## George Tridimas: When is it rational to give up rationality?

George Tridimas of the School of Economics of the University of Ulster circulates via the Kleroterians mailing list a draft of a paper, soliciting readers’ comments. The abstract is below. Please contact the author for the full text of the draft.

### Appointment to office by lot in Ancient Athens

Contrary to modern democracies ancient Athens appointed large scores of government post-holders by lottery. After describing the Athenian arrangements, I review the choice between elections and lottery from the perspective of the citizen focusing on representativeness of the population, distributive justice, minimization of political conflicts, administrative economy and policy making ability of appointees. Adopting the methodology of public choice, I then examine why a contestant for office may choose the lottery rather than elections as a method of winning office. Although the outcomes of both mechanisms are uncertain, a contestant may influence the probability of winning an election through his campaign efforts, but not of a lottery. I establish conditions for choosing one or the other mechanism depending on the availability of campaign funds and campaign effectiveness of the contestants and I show that despite its mechanical character appointment to office by lot is consistent with self-interested behaviour and can be voluntarily agreed by all contestants.

### 27 Responses

1. A very well informed paper, including many references which are new to me. Instead of the usual philosophical political theorist’s approach, what we have here is an economist’s view.

In ancient Athens most of the jobs in the public service were awarded by lot. Was this a sensible (rational) way to decide who to employ? Does it offer the most appropriate incentive for potential employees? These are the ‘economics’ questions addressed in this paper.

The answer, with the help of the inevitable algebra is “Yes, sometimes choosing who to employ by lot was the best way to do it for ancient Athens”. But can this be projected into the present day: why not a lottery for jobs instead of the arcane and futile rituals of interviews? Why not draw up a short-list of 6 from all the applicants and roll a die to decide the winner?

It is great to see someone else (apart from me) addressing the lotteries-for-jobs issue. BTW George, in the troubled political climate of Northern Ireland it is deemed appropriate to draw up short-lists for low-level public jobs (eg court ushers) using a lottery. (Details on my website)

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2. There is a mailing list?

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3. Yes – it is managed by Conall. Email him to be put on the list. There is about 1 email a month, I guess. I usually post here references to any material being sent or discussed.

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4. George,

I’ve read the paper (or at least made a first pass) and here are a few comments on the non-math part (I’ll post some comments on the mathematical analysis later):

1. The review of the literature is very useful. There are quite a few references I wasn’t aware of. Having a database covering sortition-related papers would be nice, and we could probably use your list to cover the economics/public-choice literature.

2. Page 3, middle of page, there is a typo: “This a large number”.

3. I am not sure about your distinction (note 5) between sortition and rotation. I think rotation, in the context you use it, simply means that no single person, or class of people, holds office for a prolonged period.

4. I disagree with the claim that Athenian officials did not decide policy. Like any official whose job is not purely ceremonial, they had significant discretion. The idea that they were simply carrying out orders of the Assembly is unrealistic. That is exactly the reason that the Athenian wanted the officials to be representative.

5. I also disagree that “the Athenians neither knew of the law of large numbers nor were they interested in representation.” I think everybody has an intuitive grasp of the law of large numbers, and (just as an example) the fact that seats in the Boule were allocated proportionally by the size of deme shows that representation was at the forefront of political thought.

6. The main function of elections is not to decide between the main candidates, but to legitimate the narrowing of the field to the main candidates. Thus, the high cost of participation has a very useful function as far as the main candidates are concerned – it acts as a barrier against the minor candidates. Your model ignores this effect – again, it is the main effect of elections. Any minor advantage of sortition in reducing the cost of attaining office would be completely overwhelmed by the risk of attracting more candidates.

7. Using your model to account for the narrowing-of-the-field effect of elections could be an interesting exercise.

8. Regarding incompetence of allotted officials: as I have pointed out before, this argument, despite its ancient origins and superficial appeal, doesn’t really make any sense. Allotted officials may not be particularly capable, but they would be much more capable than the public at large (due to increased resources and motivation). Thus, allotted officials could always, if they see the need to, select by vote capable advisers and set policy by following the advice of those advisers. That is, they could simply function as an improved electorate.

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5. “5. I also disagree that “the Athenians neither knew of the law of large numbers nor were they interested in representation.”

Ditto. Manin is persuasive on this:

‘Thinking about the political use of lot may have led the Greeks to an intuition not unlike the notion of mathematically equal chances. It was true, in any case, that lot had the effect of distributing something equal in terms of number (to ison kat’arihtmon), even if its precise nature eluded rigorous theorization’ (Manin, 1997, p.39).

Richard Tuck notes that the ‘estimation of probabilities’ predates Leibniz and Huygens’s mathematical studies – appearing, for example, in the writings of Grotius and the members of the Tew Circle, thereby casting doubt on Ian Hacking’s account of the context in which the concept of probability emerged (Tuck, 1979, pp.104-5).

Whenever a medieval cook stirred the chunks in a cauldron of soup and then sampled it with a ladle she was expressing a confidence that the ingredients sampled in the spoon would be proportionate to the whole cauldron (the variables being the size of the spoon, the size of the chunks and how vigorously the cauldron is stirred).

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6. George, here are my comments regarding the mathematical analysis of the paper:

1. It is not clear what purpose the discussion of the types of voters on pages 16-17 serves. The expressions relating the proportions of the various types of voters to the probability of winning do not quite make sense, since once the proportions of each type and their preferences are known they deterministically determine the winner of the elections. But in any case this discussion is summarily superseded by formula (2) which relates expenses to the probability of winning, and it is that formula that is used in the rest of the paper. For the same reason, the reference to the proportion of “A types” and “B types” (p. 21, line 7) seems out of place.

2. The fact that $\epsilon$ and $k$ are defined in a non-symmetrical way propagates throughout the analysis. Defining them in a symmetrical way would yield more transparent expressions, symmetrical in A and B.

3. The use of the parameter $S$ is unnecessary. The quantities $Y_A$ and $Y_B$ could simply be defined as disposable income.

4. I have not followed through all the calculations for the constrained case, but I think that as long as the contest is between two candidates, there cannot be a sortition $\lambda$ value for which both candidates prefer elections.

I believe that as the model is set up, there will always be a non-empty interval in which both candidates prefer sortition – an interval that will contain the equilibrium probability under elections. The reason is simple: with sortition at the election equilibrium probability the two candidates enjoy the same expected benefits, but do not have to incur the costs – thus they will both be doing better compared to elections.

This interval will have on each side an interval in which one candidate prefers elections and the other prefers sortition. Thus, of the two cases drawn in Panel II only the top one can actually exist, and similarly, case 5 of table 2 cannot occur. Do you have a particular setting of the model parameters for which both candidates prefer elections?

5. As I wrote previously, I think an interesting variant of your model could describe the tendency of first-past-the-post systems to produce two-way races. If there is only one candidate, he will reduce his spending to increase utility. At some point the entry to the race becomes cheap enough to allow a contender to afford candidacy. Those two candidates then determine the level of spending. Given that level of spending, other organizations or individuals are unlikely to have the particular configuration of resources, objective function and publicity effectiveness that would make a candidacy a positive-expectation endeavor. In other words, the arrangement in which a three-or-more way race is a stable situation is unlikely to occur.
Do you know if such an analysis exists in the literature?

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7. One more point:

I believe that the left hand side in inequality (11.A) should not be squared. It should read:
$\epsilon k G – (Y_B – S) > 0$.

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8. I’m glad to see that this highly technical debate appears to be being conducted by people with the necessary skills in mathematical logic and am relieved that they are not selected by lot.

Of course I have to take this on trust, as I don’t possess the necessary skills to judge competence in this matter — George and Yoram could be talking gobbledegook for all I know. This is why its best left to professionals, who would be able to judge objectively whether George and Yoram know what they are talking about. As in mathematical logic, so with any other field of endeavour where skills are required, such as the running of large departments of state. The UK National Health Service is second only to the Indian railways in the number of people it employs and the thought that this might be headed up by individuals chosen by lot (as Yoram has suggested on another thread) is a truly terrifying prospect.

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9. You don’t possess the necessary skills to judge competence in this matter, you say. Yet, you obviously trust in Yoram and George’s mathematical competence nonetheless.

So, if you were allotted to decide in this matter, would you call on them? If not, why not? And if you do, why are you so convinced other people wouldn’t?

Even if there were the occasional nut who saw no use for mathematical skills, it wouldn’t matter. You persist in talking about “individuals chosen by lot”, but as I just told you, it’s groups chosen by lot, not individuals. For your disaster to happen, a majority of the allotted decision-making body would have to reject or be unable to recognize competence.

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10. “So, if you were allotted to decide in this matter, would you call on them? If not, why not? And if you do, why are you so convinced other people wouldn’t?”

That’s the point, I don’t know whether they are talking mathematical logic or gobbledegook, because I’m not qualified to judge. This is why professional and academic institutions have been created to judge these matters (such as the Royal Society, London Mathematical Society, Royal Statistical Society, to name but a few UK institutions). Allotted members would not even know who to ask and (as I’ve already mentioned) there is a distinct possibility of nepotism and other forms of corruption).

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11. > Allotted members would not even know who to ask

While, Keith, of course, does.

Obviously, Keith’s position only makes sense if one accepts that Keith (like other people of erudition, sophistication and practical wisdom) has the sense to do the right thing while most people (in their ignorance, coarseness and stupidity) don’t. Accepting this premise – and assuming further that Keith has only the common good at his heart, one would have to be a fool not to grant Keith (and other people of erudition, sophistication and practical wisdom) wide ranging powers.

Keith accepts implicitly that the above holds, and thus draws the inevitable conclusion. He is then completely mystified by our inability to see the logic of his position.

[ I have little doubt, BTW, that we will now witness Keith giving his usual song and dance about how he proposes that the people will have the “ultimate power”, and how once they are educated by the experts they will have a chance to transcend their baseness and touch the wisdom of their betters. The irrelevance of this argument to the issue of his assumption of self-superiority will not in any way diminish Keith’s earnestness in offering it as a rebuttal to our fundamentalism-induced protestations against his elitist ideology and proposals.

If we are lucky, we may also get an explanation that his position is buttressed by such great personalities as Harrington, Rousseau, Montesquieu, Hansen and Pitkin, and that the fact that his proposal got ridiculed by someone in the British press for being the ravings of a deranged radical demonstrates definitively that he represents a sensible middle.

What we will not get, if the past serves as a guide, is any substantial addressing of the simple matter at issue. ]

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12. “He is then completely mystified by our inability to see the logic of his position.”

I’m only mystified by your inability to read plain English. This is what I said:

“I’m not qualified to judge.”

Which you chose to interpret as:

“One would have to be a fool not to grant Keith (and other people of erudition, sophistication and practical wisdom) wide ranging powers.”

Given my repeated call to leave matters that require expert knowledge in the hands of experts, let me make it perfectly clear that I don’t consider myself to have expertise in any subject matter that might be called on by an allotted parliament. I am a printer by trade; one of my hobbies happens to be political theory (others are rowing and playing the guitar). I am not a member of any professional body and cannot imagine any circumstances in which my (lack of) expertise would be called on.

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13. I asked you questions which you sidestepped, Keith Sutherland. Let’s take this as briefly as possible, again:

You obviously trust in Yoram and George’s mathematical competence. Why?

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14. How many times do I have to say this:

I’M NOT QUALIFIED TO JUDGE THEIR COMPETENCE

They may be mathematically competent, on the other hand they may be a couple of charlatans who are just choosing algebraic symbols at random in order to make us think how clever they are. The quality of their work can only be judged by their own peers, not by laymen like me.

This is getting really boring!

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15. > I’M NOT QUALIFIED TO JUDGE THEIR COMPETENCE

But you know who to ask, while the average person doesn’t.

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16. When to give up on rationality? After rationality has failed place after place, time after time as little more than a mass trip for human pride on an obviously endless ego trip rooted in what the preacher of Ecclesiastes called “Vanity of vanities.”

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17. Yet you do judge their competence, Keith Sutherland. When you worry about how awful it would be if someone else less qualified did what they do, that’s exactly what you’re doing. If you were really unqualified to judge, you wouldn’t even worry about that.

You have the common sense to see that it’s extremely unlikely that they are conspiring against you, making up symbols at random. That’s really all it takes. If you need more (say, to decide who of Gat or Tridimas would make most of a tenured mathematics professorship) you can ask a dozen people who your common sense tell you are at least likely to be qualified (like math grad students).

Even if you were a militant anti-intellectual who failed algebra in high school, that wouldn’t matter either, because it’s extremely unlikely that the majority of the people you were allotted with (Remember, you don’t get to make decisions alone!) shared your indifference to qualifications.

I trust in random people’s common sense to decide when to seek out experts. I also trust them to find adequately qualified advisors. Don’t you? Why not?

More importantly, I trust random people to decide when experts are needed, more than I trust the experts to decide that for themselves.

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18. “But you know who to ask, while the average person doesn’t.”

Assuming you are not being sarcastic, this is all the more reason for ensuring that balanced expert advocacy is secured by institutional arrangements rather than leaving it to happenstance.

As for giving up on rationality, random selection is the optimal way of ensuring descriptive representation, and the aggregate wisdom of crowds is the optimal way of judging the outcome of informed political debate, as Fishkin has conclusively demonstrated over the last two decades. So while authors like Dowlen commend sortition for its arational character, many of us see it as entirely rational.

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19. “I trust in random people’s common sense to decide when to seek out experts. I also trust them to find adequately qualified advisors. Don’t you? Why not? More importantly, I trust random people to decide when experts are needed, more than I trust the experts to decide that for themselves.”

Go and read Fishkin’s books, I really don’t have the time to keep restating his arguments (not mine). I’ve no wish to become the modern equivalent of Darwin’s bulldog.

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20. > Assuming you are not being sarcastic

Heh. Of course I was being sarcastic. I was naively thinking that spelling out your claim explicitly would make it clear, even for you, that it is an elitist, self-centric, self-serving position that cannot serve as a basis for the design of a democratic system.

> this is all the more reason for ensuring that balanced expert advocacy is secured by institutional arrangements rather than leaving it to happenstance.

What you euphemistically call “happenstance” is nothing but the informed opinion of the representatives of the public. You propose to have institutional arrangements that ensure that your preferred way of doing things overrules the democratic decision. Your justification for doing that is based on a claim of your own superiority over others.

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21. > rationality has failed place after place, time after time as little more than a mass trip for human pride on an obviously endless ego trip rooted in what the preacher of Ecclesiastes called “Vanity of vanities.”

Richard,

You are making a very good point. In many areas of expertise, and particularly in areas that have to do with pubic policy making (such as legal expertise, economic expertise and foreign affairs expertise), there is a long and rich history of self-proclaimed experts serving the interests of the few (the experts themselves included, of course) at the expense of the many. Furthermore, as you write, beyond sheer self-interestedness there is a large amount of vanity in the claims of wisdom made by self-appointed experts. I wholeheartedly agree that the ancient virtue of humility is utterly lacking from the corridors of power – an omission that needs to be addressed before one could expect a good government.

All that said, I do not think we should throw out the baby of rationality together with the soiled water of self-proclaimed and self-serving expertise. Any hope we have for good society and good government, any discussion we are having toward that goal, rests on rationality – attempting to understand our place in the universe and acting according to our understanding.

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22. “Heh. Of course I was being sarcastic.”

OK, I quit this forum, it’s like having a conversation with the Taliban. If you wonder why you have no members, just take a look in the mirror.

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23. I’ll refer you to my response from the previous iteration of this cycle.

And as for “no members”, I’d rather have no members and argue for what I believe is right than be part of a mass movement promoting wrongs. Anyway, of course, I don’t see your position attracting a mass following so if I were considering attaching myself to a popular movement I would have to look elsewhere. The Taliban are enjoying some popular success, it seems.

Joking aside, you really don’t have to quit. It is you who for some reason feel compelled to initiate these explosive discussions, and keep pursuing them until the bitter end. We could simply agree to disagree on those matters and pursue any common objectives while avoiding these dangerous grounds.

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24. “In many areas of expertise, and particularly in areas that have to do with pubic policy making (such as legal expertise, economic expertise and foreign affairs expertise), there is a long and rich history of self-proclaimed experts serving the interests of the few (the experts themselves included, of course) at the expense of the many.”

I wish there was some way to get Keith Sutherland to admit this. It’s probably the main reason I want political reform in the first place. Even if Keith was right, and common people were bad at seeking out experts when necessary – I’d sacrifice a great deal of government competence and efficiency in order to do something about these elites’ power.

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25. Many thanks Yoram for your comments (first batch non-technical), very useful indeed. They will be incorporated in the version to be submitted for publication. Here is the rejoinder
2. Thank you for pointing out the typo
3. YES, rotation relates to timing
4. The Assembly was the sovereign body (to use modern parlance). The Athenians practised direct participatory democracy, which is in contrast to modern representative government. The Assembly was delegating a number of “routine” tasks to citizens selected by lot – so that any citizen could perform them. In building a model there is no loss of generality when it is assumed that the latter were not acting autonomously from the Assembly and therefore they are modelled as if they were not deciding policy.
5. I agree that the Athenians were intuitively aware of the law of large numbers, but my main point is that all important decisions were taken by the Assembly.
I also thank Keith Sunderland for his contribution here.
That representation was not important to them is shown by the fact that when electing the ten generals, each tribe was proposing a name who was then voted in (or rejected) by the entire Assembly – all ten tribes – and was not therefore the representative of a tribe-constituency.
6. I agree that entering the race for office incurs substantial costs (that may even turn out to be sunk!) This is the reason why I analyze the model where one candidate is budget constrained
7. I am not sure what you have in mind here
A cynic may doubt how motivated the allotted officials are. But more generally, this is an important point to debate. What I am saying here is the following: When the environment is characterized by uncertainty the median voter is better off by delegating to knowledgeable officials (when such a group exists) who take the actions to offset the shocks to the system, provided that the cost of resources diverted by that group to their own interests does not exceed the benefits from offsetting the negative shocks.

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26. Harald,

> Even if Keith was right, and common people were bad at seeking out experts when necessary – I’d sacrifice a great deal of government competence and efficiency in order to do something about these elites’ power.

I think the issue is even more fundamental than a matter of striking a balance between competence and representativity.

Let us assume for the sake of argument that experts exist who are uncorrupted and uncorruptible. These experts are more competent than the average person and have only the best interests of the average person in mind.

Then there are two possibilities – either the average person recognizes those experts for who they are, or the average person doesn’t. In the first case, no expert-biased institutional arrangements are needed since an allotted chamber would simply always take the advice of those saintly experts.

In the other case, however, there could be no democratically legitimate way to decide upon having an institutional arrangement which grants powers to the experts, since the majority of the people would be unwilling to privilege a group which it does not recognize as uncorrupted experts.

Thus, there is really no situation in which a rationally designed democratically legitimate system would institutionalize a privileged power position for so-called experts.

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27. George,

The matter of the primacy of the Assembly is not very important in the present context, I think. I do, however, find Headlam’s theory that sortition was seen simply as a tool to buttress the power of the Assembly completely unconvincing. If nothing else, the ratification power of the nomothetai – which is far from a routine matter – should be enough to refute this claim. There is also no evidence for this rationale in the ancient political literature. Thus, it is made of whole cloth. The appeal of this unlikely theory is that it gives people who have been conditioned to see elections as being the essence of democracy a way to rationalize the Athenian rejection of elections.

> I agree that entering the race for office incurs substantial costs (that may even turn out to be sunk!) This is the reason why I analyze the model where one candidate is budget constrained

My point is that this cost should be seen not merely as a burden required to make gains against the opposing candidate, but also – most importantly – as a tool to fend off potential additional contenders. If this cost is eliminated, some other way to narrow the field would be needed.

> When the environment is characterized by uncertainty the median voter is better off by delegating to knowledgeable officials (when such a group exists) who take the actions to offset the shocks to the system, provided that the cost of resources diverted by that group to their own interests does not exceed the benefits from offsetting the negative shocks.

I agree. I actually think that the use of term “shock” understates the case. Every environment, predictable and benign as can be expected, requires discretionary public policy action on a routine basis. It is simply completely unmanageable to have those actions decided upon directly by the entire population. Thus, delegation is unavoidable in any real-life situation. (This is also, by the way, my point about the role of allotted officials in Athens – by necessity they had non-negligible policy making power.)

My point here is that, like [almost] any other group decision, the appointment of officials would be better made by a random sample of the population than by popular elections. The members of a sample would have access to better resources than the average citizen does and, due to the increased power of each member in the sample, would be better motivated to put those resources to bear. Decision making in an allotted chamber is therefore likely to produce better decisions than popular elections – whether that decision is a policy decision or the decision who to appoint to a certain office.

Thus, comparing the competence of the sample to that of an elected official is irrelevant. The appropriate comparison is between the competence of the sample and the competence of the electorate.

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