Sortition in the Bulletin of the Institute of Mathematical Statistics

The Bulletin of the Institute of Mathematical Statistics has published a column of mine that deals with the historical and theoretical connections between democracy and statistical sampling:

Democracy and statistical sampling

For about 2,500 years, statistical sampling was closely linked with democracy. “Selection by lot is natural to democracy, as that by choice [i.e., elections] is to aristocracy,” asserted Aristotle in the 4th century BC, following his own first-hand experience at Athens and the conventional wisdom of his time. Montesquieu concurred in the first half of the 18th century. It was only in the last 200 years, as democracy displaced aristocracy as the legitimate organizing principle of politics, that sortition—the delegation of power by statistical sampling—had to be air-brushed out of history and political science. […]

As part of the attempt to dismiss sampling as a political device it is sometimes claimed today that its use in Athens was motivated by the superstition that randomization allowed the gods to make the selection. However, the historical record indicates that the main motivation behind the practice was the law of large numbers. It was expected that sortition would produce a group that would mirror the population in important respects. This was often stated as an expectation of resemblance between the population and the sample in terms of wealth and social status (i.e., that most members would be poor commoners) but it was taken for granted that these characteristics would be correlated with certain interests and beliefs.

Today it is accepted that certain groups—such as those defined by gender, ethnicity and sexual orientation—should be present in a democratic government according to their proportion in the population. Again, it is taken for granted that those characteristics are correlated with certain interests and beliefs and those should be represented in government proportionally. And yet gross distortions in terms of other characteristics—for example, age, wealth, profession and education—are matter-of-factly accepted as natural, and possibly desirable. Undoubtedly, those characteristics are correlated with interests and beliefs as well, and unless [the] premise that some people are better off being represented by those who are naturally their betters is accepted, then it is hard to understand how such a government could be considered democratic. Furthermore, since such distortions are unavoidable in any electoral system, and indeed in any deterministic selection system, it is hard to understand how any system in which representation is not based on statistical sampling could be considered democratic.

35 Responses

  1. Thanks Yoram,

    Since you mention what “the historical record indicates”, I would have loved some presentation of that historical record.

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  2. Also, I liked this passage:

    Today it is accepted that certain groups—such as those defined by gender, ethnicity and sexual orientation—should be present in a democratic government according to their proportion in the population. Again, it is taken for granted that those characteristics are correlated with certain interests and beliefs and those should be represented in government proportionally. And yet gross distortions in terms of other characteristics—for example, age, wealth, profession and education—are matter-of-factly accepted as natural, and possibly desirable. beliefs as well, and unless Jefferson’s premise—that some people are better off being represented by those who are naturally their betters—is accepted, then it is hard to understand how such a government could be considered democratic.

    In the rest of that paragraph you say this:

    Undoubtedly, those characteristics are correlated with interests and Furthermore, since such distortions are unavoidable in any electoral system, and indeed in any deterministic selection system, it is hard to understand how any system in which representation is not based on statistical sampling could be considered democratic.

    I’m broadly in sympathy with this view and think it hits home logically. Nevertheless Jefferson’s aspiration is also a worthy one. By the end of his life he despaired at the fact that those being elected in Jacksonian America weren’t exactly aristoi.

    I think it’s actualy important to keep the question of merit in mind as we discuss democracy. Wikpedia works most fundamentally because it offers a reliable method of choosing better text from worse and it’s only when that problem is solved that its openness of ‘democratic’ nature further strengthens it.

    Likewise both you and I believe that chambers chosen by sortition would, generally function well as clearing houses for social and political ideas – and that whether or not they replaced elected houses – could play a powerful role in democratising and, I would say, humanising our existing politics. That having been said I always want to keep that question of merit closely alongside the question of representativeness which is why I think there’s a whole repertoire of mechanisms of choosing the meritorious and distinguished that are friendlier to the spirit of true democracy that interdict the way in the current system, gaining power and distinction is so inextricably tangled up in self-assertion as I argued here

    https://www.themandarin.com.au/83008-leadership-without-careerism-possible/

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  3. Hi Nick,

    The column has a word-limit that did not allow going into details on this issue or many others that could bear elaboration and that are often elaborated on Equality-by-Lot.

    Two pieces of evidence that come to mind regarding the expectation for proportionality in the sampling (and that I mentioned before) are Aristophanes’s complaints in Wasps about the old being over-represented in the courts, and Isocrates’s suggestion in Areopagiticus that elections are more democratic than sortition because sortition can, due to chance misrepresentation, put the elite in power.

    In general, democracy was explicitly and conventionally associated with both sortition and “equality according to number” (Aristotle, Politics, 1317b). I seems to me that one has to read the sources very tendentiously to develop a point of view that puts the association of sortition with proportional representation in doubt.

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  4. Do you really make the claim that elections are a mechanism that selects for merit? They clearly don’t. They select for those who are able to garner public attention – the rich, the famous, the well-connected.

    Nomination by an allotted body, on the other hand, is a mechanism that can produce nominees that are meritorious according to the standards the allotted (which should reflect the standards of the population from which they are drawn) and to the understanding of the allotted (which should be informed by the resources that they have at their disposal and by the motivation they have knowing their decisions count).

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  5. Elections choose on merit – it’s a meritocratic system.

    Both of us presumably find the public’s judgement of merit as reflected in the representatives they vote in, less than ideal.

    In just the same way, there are lots of useless people ‘chosen on merit’ in our bureaucracies and in all sorts of other places.

    We are living through a crisis of meritocracy. Not that merit isn’t important – indeed I’m arguing it’s very important and in some ways more important than democracy – but our own age seems poorly aware of the limitations of these putatively meritocratic systems.

    Which underscores how profound and potentially widespread would be the value of sortition and other random(ised) means of selection.

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  6. No – elections are not merit based. The issue is not that the public is making poor choices (in someone’s opinion). The public itself is unhappy with the elected politicians.

    The issue is that elections by their very nature guarantee that credible candidates (i.e., candidates whose names are even known to a significant proportion of the voters) are un-representative and thus cannot be expected to represent the interests of the citizens, and as a rule do not. By the time the people show up in the voting booths, the game is all over.

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  7. Yoram,

    We’re just using words differently here.

    There’s not much more to say on that score.

    As for the public being unhappy with elected politicians, if they’re looking for those responsible, do you think a mirror could help them home in on at least part of the problem?

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  8. > do you think a mirror could help?

    No. That’s exactly the point. Within the electoral system there is really nothing the public can do. “Electoral choice” is to a large extent a contradiction in terms.

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  9. You don’t think the electorate might have sent a message they didn’t like shifty characters by voting against Nixon, when they knew of Watergate in 1972 but relected him by a landslide or perhaps in Australia against Keating when five years after barnstorming the country arguing we’d be a banana republic if we didn’t have a VAT won an election saying a VAT would be a monster tax on every household, or voting against John Howard for saying that refugees chucked their kids in the water when it was obvious he had no evidence and evidence had emerged that they’d not done such a thing by the time of the election.

    Do you think they might have exercised some agency in getting themselves NOT lied to?

    The electorate hates negative advertising too. You can ask them and they’ll tell you that. Why do you think they get so much negative advertising? A cartel of political parties imposes it on them?

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  10. Presumably the voters felt more strongly against the alternatives than they did against Nixon, Keating and Howard. That’s not an endorsement of Nixon, Keating or Howard – it’s a condemnation of the electoral mechanism.

    As for negative advertising: parties use it because it works, presumably. That doesn’t mean that the public likes it. What is the alternative? The public is supposed to vote for someone about whom they have heard bad things simply because they “don’t like negative advertising”? Who knows, maybe all the bad things are true? Again, this is not an endorsement of negative advertising – it is a condemnation of the electoral mechanism.

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  11. Yoram,

    I’m trying to make the point that the public is complicit in the outcomes of elections – and those outcomes are not just who gets elected but their conduct in getting there. As you admit, voting for a candidate that lies, is an endorsement of that candidate at least over the alternative – an assertion that the alternative is worse.

    You bat all this back as if we were in a TV candidates debate and I’m arguing it’s all your party’s fault and you reply by saying that that it’s all my party’s fault.

    It’s clearly a constrained choice the public making, but then any way of making collective decisions constrains choices. On the way to making a collective decision options are always coraled into some form which can then be put to a vote or other determination of collective will.

    Telling me that voters bear no responsibility for the choices made in elections – regarding their implicit endorsement or disendorsement of relative alternatives regarding policies, people and conduct isn’t worthy of our time.

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  12. Nick,

    I am not trying to score debate points here – I am merely writing what I believe is the case. (Why would I try to score points? Unlike an electoral candidate I make no personal gain by manipulation or dissembling.)

    If you wish, yes, the voters have the responsibility for their choice of candidate A over B. My point is that this is not only a constrained choice – it is so constrained as to be essentially meaningless. Whoever sets up the constraints essentially has all the political power and the remaining choice is almost devoid of political power. Arguing whether that negligible remaining amount of political power was applied judiciously or not is in my opinion a distraction.

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  13. Yoram,

    the historical record [of Athenian democracy] indicates that the main motivation behind the practice was the law of large numbers. It was expected that sortition would produce a group that would mirror the population in important respects.

    I have yet to find a single historian to endorse this perspective (and the citing of the LLN is clearly anachronistic). Aristophanes may have complained about the sortition process favouring the old, but nobody complained that the legislative courts undermined the rule of the assembly. Indeed the higher minimum age and the need to take the Heliastic Oath would indicate that the 4th century reforms were designed to ensure that the courts did not mirror the population.

    Melissa Lane and Lynette Mitchell argue that delegation to juries was largely for administrative convenience and that modification of the law was a minor (and infrequent) aspect of Athenian democracy. In my thesis I argued that the sheer size of the Athenian juries indicated some sense of statistical representation, but this was the response from the external examiner:

    It is true that the Athenians seemed to equate the decisions of juries with the decisions of the demos. But this need not mean they had any idea of descriptive representation, at least not in any strong sense. As Josiah Ober has pointed out, they might have been using the demos as a synecdoche, whereby any actions by an organ of the democratic state were attributed to the demos.

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  14. *** Yoram Gat wrote : « As part of the attempt to dismiss sampling as a political device it is sometimes claimed today that its use in Athens was motivated by the superstition that randomization allowed the gods to make the selection. However, the historical record indicates that the main motivation behind the practice was the law of large numbers. It was expected that sortition would produce a group that would mirror the population in important respects. » Then Nicholas Gruen said : « Since you mention what “the historical record indicates”, I would have loved some presentation of that historical record. »
    *** About the supposed religious motivation, it could have worked underground, but the evidence for the secular motivation of sortition among ancient democrats is overwhelming : as far as I know, there is simply no mention at all of any religious motivation in any democrat text. Not once. The comment by Plato often quoted (Laws, 690c) is a sarcastic jibe by an arch-foe of democracy ! To consider it as a piece of ancient democrat ideology is not far from bad faith.
    *** An allotted magistrate, as an elected one, was subjected to clearance (dokimasia) – which would have been impiety if he would have been considered as chosen by the Gods.
    *** That sortition produces bodies which mirror the entire dêmos is implicit in democrat texts. The Theseus of Euripides (Suppliant Women, v 406-7) says : « dêmos d’anassei diadokhaisin en merei eniausiaisin », « the people rules by turns through annual successions » (magistrates and heliasts were selected annually ; jurors were selected among the heliasts). In Theseus words sortition is expressed as rotation, but it implies that the successive parts of dêmos exercising power are « representative » of the whole, otherwise the governing of the City would be chaotic.
    *** Therefore Yoram Gat is basically right, historically. But I think we must be careful before using mathematical words as « the law of large numbers » in ancient context. The ancient Greeks had some intuitive idea of the kind, but not clear theory. We must remember that the « science of chance » was created « recently » by the classical West (17th century), without as far as I know anything alike before. The paradox is that the Ancient Greek civilization, which used politically intuitive ideas about statistics, was no more able than the others to create a theory.

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  15. The fact that jurors had to be 30 years old while members of the Assembly could be 18 definitively shows that even if they intuitively recognized the representative nature of sampling, it is at least an oversimplification to suggest they saw one as statistically representative of the other. But the assembly itself was ALSO a roughly representative sample of the Demos (80% of eligible citizens were off doing other things during every assembly meeting). So it is fair to say that BOTH were deemed to be acting as representatives of the Demos as a whole. However, clearly sortition in Athens was not only about statistical representation, NOR exclusively about “ruling and being ruled in turn.” The magistrate panels selected by lot were normally small groups of ten citizens. In this case sortition was pretty clearly an anti-corruption and anti-incompetence tool. Within a random group of ten, a conspiracy could be avoided, and an incompetent individual could be circumscribed. The random selection of court jurors the morning of the trial was also clearly an anti-corruption tool (probably more than a statistical representation tool).

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  16. Andre:> In Theseus words sortition is expressed as rotation, but it implies that the successive parts of dêmos exercising power are « representative » of the whole, otherwise the governing of the City would be chaotic.

    That’s a strong claim. In modern polyarchies political parties rule by turns, and could only really claim to represent those who voted for them. When conservative and social-democratic administrations succeed each other the result is very often chaotic. The relative stability of ancient democracies is more likely the product of the limited power of most magistracies and the sense of homonoia (same-mindedness) amongst citizens. The sheer size of Athenian juries could be taken as a sign of proto-representational thought, or more likely as an indication of the need for large groups of citizens to determine important cases (given the unpracticality of all citizens attending). It would certainly suit my own thesis to argue that sortition in Athens served a representational function but I’m too wary of the charge of anachronism. The sources are largely silent regarding the motive for using sortition so claims like “the historical record indicates that the main motivation behind the practice” are unjustified.

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  17. Terry,

    > The fact that jurors had to be 30 years old while members of the Assembly could be 18 definitively shows that even if they intuitively recognized the representative nature of sampling, it is at least an oversimplification to suggest they saw one as statistically representative of the other.

    I don’t see why. The Greeks assumed the allotted would be statistically representative of the allotment pool. Limiting the pool in various ways does not change that.

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  18. Andre,

    > « the law of large numbers »

    Certainly, the term and the mathematical theory are modern. I believe I am not misleading any reader of the IMS Bulletin into believing otherwise.

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  19. >The Greeks assumed the allotted would be statistically representative of the allotment pool.

    Evidence?

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  20. *** Keith Sutherland writes : « The Greeks assumed the allotted would be statistically representative of the allotment pool. Evidence ? »
    *** But he wrote before : « The sheer size of Athenian juries could be taken as a sign of proto-representational thought, or more likely as an indication of the need for large groups of citizens to determine important cases (given the unpracticality of all citizens attending) ». The first reason is « a sign of proto-representational thought » – but representational in a statistical way.
    *** I don’t remember any example where somebody thought that a decree or a law could be crushed by a jury one day and approved another day , only by effect of chance in allotment. Most probably the Greeks underestimated the role of chance, as most Westerners today. But it seems clear they thought a huge size of juries was protecting from the decisions being governed by luck.
    *** Right, the ancient democrats did not give a clear statistical reasoning, they were « silent », as says Keith, because they did not succeed to look clearly to the chance phenomena. But the intent of sortition is clearly expressed by Theseus in the Suppliant Women: through sortition « ho dêmos anassei » « the Dêmos reigns ».

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  21. *** Terry Bouricius writes « The magistrate panels selected by lot were normally small groups of ten citizens. In this case sortition was pretty clearly an anti-corruption and anti-incompetence tool. Within a random group of ten, a conspiracy could be avoided, and an incompetent individual could be circumscribed. »
    *** Terry is right, we must distinguish ten-persons magistracies and (sovereign) juries. They were distinguished clearly by an important fact: the allotted magistrates, as the elected ones, had to submit to a clearance procedure (dokimasia), not the jurors.
    *** To Terry reasons we must add « protection from oligarchic leanings ».
    *** A text here is interesting. When Lysias was attacking Evandros (about his past oligarchic leanings) during his « clearance » (dokimasia) for the allotted « magistracy » of archon (one of the rare one-person magistracy), he said (On the Scrutiny of Evandros, §11))
    « Besides, had he qualified for the Council, he would have held his seat as one in a body of five hundred, for a year only; so that, if in that period he had wished to commit an offence, he would have been easily prevented by the others. But, if he is approved for this office, he will hold it all by himself, and as a member of the Council of the Areopagus he will obtain control over the most important matters for an unlimited time. » (English translation by W.R.M. Lamb,)
    Putting aside the reference to the Areopagus, the difference between the Council and the one-person magistracy refers to a kind of protection by numbers.

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  22. *** Terry Bouricius reminds us that the thirty tears criterion was a strong bias against statistical representativity. This point is omitted by Theseus. Was the democrat theorician under Theseus against this criterion ? Or was he blind to it ?
    *** Note that in contemporary France the criminal jury is very often considered as an example of popular sovereignty – whereas the jurors must be over 25 years, not the majority age (and voting age) of 18. And I never saw somebody discussing the fact !

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  23. Andre:> But [Keith] wrote before : « The sheer size of Athenian juries could be taken as a sign of proto-representational thought,

    But my speculation failed to impress my PhD examiners. It’s unfortunate that the historical record is not explicit as this leaves modern political theorists (and activists) free to impose whatever motives they wish on the ancients.

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  24. Andre,

    > Most probably the Greeks underestimated the role of chance, as most Westerners today.

    Why do you say this? Robert Dahl, for example, seems to have greatly over-estimated the effects of random variation in sampling. By the number of times I have been asked “but what if we get a majority of neo-Nazis in Congress?” it seems to me that his error of intuition is quite common.

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  25. Did the Greeks even have a concept of chance? I remember reading somewhere that if the dice always ends up averaging 3.5, the ancients would have attributed this to divine equanimity. We really do need to be aware of the danger of anachronistic projections of modern attitudes on the ancients.

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  26. Andre,

    > the thirty years criterion was a strong bias against statistical representativity

    Again, I don’t see why. All this criterion means is that the Athenians made an obviously conscious choice to have only a part of the citizen body represented. This is clearly a separate matter from the method of selection within the pool.

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  27. Another point about the age distinction…In a relatively homogeneous citizenry, various age cohorts were probably not seen as separate classes with different interests. The 18-year old could later turn 30 and serve in the court or council, while a new cohort of 18-year olds matured in turn. It seems likely the Athenians simply sought to benefit the entire Demos from what they believed was the added wisdom of age, rather than favoring the INTERESTS of older citizens.

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  28. Terry:> It seems likely the Athenians simply sought to benefit the entire Demos from what they believed was the added wisdom of age, rather than favoring the INTERESTS of older citizens.

    Yes I’m sure that’s right (ditto the requirement to swear the Heliastic Oath). But if the citizenry was relatively homogeneous then it does call into question the need for sortition to produce a sample as the only dimension that would need statistical representation would be wealth. Obviously this would not be the case in a modern multicultural society.

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  29. *** There must be much truth in Terry Bouricius’ comment about age distinction.
    *** But I think the difference between ages were at least acknowledged about peace and war. That would explain the repartition of powers between the Assembly and the Juries. Peace and war was left to the Assembly, because it would have been difficult to exclude the young who will fight, and to include seniors (over 60 years) who could not been conscripted.
    *** And that likewise explains that the elected magistrates were elected by the Assembly, as most of them were military magistrates (even if later some financial magistracies were added to the list of elected ones).
    *** Note that the elected magistrates were submitted to clearance (dokimasia) by a jury, which could exclude would-be magistrates with known anti-democrat leanings.

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  30. *** I wrote : « Most probably the Greeks underestimated the role of chance, as most Westerners today. »
    *** Yoram Gat answered : « Why do you say this? Robert Dahl, for example, seems to have greatly over-estimated the effects of random variation in sampling. By the number of times I have been asked “but what if we get a majority of neo-Nazis in Congress?” it seems to me that his error of intuition is quite common. »
    *** OK, I wrote too quickly. There are different errors of intuition in this field. But I was strongly impressed by the case of criminal juries, small ones, which in France decide about guilt and about punishment, by majority (no requirement of unanimity). When the opinion is divided, as about the death penalty, the sentence of a small jury is quite random. But when there was death penalty in France, in the hot debate about it the question of chance was almost omitted. And recently the size of criminal juries has been reduced, without much debate about the induced randomness. That implies a strong underestimation of chance at least for small juries.
    *** I don’t know well the US law, but it seems that the recent reducing of size for some juries implies the same underestimation.

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  31. >That would explain the repartition of powers between the Assembly and the Juries. Peace and war was left to the Assembly.

    I think it would be more accurate to say that the legislative courts only dealt with a very small number of decisions, as changes in the law were infrequent during the 4th century. This is the reason why the move to lawmaking by allotted juries drew no comment whatsoever in the literature (my PhD supervisor, a professor of Greek history wan’t even aware of it until I pointed her to Hansen and Blackwell). So although some of us like to use the nomothetai as a model for a modern demokratia we shouldn’t make anachronistic claims regarding statistical representation in ancient poleis.

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  32. André posté 21 février 2018

    *** Keith Sutherland writes : « the legislative courts only dealt with a very small number of decisions, as changes in the law were infrequent during the 4th century ». OK, that was Ancient Times, where societies were quite static outside of revolutions, and therefore legislative changes infrequent. But some could be very important, as the financial laws Demosthenes fought against, to get military money in front of the Macedonian menace.
    *** The changes asked for by Demosthenes did not come from (slow) changes in the Athenian society, or (almost inexistent) changes in technology, but from an external change : the surge of Macedonian hegemony.
    *** If the legislative juries were usually not busy, the judicial juries were. And we must remember the very wide powers of Athenian judicial juries : crushing the decrees of the Assembly as contrary to the laws, crushing the laws as contrary to Higher Principles, clearance (dokimasia) of would-be magistrates, and judgment of accused politicians (apparently a very frequent case).
    *** We can consider that Athens in the time of Demosthenes was halfway between a pure democracy-through-general assembly and a pure democracy-through-minipublics.
    *** A modern dêmokratia will need more legislative work than an ancient one. But it is bad to concentrate on legislation. The judicial powers and the overseeing of administration are basic points. Laws are what say judges and public agents.

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  33. Andre:> pure democracy-through-minipublics

    That’s all very true, but we should remember that the Athenian courts were convened on an ad-hoc basis as a result of prosecutions which were usually brought by members of the political elite against their rivals. I’m not aware of any ancient precedent for the sort of permanent oversight committee suggested on this blog, so I think the idea of a “pure” democracy through minipublics is a fanciful one. Either the allotted committee would lack the necessary skills, experience and confidence or else it would go native and cease to be representative of the target population (and be seriously open to corruption by sinister interests). The role of ad-hoc allotted juries is to listen to the evidence and then determine the outcome, not to initiate prosecutions or act as advocate for or against.

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  34. Andre,

    > pure democracy-through-general assembly

    This is not a meaningful expression. One might as well say “pure democracy-through-monarchy”.

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  35. Yoram:> This is not a meaningful expression

    Leaving aside the word “pure”, it’s disappointing that the debate on this forum is now being conducted in definitional terms. “Assembly democracy” is a meaningful concept as far as political science is concerned; what you mean is that it doesn’t fit in with your own (tautological) definition of democracy. The same can be said about representation — the statistical form delivered by large randomly-selected juries is just a different kind to that delivered by elected representatives (both forms have pros and cons). We should all be aware of the danger of disappearing up our own backsides.

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