Constitutional choice in ancient Athens: The rationality of selection to office by lot
George Tridimas*
University of Ulster, School of Economics
Newtownabbey, Co. Antrim, BT37 0QB, UK
Abstract
Contrary to modern democracies ancient Athens appointed large numbers of government
officers by lot. After describing the Athenian arrangements, the paper reviews the
literature on the choice between election and lot focusing on representativeness of the
population, distributive justice, minimization of conflicts, quality of appointees and
administrative economy. It then examines why in drawing up the constitution a selfinterested citizen may give up voting for government officials and appoint them by lot. It
is shown that appointment by lot is preferred when the effort required to choose
candidates is less than the benefit expected from their actions as government officials. It
is also found that, given the choice, office motivated candidates may unanimously agree
to selection by lot but not to election.
JEL Classification: D70; D72; D74; N40; N43
Key words:
Constitutional choice; Ancient Athens; Appointment to office by lot;
Election.
*Tel: +44 (0) 28 90368273, fax: + 44(0) 28 0366847, e-mail: G.Tridimas@ulster.ac.uk
Forthcoming in
Constitutional Political Economy
DOI: 10.1007/s10602-011-9112-1
Constitutional choice in ancient Athens: The rationality of selection to office by lot
1.
Introduction
From the viewpoint of an ancient Athenian modern representative democracy would have
been dismissed as an “elective oligarchy”. A fundamental aspect of the Athenian
democracy setting it apart from the modern one was the selection of public officials by
lot, a process also called sortition. Headlam (1891) who offered the first authoritative
modern account of the lot in ancient Athens wrote “The lot … at Athens … helped to
secure perfect equality among all citizens, a regular rotation in office, and the undisputed
authority of the assembly” (p.88). There are several contemporary examples of using the
lot to allocate scarce resources. These include lottery money, hunting permits, school
places and tickets to popular events. Similarly, lotteries are used for the selection of jury
members and may be used to allocate a burden, like the military draft. However, posts in
legislative or executive bodies are filled by candidates who succeed in popular elections.
Nevertheless, ancient authors considered sortition more democratic than election. A
lottery generates a fixed number of outcomes with given probabilities implying that
appointment by lottery is a mechanical form of decision making that does not reflect any
rational calculation behind the result. It is, as Dowlen (2008) put it, “arational” and no
individual agent can be held responsible for its outcome. On the other hand, when
electing candidates voters acquire information about politicians and their policy platforms
and politicians acquire information about the issues that affect voter welfare and
campaign to win votes. In other words, the outcome of the election is determined by the
choices of voters but the outcome of the lottery is not. How can then the a-rational
sortition be rationalized?
In examining the lot as a mechanism of selection to office, scholarship in economics,
political science and philosophy has investigated whether it can promote the welfare of
citizens and especially whether it contributes to representation of voter preferences, unity
of the citizenry, equality of opportunity to occupy office and selection of suitable political
leaders. No doubt, the above criteria can provide a powerful normative justification for
1
the desirability of sortition. The present study pursues a complementary line seeking to
explain the constitutional choice of the ancient Athenians in the way the economist
explains economic outcomes, that is, self-interested behaviour. It focuses on the choice of
utility maximizing citizens at the constitutional stage to introduce the method of
appointment to office expected to secure the highest expected payoff. It is argued that
since voting in elections requires that the citizen is informed about the issues involved in
collective choice and the quality of the candidates for office, sortition will be preferred
when the expected marginal benefit from casting an informed vote is smaller than the
marginal cost of being informed.
The paper is structured as follows. Section 2 discusses some features of appointment to
office by lot in ancient Athens. Section 3 offers a short review of the properties of
sortition focusing on its ability to serve representativeness, equality of opportunity and
social peace, and the risk to select unqualified candidates for office. Section 4 models the
decision of the citizen at the constitutional stage to choose the rules for appointment to
office, that is, to select a public post-holder by competitive elections or by lottery. A
citizen is prepared to invest time and effort into answering the question of “who is to
govern” when the actions of the government official affect significantly his welfare.
However, when the actions of the person in office do not require special skills, any
citizen is suitable to carry out the responsibilities of office. In this case it is not worth for
the citizen to spend the resources in identifying who is best suited for office and the
random selection process emerges as an appropriate least-cost method of appointment.
Section 5 turns to the complementary issue of whether a citizen may seek office through
election or lottery, when office confers rents but not the right to decide policy. By
holding office the citizen gives up his time and therefore foregoes income from work,
while if he contests an election he also incurs campaign costs; the latter, however, are
eliminated if he is selected to office by lot. His labour productivity, or equivalently the
opportunity cost of his time, and the size of his non-earned income in comparison to the
rent from office turn out to be crucial factors in the decision to seek office. In addition,
the section inquires when, given the choice, a citizen as a candidate for office chooses to
fight an election to win office or he prefers to win office by lottery. Such choice turns out
2
to depend on the balance between the probability of success in the two different methods
and the cost of election campaigns. Section 5 concludes.
2
Athenian practices of appointment to public office by lot
The ancient Athenian direct democracy that lasted between 508 and 322 BC, started with
a series of institutional changes introduced by Cleisthenes in 508 defining citizenship and
the powers of the Assembly of citizens of Athens1 and was completed in the mid 5th
century with the reforms introduced by Ephialtes and Pericles removing residual powers
of aristocratic magistrates. Throughout the period of democracy the Assembly of (male
only) citizens was the principal decision making body. It held ten obligatory meetings per
year and as many additional sessions as necessary up to a total of forty. It decided all
issues of public interest including public finance, foreign policy, war and peace, and any
citizen could introduce a motion for discussion. It also elected one hundred executive
officers including the ten military generals, who served as commanders of the army and
navy and carried out some additional functions in domestic and external policy, and a
score of financial officers and religious commissionaires.
However, what was unique about ancient Athens was the use of lot for appointing large
numbers of public post-holders. During the 4th century out of a total population of 30,000,
more than 7000 public officers were annually appointed by lot.2 As the minimum age for
holding a public post was 30 years (while all Athenians above the age of twenty could
attend and vote in the Assembly) the pool of eligible candidates during the 4th century is
estimated at 20,000 citizens, see Hansen (1999). The offices filled by lot can be divided
1
See Aristotle (1984), Hansen (1999) and Ober (2008). For a short review of the
establishment of democracy in ancient Athens and its principal institutions of governance, see
Tridimas (2011). The interested reader is also referred to the volume by Raaflaub et al. (2007) for
the lively debate surrounding the origins of democracy, and Cartledge (2009) for a discussion of
various political institutions of ancient Athens. Bitros and Karayiannis (2010) show how
institutions and the moral norms of Athens were instrumental in her economic success. Pitsoulis
(2011) discusses the origins of the majority voting rule.
2
The sophisticated allotment machines operating with bronze and wooden tickets at a
time when there were neither paper tickets nor plastic balls, how they worked and how they
ensured that no foul play took place, are described in Aristotle (1984). A summary of the stages
of the process and related issues can be found in Engelstad (1989).
3
into the following categories: (a) 500 members of the Council of the Five Hundred. The
Council (Boule), set up by Cleisthenes, prepared the agenda for the Assembly, was
responsible for the day-today administration of the state and oversaw the implementation
of the various projects approved by the Assembly, and met at least 250 days a year. (b)
600 executive magistrates responsible for a variety of functions as voted by the
Assembly. Amongst others these included the nine archons. In Archaic Athens (750 –
500 BC) the nine archons were the principal government officers; they were elected by
the aristocracy and from its members only, had religious, military and administrative
responsibilities and after completing their terms became members of the Council of
Areopagus a powerful body which oversaw laws and magistrates and conducted trials. (c)
6,000 members of the Court responsible for trying civil, penal, as well as political cases
and for reviewing the policy decisions of the Assembly. The Court met about 200 days a
year and on each court day about 2,000 out of the 6,000 were selected by lot to serve as
jurors; they were then allocated to cases after another lot. Moreover, during the 4th
century citizens who had been selected as members of the Court, could also be called by
lot to serve in boards of “legislators”, whose membership numbered in the hundreds, and
were responsible for ratifying general constitutional provisions called “laws” including
criminal and procedural rules of unlimited duration (as opposed to ordinary decrees
passed by the Assembly in accordance to the laws).
Office terms were annual. Appointed officers received a monetary compensation for their
services whose size varied from office to office. Council members received the average
wage rate and jurors half the average wage rate. The sums of money involved where
substantial. Reliable information for the 340s suggests that out of 400 talents of public
revenue, the expenditure for the Council was 15 talents, while the Courts claimed another
22–37 talents, see Kyriazis (2009) for details. A man could only serve twice in his
lifetime on the Council, but not in successive years, and once in other magistrate offices.
He could hold different offices after his tenure in one office was completed and reviewed
by the Court, which effectively meant that he could potentially serve in different offices
every other year. The annual term limits meant that substantial rotation took place. Thus,
sortition implied that any citizen might hold office, while rotation implied that every
4
citizen might hold office at some time, see Engelstad (1989). Using the estimate of
20,000 eligible citizens, Hansen (1999) concludes that in the 4th century the rule that a
man could be councilor no more than twice in his life implied that “over a third of all
citizens over eighteen, and about two thirds of all citizens over forty, became councilors,
some of them twice”, p.249. The various magistrates and judges of the Court were
amateurs – ordinary citizens – without any specific training for the functions allocated to
them.3
It is essential to appreciate that the lottery was used to appoint officers for implementing
the policy which had been decided by the Assembly of citizens; officials selected by lot
carried out routine duties. Lot randomized appointment to office and the consequent
distribution of monetary rewards from holding office. Citizens had the right but not the
obligation to serve in office. Lots were drawn between those citizens who volunteered for
public service rather than all those eligible. Those wishing to be selected for office were
subject to triple Court review: Before assuming office they were checked for their
eligibility based on reputation of character and conduct but not competence. During
service they were held accountable if an accusation for misconduct arose. Finally, they
were again reviewed by the Court upon leaving office accounting for conduct during
service, especially if they were in control of public funds. Thus, a citizen who chose to be
selected for office by lot did so in full knowledge of the scrutiny that was going to take
place before, during and after the period of service.
Although religious considerations may be invoked to rationalize the use of lot, in the
sense that the outcome of the lot revealed the will of the gods, this explanation ill-fits
ancient Athens. There is no evidence in the sources that any appointee attributed his
selection to divine intervention; nor was opposition to the lot considered as blasphemous
– see Headlam (1891) for a discussion of the arguments. Historians debate the date the lot
was introduced, as the sources are not very clear. The Council of the Five Hundred
3
See Ober (2008) for an incisive analysis of how the institutions of the direct democracy
of the Athenians succeeded in revealing, collecting and transmitting the required knowledge to
enable a large and diverse body of ordinary citizens to make the policy choices which resulted in
the elevation of Athens to a great economic and military power.
5
founded by the Cleisthenes reforms was probably filled by lot from the start. Lot was
certainly used in selecting the nine archons in 487/6 BC.
Socrates thought it was ridiculous that the Athenians appointed magistrates chosen by lot
when they would never have thought of choosing a helmsman or architect or flute-player
that way. Quoting ancient authors, Hansen (1999) maintains that Athenians did not think
that all citizens were equally qualified to serve as public officers, but that all men were
sufficiently qualified at what they were chosen for. The argument is essentially that
serving in public office was something that could be done without specialized expertise.
Hansen goes on to argue that “In the selection of magistrates the Athenians preferred the
lot to election because it safeguarded the powers of the People and obviated factionalism
and corruption, not because they believed in the equality of all citizens” (pp. 341-2). In
his thesis that the development of the Athenian democracy was incidental rather than by
conscious design, Lyttkens (2008) argues that the Athenian aristocracy introduced the
lottery as a mechanism to reduce intra-elite competition for power, since such
competition weakened its traditional dominance. He considered the lottery as a form of
self-regulation among the members of the elite to avoid costly contests for power.
However, his argument goes, rather than strengthening the position of the elite it had the
opposite effect. The use of the lottery implied that no special abilities or skills were
required to hold office, reducing the status associated with the post of archons. Access to
the office was then opened to all citizens and its importance diminished. The next step
was to extend the practice to other offices too.
Athens was not alone in the use of sortition. It was also used in ancient Rome, some
medieval and renaissance Italian city-republics, most prominently Florence (1328-1434
and again 1494-1512) and Venice (697-1797) – although in comparison to Athens all of
the above restricted severely the number of participants.4 Mayors were also selected by
sortition in some of the Swiss Landsgemeinden during the period 1640-1837, when
according to Engelstad (1989) it was used as a mechanism to distribute the perks from
4
See Engelstad (1989), Manin (1991) and Dowlen (2008) for details.
6
public office.5 Appointment by lot was also supported by later distinguished thinkers.
“...political writers of the calibre of Harrington, Montesquieu and Rousseau..., each from
his own standpoint and in his own manner, had advanced the same proposition, namely
that selection was aristocratic in nature, whereas lot is par excellence the democratic
selection procedure.” Manin (1997), p. 79. However, the appeal of the lot as a way of
appointment to office disappeared with the rise of contemporary democracy in the 19th
century (with the obvious exception of appointment of jury members in law courts – see
below).
3.
Democratic government and appointment to political office by lot
Random selection is a mechanism to allocate a scarce resource. In the context of private
goods it is an alternative to the market mechanism, while in the context of selection to
office it is an alternative to elections. The present work focuses on the latter. 6 Mueller et
al. (1972) support randomized selection of representatives in a legislature in order to
reduce the incentive for pork barrel activities, achieve ex ante equality of voters,
represent minorities in their correct proportion to the population and avoid intransitivity
in voting outcomes. Amar (1984) discusses the benefits of choosing representatives under
lottery voting, a system where citizens vote for representatives (as per usual practice), but
the election winner is decided by a lottery of the ballots cast, so that a candidate who
receives, let us say, 51% of the vote has a 51% ex ante probability to be elected to office,
rather than 100%. Lottery voting would encourage voters to vote sincerely rather than
strategically, ensuring representation of voter preferences, diminishing the hold of the
two-party system, securing rotation in office and, unlike pure lottery, it would preserve
political accountability. In a similar vein, Lockard (2003) argues that lottery voting, as
opposed to majority voting, increases political participation, reduces rent-seeking
“To hold political office implied the possibility of acquiring economic gain by
procuring mercenaries to foreign princes among other means. Such income fell to those holding
the post of chairman in the community. The idea that everyone should have an equal chance of
getting the gains of such position quickly emerged. Consequently the office was filled by the
drawing of lots. If the lot fell to poor people ... they had the right to sell the office to the highest
bidder”. (Engelstad, 1989, p.26)
6
Vergne (2010) presents a brief review of the literature and a systematic classification of
contributions that explore random selection and of authors who advocate its adoption.
5
7
expenditure by interest groups, and may lead to less extreme public policies.7 These and
related issues are briefly reviewed in the present section.
3.1
Representativeness of appointees by lot
Appointment to office by lottery may satisfy the objective of selecting a representative
sample of the population to serve in office because of the ‘law of large numbers’, which
shows that the result of a trial performed a large number of times converges to the
expected value of the underlying variable. This implies that when appointing members of
a board by lot, as the number of appointees increases the proportion of their
characteristics, be it political preferences, socioeconomic status, race, religion, etc, will
tend to reflect accurately the composition of the characteristics of the entire population.
Thence, the decisions made by such a board will be accepted as the decisions made by
the population. The Athenians did not know of probability theory but they were
intuitively aware of the law of large numbers.8 Tangian (2008) evaluated the ability of
boards selected by lot to represent the preferences of Athenians using three criteria:
Popularity, which reflects the number of citizens represented by the randomly selected
board; universality, which reflects the number of times a majority of the population is
represented by the board, and goodness of representation, a measure of accuracy, which
is the ratio of the average group represented to the majority of the population on an issue.
Applying computational formulas as used in fourth-generation computer languages he
shows that the representative capacity of the appointment to office by lottery as it has
been practiced in Athens was “quite high”. The argument that lotteries pick
representative samples underpins the surviving practice of jury selection by lot.9
7
Sortition has also been the subject of recent reform proposals. For example, in a widely
discussed proposal about the reform of the UK previously hereditary House of Lords (which
scrutinises legislation passed by the House of Commons, the elected chamber of the Parliament),
called “the Athenian option”, Barnett and Carty (2008) proposed that its members will be selected
by lot rather appointed by the government.
8
‘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).
9
On the rationale for choosing jurors by lot, Mulgan (1984) p.554, writes: “Trial by jury
is trial not by experts but by good men and true, average citizens...Athenian juries may have
been much larger and may have had much wider discretion and jurisdiction; nonetheless, modern
8
3.2
Distributive justice and equality of opportunities
A fundamental condition of modern democracy is that all citizens have an equal right to
choose the government in a competitive election. Manin (1997) attributes the use of
election in modern representative government to the legitimacy it confers to those
occupying office, where legitimacy means that the decision taker is recognised to have
the right to do what he does. Since the governed are obliged by what they have consented
to, the winner of the election occupies office legitimately because he has earned the
consent of the governed. The struggle for democratization during the 19th and early 20th
centuries centered to a large extent on extending voting rights to all citizens, irrespective
of their wealth and other characteristics.10 Equality of citizens to consent to power is one
aspect of democracy; in ancient Athens, this element was satisfied by the participation of
citizens directly in the Assembly.
Another aspect of democracy is equality of opportunity that citizens may occupy public
office, an attribute however which is hardly satisfied by the election process of modern
representative government. Manin (ibid.) gives four reasons for the latter. First, voters
treat different candidates unequally; in the privacy of the ballot booth they use whichever
abstract or specific criterion they like to choose between candidates. Second, candidates
for office distinguish themselves from each other; a candidate emphasizes what makes
him different from other competitors in order to stress his superiority and suitability for
office. Third, an election contest favors candidates who are perceived positively by the
voters, so that individuals who for whatever reasons are prominent enjoy an electoral
advantage. Fourth, as candidates need to spend resources in order to become known and
finance their campaigns, candidates with unequal sums of resources have unequal
chances of electoral success. As a result of those reasons, an election will produce office
holders with distinct characteristics from those of the voters, and the political class may
be perceived as superior to ordinary voters. In this respect, the nature of elections is
and ancient trial by jury shares the same idea of trial by random cross section of citizens on behalf
of the citizen body as a whole.”
10
Note that in practice equality of voting rights may be violated because of the intricacies
of voting rules and differences in the numbers of voters across different constituencies).
9
“aristocratic” (or “elitist”) as Aristotle had argued, and elections as a method of
appointment to office fail to satisfy the condition of equality of being chosen.11
A number of contemporary authors support the use of lotteries as a mechanism to pursue
distributive justice; see amongst others Goodwin (2005) and Stone (2007) and (2009a and
b). According to Stone (2009a) the lottery satisfies three principles of justice, namely,
efficiency of outcomes, fairness of outcomes and fairness of treatment. Efficiency of
outcomes means that it is more just to satisfy an individual claim to obtain a resource
than not; it mirrors the standard economic criterion of Pareto efficiency. Fairness of
outcomes means that claims should be satisfied in accordance to their strength. This
involves two principles, notably, priority (or vertical equity), which stipulates that the
stronger claim must be satisfied first, and impartiality (or horizontal equity), which
demands that like cases must be treated likely. Fairness of treatment means that in cases
of indeterminacy, where claims for a scarce resource are of equal strength but there is not
enough resource to satisfy every claimant, the agent charged with the allocation of the
resource must not favor any claimant. Selection therefore must not be based on any
reason. This is satisfied by the lottery whose outcome is impartial and selects claimants
on the basis of no reason. Stone (2009b) terms the removal of reason from the outcome of
decisions made by lottery the sanitizing effect of the lottery. The sanitizing effect offers a
strong argument to use the lottery when it is feared that a decision will be made for a bad
reason (or because the bad reasons outweigh the good reasons). The implication for
selection to office is clear: When there is no reason to prefer one citizen to another in
discharging the duties of office and obtaining its benefits, appointment by lottery satisfies
the above principles of justice.
Returning to ancient Athens, Taylor (2007) carries out chi-square tests on surviving data
on the geographical origins of the elected generals and magistrates appointed by lot. She
shows that a disproportionately large number of elected generals came from areas close
11
The attachment of present-day democracy to electoral outcomes is nicely illustrated in
the following example given in Tangian (2008): In 1985 the French Constitutional Council
(constitutional court) struck down as non-democratic and illegal a proposal to introduce selection
by lot (of 3/4 of members) in the French Superior Council of Universities.
10
to the city of Athens, while no such bias was detected in the origins of officers appointed
by lot, who originated evenly from places throughout Attica. She explains the difference
by the high opportunity cost of time and expenses confronting citizens coming from the
outer regions when competing in elections in the city. On the other hand, there is no bias
in the geographical distribution of those who proposed decrees to the Assembly. Her tests
show that proposers came from places throughout Attica, rather than just those
concentrated in the city. Based on such evidence Ober (2008) contends that the use of lot
for appointment to office and the payment for service greatly equalized opportunities for
political activity among Athenians, where otherwise significant inequalities remained
between elite and non-elite classes.
3.3
Conflict, corruption and power
Selection of post-holders by lot serves to restrict the powers of government officials and
reduces factionalism and corruption. Holding power for no other reason than the luck of
the draw diminishes the impositions that government officials can make on the governed
and so does the frequency of alternating between governing and being governed.
Similarly, by enabling large numbers of citizens to hold office for short periods of time,
citizens are given the opportunity to experience office irrespective of personal wealth or
social class. Further, as office may be desired because of the advantages and prestige,
competitive elections open the way for rivalry and even civil war. On the other hand, as
appointment by lot implies that that its occupant is decided by chance, it may diminish
competition for office and even make office less attractive as a means to acquire power.
Since the outcome of the lot is unpredictable, no party can plan to place its supporters in
positions of power or systematically advance its interests. Dowlen (2010) notes that
appointment by lottery enables citizens to participate in government without requiring
that they first obtain power through political partisanship. As a result, no actor has the
power to distribute the rents from office to any other actor. It follows that appointment by
lottery severely restricts the ability of the elite to hold on to posts of authority and enjoy
the benefits from office and patronage. In this light, sortition also serves as a mechanism
to control self-promoting proclivities of officials. In addition, by sharing the benefits
11
from office among a large number of citizens it acts as an instrument to integrate citizens
in the community.12
Nor can randomly selected and frequently alternating officers be bribed in advance13, an
argument that applied equally to the selections of councilors, magistrates and judges.
Looking specifically at the judges, a prerequisite for maintaining confidence in the
impartiality of judicial rulings is that no disputant is able to intimidate or bribe the judges.
Incorruptibility was well served by the large number of judges appointed by lottery on the
day of the trial in Athens and the random allocation of judges to trials each day.
Even a sovereign assembly of citizens needs to delegate administrative functions. But a
body of government officers put in place to work for the assembly may develop its own
authority in opposition to the assembly. Headlam (1891) was the first to emphasize that
the diminution of the authority of post-holders appointed by lot together with office
rotation also served to preserve the primacy of the Athenian Assembly.14 Levy (1989)
examines the statistical basis of the Athenian constitutional arrangements and concludes
that random selection of the members of the Council and rapid turnover diminished the
ability of politicians to manipulate policy outcomes and made it more likely that decision
outcomes in the Assembly reflected the median voter. Dowlen (2008) argues that the
unpredictability and impartiality of sortition made the lottery one of the most effective
deterrents of factionalism and civil war, an aspect that he considers as perhaps more
important than the equalisation of opportunities. Finally, Tridimas (2011) argues that
sortition was an integral part of the governance of ancient Athens consistent with direct
democracy under majority voting and the absence of political parties. Appointing
officials by lottery obviated the intermediation of politicians strengthening the primacy of
the Assembly, while majority voting in the Assembly implied that all citizens carried the
same weight in deciding issues of public interest, leading to equality of political and legal
12
See Goheler (2010) for further discussion of sortition as an instrument of control.
Attempts to bribe serving officers cannot be ruled out; the intensity of this problem was
addressed by the scrutiny carried out by the Athenian courts.
14
See Mulgan (1984) and Levy (1984) for further discussion.
13
12
rights (isonomy) and therefore the right to hold office which was pursued by random
selection and rotation.
3.4
Policy expertise and political leadership
In a complex and uncertain world, where policy outcomes are adversely affected by
stochastic shocks, citizens may lack the skills to resolve every issue of public interest for
themselves and will be better off by appointing a policy expert, a political leader, to
determine policy. A political leader is a person knowledgeable of public affairs,
competent to manage the internal and external relations of the community and able to
motivate fellow citizens, so that his actions are expected to improve voter utility.
Formally, the benefits of policy making by elected representatives are illustrated in
models assuming an uncertain economic environment subject to stochastic shocks which
reduce welfare, and informational asymmetry between rationally ignorant voters (the
delegating principals) and well informed politicians (the agents) who are able to pursue
policies that offset the random shocks and increase welfare. Nevertheless, as politicians
are granted discretionary powers, the delegation of policy making also involves costs,
since citizens neither know the intentions of politicians nor can they bind their future
actions. When the welfare losses from an adverse environment exceed the losses from the
inability to control politicians, voters will choose policy making by elected
representatives.15
This conclusion implies that the sanitizing effect of the lottery may not extend to the case
where voters are choosing the most talented political leaders with policy making
responsibilities. Appointment by lot removes the opportunity to select the person thought
as most qualified for office. Equivalently, it removes the ability to get rid of incompetent
and corrupt government officials, which implies that officials are no longer accountable
to the electorate. In addition, with sortition the incentives of public post-holders to
15
See, for example, Bendor et al. (2001) for a review of the literature on delegation,
Kessler (2005) for a critical comparison of policy making by policy experts in indirect democracy
and ignorant citizens in a referendum using the median voter framework and Maskin and Tirole
(2004) for a comparison of accountability of elected officials, who may pander to public opinion,
and politically independent policy agents.
13
acquire the knowledge and expertise on policy issues weaken. Significant numbers of
inexperienced candidates may then be appointed to office reducing the quality of policy
outcomes and citizen welfare. Finally, if sortition is based on voluntary participation and
the incentives to serve in office are not sufficiently large, few candidates will come
forward to serve and public posts will be left vacant. This problem may be solved by
making participation compulsory – in which case the lottery resembles a mechanism of
distributing burdens. In view of all these disadvantages of the lot and as already said, the
Athenians filled by election positions requiring leadership skills, like the posts of
generals. Specifically, the lot was used “for all offices but those which require experience
and skill” (Aristotle Politics 1317b 22, quoted by Mulgan 1984, p.546).
3.6
Resource cost of the appointment mechanism
An additional consideration in choosing institutions of collective choice relates to the
resource cost of the decision mechanism. Briefly, the lottery has several desirable
properties. It is relatively cheap to operate, simple to understand and quick to produce
results. These characteristics compare favourably to elections, which are not only more
expensive to organize and run, but also establishing a clear winner may depend crucially
on the voting rule adopted, majoritarian or one or another form of proportional
representation. Of course, this is not to argue that sortition is preferred to election because
it is relatively less costly; it is however to remind that a full evaluation of any decision
mechanism must consider its administration cost too.
4.
The constitutional choice
4.1
The payoff for the method of selection to office under risk neutrality
The present section addresses the question of why at the constitutional stage the citizen
decides to appoint some public officers by elections and others by lottery, and identifies
why, over and above the arguments reviewed before, a citizen motivated by self-interest
may be better off by appointing public post-holder by lot rather than election. The formal
model builds on the constitutional political economy framework developed by Mueller
(1991), (1996) and (1997), and Buchanan and Tullock (1962) in analyzing the choice of
14
rules in a democracy. When drawing up the constitution the citizen aims to set up the
policy making institutions, including the method of appointment to office, that are
expected to maximize his utility. The citizen is uncertain whether or not he will benefit
from the actions of the appointed government official. Let  denote the probability that
he benefits from the policy decided by the public post-holder, with 0 1, and let G>0
be the corresponding benefit. Correspondingly, the probability that the citizen suffers a
loss is 1–and let X>0 be the loss inflicted. Further, let the loss be expressed as a
proportion of the gain, so that, X = kG with k>0. In the special case where collective
action decides issues of pure redistribution the policy gains exactly match the policy
losses, so that G= –X and k=1.
In an election for public post-holders the citizen chooses between candidates while in
sortition he does not. Exercising choice requires that the citizen makes an effort to
become knowledgeable about the issues of policy decided by the public post-holder and
about the quality of candidates for public office. It is reasonable to expect that the larger
the effort invested by the citizen, the more likely that the citizen chooses an officer whose
decisions will confer him a benefit. Formally, denoting effort by Z, the probability 
depends positively on Z. Further,  is assumed to be increasing in Z, but at a decreasing
rate. That is, the more effort the citizen invests in the selection of the public officer the
more likely it is that the citizen will benefit from the policy decided by the public officer,
but effort is characterized by diminishing returns. Formally, this is expressed as =
(Z) with Z  /Z > 0 and ZZ  2/Z2 < 0. On the other hand, recalling that
sortition generates outcomes with fixed probabilities, it follows that under sortition the
effort of the individual citizen does not affect the probability that he selects a public
officer whose actions confer a gain to the citizen. Therefore, appointment to office by
lottery can be represented as the case where the citizen invests zero effort in selecting
public officers. Thus, under lottery  is exogenous and we may write (Z=0) = with
0<<1. It may of course be argued that even under sortition a minimum effort Z0 by the
citizen is still required so that the cut-off point between sortition and election for office is
positive rather zero, so that election to office will be introduced for Z>Z0, rather than
15
Z>0. For example, the eligibility of the candidates wishing to be selected by lot has to be
ascertained, requiring some effort and the like. This slightly complicates the algebra and
the graph that follows but does not affect the intuition gained by the analysis; we then
work on the assumption that appointment by lot is associated with zero effort.
The decision costs that the citizen incurs in order to make an informed choice increase
with the effort invested, K=K(Z), while for simplicity but without loss of generality we
abstract from other resources costs. Specifically, time spent on the effort to increase the
probability of realizing a gain from the collective choice process is time spent away from
work and leisure; with W denoting the productivity of the citizen per hour, then K = WZ.
Further, letting F denote the pay offered to the office-holder by the citizen as
compensation for his services (office rent), the citizen’s pay-off from the collective
choice gain is written as
U = G[(1+k)–k] – WZ – F
(1)
Maximizing the above with respect to the effort Z yields the conditions
UZ = G(1+k)Z –W = 0
(2.1)
UZZ = G(1+k)ZZ < 0
(2.2)
The expression G(1+k)Z is the marginal benefit from effort invested in influencing the
probability that the selected public post-holder implements a policy that confers a gain to
the citizen. The productivity W represents the marginal cost of effort, that is, foregone
earnings when time is invested in acquiring information about politics. As usual, the
optimal level of effort that the citizen should invest in choosing public officers is found at
the point where the marginal benefit equals the marginal cost. This is found by solving
(2.1) with respect to Z. In the present setting, the optimal size of effort depends on the
expected gain or loss from the decision of the appointed official and the labour
productivity of the citizen. When the optimal effort in selecting public officers is positive,
Z>0, the citizen chooses election as the method of appointment to office. On the other
hand, if the optimal level of activity turns out to be zero, Z=0, the citizen chooses to
appoint public officers by lot, and he accepts an exogenous probability that he will
benefit from the decision of the public officer. Obviously, when the decisions of the
public officer relate to routine duties that can be performed irrespective of the skills of
16
the office holder, the citizen finds too expensive to invest time in ascertaining the quality
of office-holders; he is better off by using his time in more profitable activities and
appoints officers by lot.
Figure 1 shows diagrammatically what is involved. The downward sloping lines MB1
̅ shows the marginal
shows the marginal benefit from effort and the horizontal line 𝑊
cost of effort equal to the labour productivity of the citizen. The citizen’s optimal effort is
at Z* which corresponds to the intersection point A. In this circumstance, a positive level
of effort is made implying that the citizen chooses to select officials by elections. Assume
now that for another policy issue the marginal benefit is represented by the line MB2
(below and to the left of the original MB1). For this low marginal benefit, the citizen is
better off by not investing any effort, see the intersection at point A, and therefore he
chooses to install the corresponding officer by lottery. Or consider the choice of the
̿ , above 𝑊
̅ . At point A, the
citizen when his productivity is very high, at the level 𝑊
optimal effort is zero, so that the citizen chooses again appointment by lottery. More
generally, zero effort is optimal for every office characterized by a marginal benefit that
intersects the vertical axis below the productivity intercept point, as, for example,
̅ . It then follows that all posts that generate a marginal benefit
represented by MB3 and 𝑊
of effort below the lowest productivity will be filled by sortition. Moreover, sortition will
be unanimously agreed for all posts that generate a marginal benefit lower than or equal
to the citizen with the lowest productivity. This representation fits well the case of routine
public office duties in ancient Athens where large numbers of citizens tending their farms
and olive groves could not always afford the time to participate in political activities and
monitor closely public officers. In addition to serving representation, equality of
opportunity and non-factionalism, sortition for filling posts of routine duties, combined
with a fee for the time of the serving officer, minimized the cost of political participation.
Further, differentiating equation (2.1) with respect to its determinants and applying the
implicit function rule we obtain (where, as before, a subscript denotes the derivative with
respect to the relevant variable) UZG= (1+k)Z >0; UZk= GZ>0; UZW= –1 and UZR= 0.
17
Figure 1: Optimal effort and the choice of the rule of appointment
Marginal benefit
& Marginal cost
of effort
A
MB1
A
A
MB2
MB3
Z*
Effort
O
Zero Effort Positive Effort
Lottery  Election
The comparative static properties of the optimal level of effort are then as follows:
dZ/dG = – UZG /UZZ > 0
(3.1)
The higher the benefit the citizen expects from the decision of the public post-holder, the
more effort he invests in influencing the probability that he benefits from the mechanism
of selection to office.
dZ/dk = – UZk /UZZ > 0
(3.2)
As above, the higher the loss that may be inflicted by the decision of the public postholder, the more effort the citizen invests to avoid such a loss.
dZ/dW = – (–1) /UZZ < 0
(3.3)
The higher the productivity of the citizen, the less time he spends trying to influence the
appointment of the public post-holder; his time is more valuably invested in income
earning activities.
dZ/dF = 0
(3.4)
18
The size of the reward paid to the public post-holder does not affect the effort of the
citizen for the reward for the services of the post-holder has to be paid irrespective of
whether or not the citizen benefits.
As a corollary, it follows that it is not optimal for all public offices to be filled by the
same rule of appointment, and that the larger the stakes for the citizen the more likely he
is to choose public officers by election.
4.2
The payoff for the method of selection to office under risk aversion
So far it has been assumed that the citizen is risk neutral when faced with the random
outcome, benefit or loss, of the collective choice mechanism. We now examine how risk
aversion may affect his choice of the method of appointment to office. Suppose that the
citizen has Euclidean preferences over the random benefit he expects from the institution
of collective choice, so that his utility loss increases with the distance between his ideal
point and the actual policy outcome. This is described by the familiar quadratic loss
function U = –E[𝐺̂ –Gi]2, where E denotes the expectations operator, 𝐺̂ denotes the
citizen’s ideal benefit and Gi is the random outcome that takes the value G (benefit) with
probability  and –X= –kG (loss) with probability 1–. The expected loss is written in
terms of the mean, and the variance of the random Gi as U = –[𝐺̂ –E(Gi)]2–2. The benefit
from the collective choice process has a mean of E(Gi) = G[(1+k)–k] and a variance of
2= [G–E(Gi)] 2+(1–)[X-E(Gi)] 2 which after rearranging gives 2 = (1–)(1+k)2G2.
Setting 𝐺̂ =G, we obtain the citizen’s pay-off from the collective choice mechanism as
 = –(1–)(1+k)2G2 – R – WZ
(4)
Maximization of the latter with respect to effort Z produces the condition
Z = (1+k)2G2Z –W = 0
(5)
Noting that (1+k)2G2>(1+k)G and given that ZZ<0 the optimal level of effort Z**
which emerges from solving (5) exceeds its analogue Z* from solving (3) under risk
neutrality. Hence, in accordance with intuition, risk aversion is associated with more
effort to influence the probability of a benefit and makes appointment to office by
elections more likely. On the other hand, under risk neutrality appointment to office by
lottery is more likely. On this account frequent use of sortition as practiced in Athens
19
may be interpreted as an indirect indication of risk neutrality. Otherwise, Z** and Z*
have the same comparative static properties as described in (3.1) – (3.4).
5.
The calculus of a candidate for office
The present section completes the analysis by examining why citizens decide to compete
in an election or are willing to be selected by lot to serve in public office. Since in ancient
Athens public officers selected by lot performed routine duties but did not decide policy
(which was determined by the assembly) we assume a setting where candidates for office
are only interested in the personal benefits from office and not in policy outcomes. This
assumption rules out the ability to pursue policy objectives as a motive for seeking office.
For concreteness, we focus on the case of a man interested in being a councillor – a
member of the Council of Five Hundreds – where according to Hansen’s calculation (see
Section 2) the probability that a citizen above the age of forty would become councillor
over his life-time was two-thirds.
5.1
The citizen
Each citizen j maximizes a utility function defined over private consumption, Q, leisure,
L, and the intrinsic value placed in occupying office S, U=lnQ+(1–)lnL+S. Utility is
maximized subject to the budget constraint that consumption is financed by the sum of
labour income WN(1–L), where W denotes the productivity of the citizen and the time
endowment is normalized to unity, and property income, Y. After the relevant
manipulations, and denoting Aln+(1–)ln(1–)<0, the indirect utility of a citizen
earning his income from private sources, that is, not serving in public office, is
V0 = A+ln(Y+W)–(1–lnW
(6)
It is next assumed that when a citizen serves in public office he spends an exogenously
determined proportion of his time endowment H to deal with the responsibilities of
government and receives a fee for his service at a rate R. Earned income is then W(1–L–
H)+RH. Maximizing utility subject to the latter and solving, yields the following
expression for indirect utility
VS = A+ln[Y+W+H(R–W)]–(1–)lnW+S
(7)
20
5.2
Election
The citizen who wishes to be elected to office incurs the cost of fighting the election
campaign to become known to the voters, explain his policies and the like, denoted by C
and assumed to be exogenous. Let P denote the probability that the citizen wins the
election to office. Consequently the probability of losing the election and remaining in
private life is 1–P. His expected utility from competing for office in elections is then VE=
PVS+(1–P)V0–C, or upon substitution
VE = A+P[ln(Y+W+H(R–W)+S]+(1–P)ln(Y+W)–(1–)lnW–C
(8)
The citizen is willing to contest an election for office, when the expected utility from
office exceeds the utility from private life, that is, E0  VE–V0 > 0. Substituting from (6)
and (8) we find
E0 > 0
for
ln[Y+W+H(R–W)]–ln(Y+W) + S > (C/P)
(9)
It is straightforward to see that a citizen will be interested in occupying elected office if
the fee for service is larger than his labour productivity, R>W, and / or office confers
large value to its occupant, so that the sum in the left-hand-side of (9) is positive and
greater than the quantity C/P. Similarly, the citizen will be more likely to contest an
election for office, the lower the campaign cost of election, C, and the larger the
probability of winning the election, P.
5.3
Sortition
The citizen who is appointed to office by lot is again assumed to spend the same
proportion of his time H to carry out his duties, receive an office rent R and place a value
S in being in office; however, he no longer has to spend resources in campaigning. Let
denote the probability that he is selected to office by lot; correspondingly the
probability that he is not appointed is 1–. His expected utility from being a candidate for
office under sortition is V = VS+(1–)V0, or
V =
A+ [ln(Y+W+H(R–W)+S] + (1–)ln(Y+W)–(1–)lnW
(10)
Taking the difference of the utilities under sortition and as a private citizen, 0  V–V0,
we obtain that the citizen is willing to be considered for office service by lottery when
0 > 0
for
ln[Y+W+H(R–W)]–ln(Y+W)+S > 0
(11)
21
Two important observations follow. First, contrary to the election participation, whether
or not the citizen decides to be considered for sortition is independent of the probability
of being appointed . Second, for the same value of S under both election and sortition, it
is easily ascertained that the minimum fee for office service required to contest an
election exceeds its analogue for sortition. Alternatively, for the same value of financial
reward from office, a citizen will be interested in seeking office through election only if
office won through election confers higher intrinsic value, S, than appointment to office
through sortition. Such findings confirm the intuition regarding the diminution of the
value of office occupied by sortition discussed in Section 3.
To gain a better understanding of the meaning of condition (11), let us focus on the case
of a poor citizen, defined as one with zero non-earned income, Y=0, serving in office and
̅ , (at was the pay of the members of the Council of
paid the mean wage, 𝑊
Five
̅
Hundreds), and derives no intrinsic value from holding office, so that S=0. Setting R=𝑊
and substituting, condition (11) yields that the necessary condition for a citizen to
̅ . This implies that all Athenians with no means
volunteer for public office is that W < 𝑊
to support themselves but their own work, and with labour productivity less than the
mean, were prepared to serve in public office. It then follows that whatever their ethical
motivations, participating in government was fully consistent with selfish financial
motives of utility maximization and explains formally why the ancient Athenian
democracy was highly participatory.
5.4
The choice of the candidate for office: Elections V Sortition
We now turn to query if, given the option, a candidate for office prefers to fight an
election campaign or the lot as a method to win office. In practice, candidates do not
choose whether to compete in an election for office or to enter a lottery, as the rules of
appointment are determined at the constitutional stage and therefore cannot be chosen by
the candidates themselves. However, we focus on the choice of a constitutional framer,
who is actually interested in winning office in the post-constitutional politics. This setting
violates Mueller’s “first law of constitution writing”, which states that those who are likely
to hold office under the new constitution should not be involved in writing the constitution
22
because they may establish institutions which serve their own interests rather than those of
the citizens” (2005, p.67). However, the setting described may fit well the circumstances of
ancient Athens at the time of the introduction of sortition, where the number of citizens
with full political rights and therefore eligibility for office, was sufficiently small to
generate a reasonable expectation that a citizen – constitutional writer would at some
point in his life-time serve in office.
Substituting from equations (8), (9) and (10), the difference between the expected utility
of a candidate for office by election and by sortition is E VE–V= (P–)(0/)–C.
Assuming that the citizen volunteers for office via sortition, that is, 0>0, we derive that
E>0
for
P >  [1+ (C/0)]
(12)
That is, a contestant for office will be prepared to compete in an election rather than seek
office via sortition only when the probability of winning the election exceeds the
probability of winning the lot by at least the quantity C/0, which represents the cost of
election campaign discounted by the net utility of office by sortition. In the opposite case,
he chooses sortition.
As a final issue, let us consider two competing constitutional writers, J and N, who, in
view of the small number of eligible citizens, anticipate that at the post-constitutional
stage they will be competing for office, and inquire whether they cam unanimously agree
on the method of selection to office. The probabilities of success in the election and the
lot are respectively P and  for J, and 1–P and 1– for N. Using (12), we have (where CJ
and CN denote the corresponding campaign costs)
JE > (<) 0
for
P > (<)  [1+ (CJ/J0)]
(12.1)
NE > (<) 0
for
1–P > (<) (1–) [1+ (CN/N0)]
(12.2)
When JE>0 and NE>0 both candidates are ex ante better off by appointing the winner
of a competitive election to hold public office, so that they unanimously agree to
elections. When JE<0 and NE<0, they both unanimously choose appointment by
lot. If JE>0 and NE<0, J is better off with elections and N is better off with sortition,
23
and vice versa if JE<0 and NE>0. In the latter two circumstances, the candidates fail
to voluntarily agree on the method of appointment to office. In this case, the method of
selection will be decided by whoever emerges victorious from the conflict between them
and writes the constitution unilaterally, or by a third-party enforcer.
Adding (12.1) to (12.2) we obtain that for JE>0 and NE>0 simultaneously, it must be
(CJ/J0)+(1–)(CN/N0) < 0, a condition which is always violated, since all elements
on the left-hand-side are positive. This implies that the two candidates will never
unanimously agree to appoint officers by elections; one of them expects a higher ex ante
pay-off from sortition. On the other hand, for JE<0 and NE<0 to hold simultaneously,
it must be 0 < (CJ/J0)+(1–)(CN/N0), a condition which always holds, so that it is
possible for the candidates to unanimously agree to the lot. Intuitively, the reason is that
with appointment by lot both candidates save the campaign cost of elections. This logic
offers formal proof of Lyttkens (2008) view that the Athenian aristocracy introduced
sortition to avoid infighting, where J and N can be thought as intra-elite factions.
However, even though the condition 0<(CJ/J0)+(1–)(CN/N0) may hold, sortition
will not be automatically agreed. One of the candidates may still be ex ante better off
with elections. For example, if the probability of winning the election is sufficiently high,
he will not give up such a prospect of success, despite its cost, by consenting to
sortition.16 It follows, that elections will be established when the contestant who expects
the highest benefit from elections also acts as constitutional framer.
5.
Conclusions
Contrary to the modern democratic government where election to office prevails, the
democracy of ancient Athenians appointed annually scores of officials by lot. The present
paper inquired two issues, namely, when it is optimal for a self-interested constitutional
writer to appoint public officials by lot and, if given the choice, candidates for office
Formally, J prefers election and N prefers sortition when P>[1+(CJ/J0)] and 1–
P<(1–)[1+(CN/N0)],
which
after
manipulating
yields
the
condition
J J
N N
N N
P>+(½){[(C / 0)+(C / 0)]–(C / 0)}, which cannot be ruled out a priori. Similar
considerations apply to the case J prefers sortition and N prefers election.
16
24
prefer to compete in an election or to be appointed by lot. Recognizing that the decisions
of officials appointed under one or the other mechanism may affect his utility differently,
a citizen will choose to establish the selection mechanism expected to maximize his
payoff. Several justifications of appointment by lot have been offered in the literature,
most prominently, representativeness of the preferences of the population, absence of
good reasons to favour one candidate over another, rotation in office, reduction in
factionalism, decrease in corruption and weakening the influence of the elites, and
administrative economy. The present paper complements this literature by applying
standard economic rationale and focuses on the cost – benefit calculus of the citizen in
choosing the method of appointing officials to office. The cost relates to the certain effort
that must be invested in making an informed choice when voting for officials. The benefit
relates to the uncertain gain that the citizen derives as a result of the actions of the
officials. When the marginal benefit from the extra effort is small in comparison to the
cost of that effort, either because the uncertain extra gain is small or the cost of time
given up to make an informed choice is large, the citizen is better off by eschewing such
choice and allocating public offices randomly across those interested in serving as public
officers. Next, the paper investigated, when a citizen is willing to give up his time in
order to occupy office, where office confers rents but not the right to decide policy. For
election to office the choice depended on the probability of electoral success and the rent
from office in comparison to the productivity of labour and campaign cost of election. On
the other hand, since sortition does not involve campaign costs, a candidate prefers
appointment by election rather than the lot if the probability of winning the election is
greater than the sum of the probability of lottery success plus the relevant adjustment for
campaign costs. Finally, assuming two contestants for office standing against each other,
it was found that there are circumstances where both expect a higher ex ante payoff from
sortition, but no such circumstances arise for elections. Hence, if given the choice, the
contestants may unanimously agree on sortition as a method of selection, but they will
never both voluntarily agree to elections.
Perhaps the most important message from the present inquiry has been that appointment
to office by lot is consistent with purely self-interested behaviour. That is, a method of
25
selection to office which denies the citizens and the candidates the ability to choose, and
is almost alien to modern political practices, can actually be attributed to the hard-nosed
utility maximizing choices by the players who are the beneficiaries of the mechanism.
Acknowledgement: I wish to express my gratitude to Dennis Mueller for a number of
stimulating comments during the undertaking of this research. My thanks are also due
to Andreas Bergh, Nigar Hashimzade, Carl Hampus Lyttkens and participants to the
2011 European Public Choice Society Conference for their comments and suggestions
on an earlier version of the paper. The usual caveat applies.
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