastly different sizes. A survey to estimate the monthly amount of retail sales in Phoenix, for example, might select stores such as Walmart and Target with higher probabilities than boutique stores with small sales. This reduces the standard error of the estimate because the large stores contribute much more to the total sales amount than the small stores.² It is essential, however, to use the sampling weights when calculating estimates from samples with unequal selection probabilities — otherwise, your estimates can be badly biased.
Each Athenian citizen selected for a jury was treated as if he had equal weight — Antiphon’s vote was not counted “more” than Glaucon’s vote, even if Antiphon had a lower probability of selection and was representing more citizens that day than Glaucon. Was this fair?
Principle 3: Restriction. A simple random sampling design gives each possible sample the same chance of being selected. The restriction principle excludes some population subsets from being selected as the sample. As we saw above, systematic sampling is a form of restricted sampling. So is stratified sampling. The Athenian stratified sampling procedure forces the sample to have the same number of representatives from each tribe — samples that have unequal representation from the tribes cannot be selected under the procedure.
When used well, the restriction principle exploits auxiliary information known about the population units to prevent “bad” samples, such as those in which some tribes would have no members selected. Stratified sampling with proportional allocation forces the sample to have the same proportion of members in each stratum as the population. The sample is thus perfectly representative of the population with respect to the variable defining stratum membership, and is expected to be more similar to the population for characteristics associated with stratum membership than a simple sample of the same size.
One can restrict the randomization even more by using balanced sampling. Balanced sampling designs select a sample so that sample estimates closely match the population means for key characteristics where the population means are known. For example, you can select a balanced sample of citizens in which the average income, height, age, years of education, blood pressure, number of musical instruments played, etc. from the sample equal the population means of those characteristics. Stratified sampling is a special case in which the key characteristics are the counts in the cross-classification of the stratification variables.
The restriction principle clashes somewhat with the randomization principle, since some population subsets have zero chance of being selected as the sample when there are restrictions on the randomization. Each restriction moves the sample further away from pure random selection. If you add too many constraints to the balanced sampling, it may be impossible to find a sample that meets all of them. Or there may only be one or two possible samples that meet the restrictions, and you may also be able to predict in advance which population members will be chosen for the sample.⁴ How should one balance randomization with restrictions?
Candidate Selection in “Franchise”
The authors of The Federalist Papers rejected direct democracy and sortition as a method for selecting members of the U.S. Congress. They instead advocated for a system in which voters elected men to represent them in Congress. As in Athens, the right to vote was restricted to free men, and most state limited the franchise to landowners. Isaac Asimov’s story “Franchise” explores an extreme limitation of the right to vote.
The teaser for “Franchise” reads: “It was a frightening thing to happen to a person; the responsibility was just too great. But Norman Muller couldn't back out. Multivac had chosen him, and the entire nation waited…” (Asimov, 1955, p. 2).
Multivac is Asimov’s remarkably accurate imagining of an AI data center. At “half a mile long and three stories high” (Asimov, 1955, p. 12), Asimov’s fictional computer is comparable in size to today’s data centers: Microsoft’s Fairwater facility in Wisconsin covers 315 acres (half of a square mile).³ By the year 2008, when the story takes place, Multivac makes all the decisions about political candidates but chooses one (male) voter to provide “input” into the process.
According to Norman’s father-in-law, the road to Multivac determining all the election results began with people’s impatience to learn election results. At first, computers were used to forecast election results from the first few votes that were cast (much like news organizations do today, using early returns and exit polls). As computers improved, “they could tell how the election would go from fewer and fewer votes. Then, at last, they built Multivac and it can tell from just one voter." (Asimov, 1955, p. 7).
Secret service agent Phil Handley explains to Norman how he was chosen as the one voter to represent the United States in the election of November 4, 2008:
Multivac weighs all sorts of known factors, billions of them. One factor isn't known, though, and won't be known for a long time. That's the reaction pattern of the human mind. All Americans are subjected to molding pressure of what other Americans do and say, to the things that are done to him and the things he does to others. Any American can be brought to Multivac to have the bent of his mind surveyed. From that the bent of all other minds in the country can be estimated. Some Americans are better for the purpose than others at some given time, depending upon the happenings of that year. Multivac picked you as most representative this year. Not the smartest, or the strongest, or the luckiest, but just the most representative. Now we don't question Multivac, do we? (Asimov, 1955, p. 9)
Multivac does not ask Norman about his political opinions or candidate preferences. As Handley puts it: "Multivac already has most of the information it needs to decide all the elections, national, state and local. It needs only to check certain imponderable attitudes of mind and it will use you for that. We can't predict what questions it will ask, but they may not make much sense to you, or even to us. It may ask you how you feel about garbage-disposal in your town; whether you favor central incinerators. It might ask you whether you have a doctor of your own or whether you make use of National Medicine, Inc." (Asimov, 1955, p. 13). After the three hours of questioning, Norman can remember only one question: “What do you think of the price of eggs?” to which he responded “I don’t know the price of eggs.”
Although he has not voted in any sense recognizable to us, and has no idea which candidates were chosen by Multivac or how his answers contributed, at the end of the story Norman feels proud that he has represented the entire American electorate. “In this imperfect world, the sovereign citizens of the first and greatest Electronic Democracy had, through Norman Muller (through him!) exercised once again its free, untrammeled franchise” (Asimov, 1955, p. 15).
Some Class Activities and Questions for Discussion
Have the class carry out a reenactment of the Athenian sortition process. How should the tribes be formed so that the procedure:
a. Has the highest possible degree of randomness?
b. Gives every student the same probability of being selected for the sample?
c. Gives each male student a lower chance of being selected than each female student? (Hint: tribes do not have to be the same size)
When does the kleroterion sampling procedure result in a self-weighting sample of the citizens who show up on selection day? (Also see exercise 3.11 of Lohr, 2022, which asks students to calculate the selection probabilities for the sample.) Under what circumstances does the sampling procedure result in a self-weighting probability sample of the citizens in the ten tribes?
Would you want to use overrepresentation when selecting a jury or council by sortition? Or would you want a self-weighting sample, in which each population member has an equal chance of being selected for the sample? Why? What are the advantages and disadvantages of each type of sample in this context?
Suppose a wealthy would-be tyrant wants to corrupt the sortition process to obtain a council sympathetic to his interests. How might he exploit:
a. A sampling design with a low degree of randomness?
b. The tribe formation process?
c. Criteria for citizenship eligibility?
d. The ticket-insertion process?
One way in which some people try to influence elections is through gerrymandering — manipulating district boundaries to favor one party or group (for example, packing members of a group into one district so that the group gets only one representative). How would gerrymandering tribal formation affect the fairness of the Athenian sortition process?
How would you improve the sortition procedure used in ancient Athens?
For most of U.S. history “jurors were overwhelmingly male, jurors were overwhelmingly white, and jurors disproportionately hailed from the middle and upper social classes” (Frampton, 2025, p. 372). Congress first mandated random selection of juries in The Jury Selection and Service Act of 1968. How are juries selected in your community? Are they a random sample of adult citizens?
Read The Federalist Number 10. What are Madison’s arguments for delegating government “to a small number of citizens elected by the rest”? What are the relative advantages and disadvantages of representative democracy through election and choosing citizens at random through sortition, for (a) choosing a legislature? (b) choosing a jury? (c) selecting registered voters of a political party for a convention that will choose a new candidate to replace a candidate who withdrew after the primary election?
What kind of sampling is used in Asimov’s story “Franchise”? How “representative” is Norman, when compared with the sample of persons who vote in a typical election, or with a sample of citizens chosen through a random sortition process? How do you think Multivac selected Norman as “Voter of the Year” and used his responses to questions?
Is Asimov correct that you can predict an election result from relatively few voters? What about no voters? In the 2024 U.S. House of Representatives elections, 94% of incumbents (366 out of 381) won their bid for re-election. What other variables might be used in a regression model predicting election results?
How close is Asimov’s imagining of early election forecasting on p. 7 of “Franchise” (“they invented special machines which could look at the first few votes and compare them with the votes from the same places in previous years”) to the procedure media outlets use to call winners after an election, as described in https://electioninnovation.org/research/how-election-results-coverage-really-works/?
Copyright (2026) Sharon L. Lohr
Footnotes and References
1Entropy is sometimes used as a measure of a design's randomness. Let P(S) equal the probability that population subset S is chosen as the sample under the design. Let Q denote the set of all possible samples of size n from a population of size N that have P(S) > 0. Then the entropy of the sampling design is
I = – ∑S ∈ Q P(S) log[P(S)].
With a high entropy design, it is difficult to predict in advance which sample will be chosen (see Tillé and Haziza, 2010, and Grafström, 2010).
Question: For a simple random sample, show that the entropy is log N! - log n! - log (N-n)!, and that this is the maximum entropy possible for a design that draws a fixed sample size n. What is the entropy for a systematic sampling design?
²I used unequal selection probabilities in my stratified random sampling design to estimate the crime counts for the set of Arizona law enforcement agencies that did not report their 2021 data to the FBI (Lohr, 2026). All five agencies in the stratum containing the Phoenix, Tucson, Glendale, and Tempe Police Departments and the Maricopa County Sheriff’s Office were included in the sample. These agencies account for a large fraction of the total number of crimes in the state, so sampling them with probability 1 means that we get their exact crime count and the variance of the total number of crimes for that stratum is zero. Law enforcement agencies for cities with population less than 10,000, on the other hand, have relatively few crimes, so I sampled 4 of the 32 agencies in that stratum and each sampled agency had a weight of 8. Using different sampling fractions for the strata reduces the variance of the estimated total number of crimes, since the larger agencies, which have more variability in crime counts, are oversampled relative to the smaller agencies.
³In a later Asimov story, “All the troubles of the world,” Multivac “had grown in fifty years until its various ramifications had filled Washington, D.C. to the suburbs and had reached out tendrils into every city and town on Earth” (Asimov, 1958, p. 34). In this story, Multivac directs Earth’s economy and is “the central clearing house of all known facts about each individual Earthman.”
⁴Question: Generate a population of size 12 and a balanced sampling scheme in which no sample of size 6 approximately meets the balancing constraints (hint: use income as a balancing variable). Generate another population of size 12 in which exactly two of the possible samples meet the constraints. By contrast, how many possible simple random samples of size 6 can be selected? How many stratified random samples can be selected, when the population is divided into three strata and two units are randomly selected per stratum?
Asimov, I. (1955). Franchise. If: Worlds of Science Fiction, August, 2-15.
Asimov, I. (1958). All the troubles of the world. Super-Science FIction, April, 34-52.
Frampton, T.W. (2025). The radical roots of the representative jury. Yale Law Journal, 135: 372-460.
Grafström, A. (2010). Entropy of unequal probability sampling designs. Statistical Methodology, 7, 84-97.
Lohr, S. L. (2019). Stratified random sampling, Aristotle, and democracy, https://www.sharonlohr.com/blog/2019/11/20/stratified-random-sampling-aristotle-and-democracy.
Lohr, S. L. (2022). Sampling: Design and Analysis, 3rd edition. Boca Raton, FL: CRC Press.
Lohr, S. (2026). Estimating crime counts and characteristics from NIBRS Data. Journal of Quantitative Criminology, http://dx.doi.org/10.1007/s10940-025-09650-6, published online 12 March 2026. You can access a view-only version of the article through this link.
Lopez-Rabatel, L. and Sintomer, Y. (2020, eds). Sortition and Democracy: History, Tools, Theories, Exeter, UK: Imprint Academic.
Roberts, J.T. (2024). Out of One, Many: Ancient Greek Ways of Thought and Culture. Princeton: Princeton University Press. Chapter 4 describes the historical context of Athenian democracy.
Tillé, Y. and Haziza, D. (2010). An interesting property of the entropy of some sampling designs. Survey Methodology, 36(2), 229-231.
Tillé, Y. and Wilhelm, M. (2017). Probability sampling designs: Principles for choice of design and balancing. Statistical Science, 32(2), 176-189.