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The Athenian Trierarchy: Mechanism Design for the Private Provision of Public Goods

Published online by Cambridge University Press:  29 May 2007

Brooks A. Kaiser
Brooks A. Kaiser
Affiliation:
Associate Professor, Department of Economics, Gettysburg College, Box 391, 300 N. Washington St., Gettysburg, PA 17325. E-mail: bkaiser@gettysburg.edu.
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Abstract

The liturgical system in Classical Athens (479–322 BCE) privately provided public goods, including naval defense. I use it to evaluate mechanism design policies and to address uncertainties in the historical record by adding predictive economic theory to research by ancient historians. I evaluate the system's success at meeting the conflicting goals of efficiency, feasibility, and budget balance by analyzing the Athenian citizens' incentives within a game of asymmetric information. In the game, multiple equilibria occur; citizens may or may not volunteer for duty or avoid it. I relate the game theoretic findings to historical events.

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The Journal of Economic History , Volume 67 , Issue 2 , June 2007, pp. 445 - 480
Copyright
© 2007 The Economic History Association

In a private market, public goods tend to be undersupplied because they are nonrivalrous and nonexcludable. Government provision is the general solution to this inefficient level of public goods today, but economic theory suggests other possibilities, most notably mechanism design, which uses incentives to induce agents to purchase the optimal amount of the public good. The problem with such mechanisms, however, is that it is impossible to achieve this optimal level of production and at the same time meet budget balance requirements and induce agents to comply. As a result, mechanisms of this sort have rarely been implemented by governing bodies.

One remarkable exception is the Athenian liturgical system in the Classical period (479–322). (All dates are BCE.) This liturgical system provided a solution for the provision of public goods where direct government taxation and procurement were not feasible. The trierarchy, or the command, outfitting, and maintenance of a war ship for one year, was at the core of this liturgical system, and I evaluate its success in advancing the private provision of a public good—namely naval military services. Using mechanism design theory and the surviving evidence regarding public goods provision in Athens, I investigate the institution of the trierarchy as a revelation mechanism and identify problems with using such a mechanism to provide public goods in general.1

Fudenberg and Tirole, Game Theory. Note that game theory, of which mechanism design is a subset, is a model of behavior in general; it is not restricted to economic dealings narrowly defined.

The article models the provision of Athenian naval defense in light of the resource base, institutional constraints, and asymmetric information among citizens and the government. Mechanism design is the appropriate tool here because the system was introduced following Kleisthenes's democratizing reforms at the end of the sixth century, and can thus be considered a departure from the historical mold. It was, roughly speaking, a new institutional solution to a problem—just the sort of thing for which mechanism design was created. Mechanism design has the added advantage of providing a theoretical framework for investigating welfare questions of efficiency, feasibility, and budget balance. This enhances our ability to understand the evolving constraints facing Athens through the fifth and fourth centuries, and the resulting insights should interest not just economists or economic historians but all ancient historians as well.

Traditional explanations of Athenian compliance rely on altruistic or noneconomic incentives, particularly the concepts of aretē, a complex form of military honor, and timē, another form of public honor.2

Rahe, “Primacy”; and Finley, Studies. See also Whitehead, “Competitive Outlay.”

The frequently held belief that the Athenian economy existed solely as an imbedded function of socio-political and familial relationships has also served to portray Athens as a society to which modern economics cannot be applied. Yet recent scholarship (on financial transactions in particular, albeit not always in agreement) has begun to change that view, with Edward Cohen showing, for example, that loans between unrelated individuals occurred frequently.3

Millett, “Maritime Loans”; Cohen, Athenian Economy; Silverman, “Trierarchy”; and Shipton, Leasing.

This article extends the investigation into the arena of public goods provision within the context of Athenian democracy.

Although ancient historians have examined the liturgical institutions of Athens and extant evidence surrounding them, mechanism design theory yields a deeper understanding of the behavior involved.4

For example, Gabrielsen, “Diadikasia Documents” and Financing the Athenian Fleet; Whitehead, “Competitive Outlay”; and Athenian Institution.

It does so whether trierarchs were motivated by financial gain, public honor, or by other motives, and it reveals complications unresolved by the tools historians usually use. In particular, because the theory shows that this sort of mechanism cannot satisfy budget balance, feasibility, and efficiency simultaneously, one or another of these characteristics must have failed at any given time. Thus, when describing the evolution of the institution over two centuries, we can use the theory and its requirements and the existing evidence to make rational systematic hypotheses about how the institution changed and what these changes may have meant.

From extant records pertaining to the trierarchy, family wealth, liturgical history, and the political structure of Athens, the article tests the functionality of the institutional mechanism of the trierarchy by analyzing the incentives and behavior of the individual agents affected by it.5

On trierarchy, see Davies, Athenian Propertied Families; Gabrielsen, Financing the Athenian Fleet; Inscriptiones Graecae (IG) II2: 1604–1632; IG II2: 1928–1932). On family wealth and liturgical history, see Davies, Athenian Propertied Families. On the political structure of Athens, see Traill, Political Organization; Osborne, Demos; and Whitehead, Demes.

The analysis of these records indicates Athenians sought to protect their assets and interests. The collective, democratic actions that determined the institutional framework and evolving changes over the Classical period are shown as responses to changes in the resource base. Constricted resources required institutional change in order to decrease the dependence on voluntarism within the trierarchy and ended up spreading the private burden of providing public goods across the citizenry.

Although the data are limited, the article adds to our understanding of Athenian democracy and economy by placing the trierarchy into the framework of a mechanism design problem for the private provision of national defense under asymmetric information. The mechanism successfully created incentives that provided privately for a public good in an efficient manner. Data analysis also strengthens our understanding of the Athenian behavior, as those who exchanged properties formally, probably at court order, give many indications of having hidden or greater wealth to protect.

HISTORY

The first major victory for the Athenian navy came at Salamis in 479. By repelling the Persians with perhaps as many as 200 new triremes, the Athenians established themselves as the pre-eminent Greek polis.6

Thucydides 1.14, 1.74, and 1.112; and Gabrielsen, Financing the Athenian Fleet, p. 37.

This first heavy reliance on triremes, which were narrow, fast, relatively unstable vessels designed specifically for warfare, signified a shift from having naval services provided by individuals (who were mainly protecting transport goods) to having a state naval force protect the homeland and its assets. Though there is some historical controversy over the source of these new ships, most ancient historians agree that in the 480s the citizenry decided to use recently obtained funds from nearby silver mines to upgrade the navy from a collection of at most 80 private vessels for war and trade to one that included over 200 triremes.7

Herodotus 7.144; Aristotle Athenaion Politeia 22.7; and Wallinga, Ships.

By 480 it is clear that Athens had formally developed its liturgical system for the provision of public goods ranging from choregia (festival plays) to the trierarchy. This liturgical system probably stemmed from the democratic reforms of the ruler Kleisthenes in 508/7. Peter Wilson provides an in-depth investigation of the choregia which supports the idea that public munificence was driven by economic interest in prestige and that this was manipulated by the state to improve the quality and preparedness of the trierarchs as well.8

Wilson, Athenian Institution, p. 48.

Carl Lyttkens, for one, attributes the origins of the liturgical system to rational actors signaling their eligibility for public service under the new requirements that began to separate aristocracy from civic opportunity.9

Lyttkens, “Effects.”

Under these reforms, Attica had been reorganized politically into a more democratic structure, with a boule (council) of 500 chosen (by lot) from ten approximately equal tribes, made up of 139 demes, where a deme was a small community akin to a village (though membership did not necessitate residence). Each deme had its own local government and well-developed political system, but Athens was the cultural, political, and legal center of Attica, and the location of the council meetings and courts that determined the fate of potential liturgists.10

Whitehead, Demes.

Demes were aggregated into 30 trittyes and ten tribes, where each tribe was composed of three trittyes, one identified as coastal, one inland, and one city.11

Traill, Political Organization. Though much is unknown about the trittys' purpose (Whitehead, Demes, introduction), Aristotle (Athenaion Politeia 21.2) indicates that the country was divided into trittys so that each tribe might share resources across city, land, and coast. As a risk-sharing strategy, this is reasonable.

Demes varied in status and wealth. As such, the burden of trierarchies fell unequally across demes. In the early sixth century, Solon had divided citizens into four groups, based on their properties' annual agricultural output. The three upper groups were landowners and these persons formed the base for liturgical service. Amongst these landowners, wealth took three main forms: visible, self-proclaimed, and actual. Lyttkens investigated the theoretical marginal effects of the taxation mechanisms (direct and indirect) on the citizenry and found significant incentive to hide wealth.12

Lyttkens, “Effects.”

The disparities, as well as the expectations of fellow citizens regarding one's wealth, or one's perceived wealth, define the core of the asymmetric information that required a mechanism design solution to the problem of providing public goods.

THE TRIERARCHY

The Mechanism

Under Kleisthenes's reforms, we see a revelation mechanism constructed that attempts to align true wealth with civic duty. The council does not observe true wealth, only visible wealth. Visible wealth (

) is the amount of wealth that the community might easily inspect. The most prominent form is landholding, but it also includes slaves, mine contracts, ownership of a workshop, or similar assets.

13

Gabrielsen, Financing the Athenian Fleet, pp. 43–67.

Self-proclaimed wealth (

) might be identical to visible wealth, or might either exaggerate or diminish the value of one's property. It represents a citizen's willingness-to-pay. We label the difference between visible wealth and self-proclaimed wealth as

. This may have either a positive or negative value; if political standing or other nonmonetary rewards accrued from performing liturgies, then one might overstate one's wealth.

True wealth (θi) might also equal visible or self-proclaimed wealth, but might also include monies lent out to bankers or in other private arrangements that could potentially be kept secret. Keeping wealth secret put that wealth at risk, because the secrecy made its holders less accountable.

14

Cohen, Athenian Economy.

For many reasons, self-proclaimed wealth might be higher or lower than actual wealth. It was visible wealth (

) that first determined the individuals liable for liturgical service in any given year.

15

Gabrielsen, Financing the Athenian Fleet, p. 42.

Once the boule identified the purportedly wealthiest citizens, visible wealth determined whether or not an individual actually carried out the service or attempted the antidosis-challenge to avoid it instead. This challenge allowed an individual charged with performing a trierarchy the opportunity to prove another individual more fit (wealthier) to carry it out. The mechanism was clever; if an individual challenged another in the antidosis, the challenged citizen had three choices. He might agree that he was indeed wealthier (

), where citizen i is the challenger and citizen j the challenged, and perform the trierarchy himself. If the challenged citizen did not agree, two choices remained. He might simply have offered to swap his visible wealth for that of his challenger's, and then the challenger would have had to perform the trierarchy with this new level of wealth. Alternatively, he might rather have let the court decide, based on investigation of wealth. In that case, the court would designate either the challenger or the challenged citizen (each one facing a positive probability of being selected); the selected one would have kept his own wealth and had to perform the trierarchy. The intention of the mechanism was to shift responsibility for public expenditures from those who appeared to have the most wealth to those who actually did by creating incentives that either revealed true wealth and enabled a state-mandated shift of responsibilities accordingly, or induced a private redistribution of the responsibilities to the parties who benefited most from performing the liturgies.

The Game

If we model the liturgical system as a one-shot game, there are multiple potential equilibria: to participate without using the antidosis; to go to court; or to trade properties privately such that the offer is attractive to the challenger because it is more beneficial than the expected court outcome but is attractive to the challenged because it is less costly than the expected court outcome. The different equilibria are possible in particular because though outlays on the ship itself might be expected to be approximately equal across trierarchs, the opportunity costs may have varied greatly. Independent farmers, for example, would have had more difficulty being away from the fields during the summer, which was the campaign season. Aretē, timē, or some other public honor that was not directly economic might have increased political power and the potential for welfare gain through better seats at festivals or financial opportunities, effectively reducing the cost of the trierarchy by differing amounts according to individual preferences.16

Carter, Quiet Athenian; and Gabrielsen, Financing the Athenian Fleet, pp. 10–11.

Because the welfare gain from political power and social prominence may actually have been higher from performing choregia rather than trierarchies, I investigate whether these liturgical duties are substitutes.17

Wilson, Athenian Institution, pp. 111–13.

Economic reasons for participating without a further challenge include having a high valuation for the expedient provision of naval protection and also the potential for spoils of war.

FIGURE 1 GAME TREE FOR TRIERARCH DECISIONS

I define the conditions for the equilibria by backward induction. Appendix 1 presents the formal mathematical analysis; the workings of the game and its conclusions are described here.

First, I define the game. The possible actions of the players are listed first, with a quick explanation of the real-world scenario. See Table 1 for a visual representation of the mechanism.

STAGE ONE: GENERALS ASSIGNED TRIERARCHIES

Each year the demes reported on the visible wealth (

) of their members (though the exact procedure is unknown) so that the generals (strategoi) could assign trierarchies to the Athenians with the highest levels of visible wealth.

18

The number of trierarchs increases from about 400 to 1,200 throughout the time period in question, while the number of ships remained about 300. Four hundred or so trierarchs were selected; exemptions were given to unsuitable cases including orphans, very old men, and individuals who were already providing another liturgy in that year, or had performed a trierarchy in the previous year (Demosthenes 14.16). These amounted to about 100 individuals per year.

These individuals were assigned a ship and waited to see if their services would be needed.19

Gabrielsen, Financing the Athenian Fleet, pp. 68–102.

Thus citizens were ranked by

, or their visible type (wealth).

STAGE TWO: PLAYER ONE (ASSIGNED A TRIERARCHY) CHOSE TO PAY OR CHALLENGE

Player One chose between paying for the trierarchy (resolving the game) and challenging Player Two, an individual not assigned a trierarchy, to the antidosis. In the case of a challenge, the interaction proceeded. Without a challenge, the payoffs were simply Player One's true wealth adjusted for the tax as he bore it (in other words the cost of the trierarchy to him), T1. Though we do not know with what frequency the antidosis was invoked, discharge of another's assigned trierarchy may have been fairly commonplace in spite of the limited records mentioning it directly. For example, Demosthenes suggests by casual acknowledgement that the practice was not unusual.20

The First Phillipic, in which Demosthenes describes the slow and haphazard way in which the trierarchy could hamper war efforts, and states, “it is not until the news comes that we appoint our trierarchs and institute exchanges of property for them, and inquire into ways and means.” (Demosthenes, Speeches, 4.36). Against Meidias, in which Demosthenes describes Meidias and Thrasylochus entering his home and challenging him to take over their trierarchy. (Demosthenes, Speeches, 21)

STAGE THREE: PLAYER TWO (CHALLENGED) PAID OR TRADED PROPERTY

In the case of a challenge, Player Two chose between accepting responsibility for the trierarchy (resolving the game) or making a property exchange offer. If Player Two accepted the trierarchy, the payoffs were such that Player One maintained his true wealth, and Player Two's true wealth was reduced by the cost of the trierarchy to him, T2. If Player Two contested, then a property exchange offer was made. In making a property exchange offer, Player Two chose to list the property that he would exchange for Player One's self-proclaimed wealth (

).

STAGE FOUR: PLAYER ONE ACCEPTED OR REJECTED PLAYER TWO'S OFFER

Player One decided whether or not to accept Player Two's offer of exchange (

).

21

This exchange would take the form of a self-disclosed, “exhaustive” property listing.

Here, x was the amount that Player Two was willing to add to his visible wealth in order to facilitate the switch. If Player One accepted, the game ended, property was exchanged, and he discharged the trierarchy. Player One's payoff was then his initial wealth minus his professed wealth and the discharged trierarchy, plus the wealth received from the trade with Player Two. If Player One rejected the offer, the case went to court, and the outcomes were as described in the next section.

STAGE FIVE: THE COURT MADE A DECISION

With probability P1, Player One was found to be the in the right and would not have to pay for the liturgy. Player Two would have been spared paying with probability (1 − P1). P1 is a decreasing function of both proclaimed and visible wealth of Player One, and an increasing function of proclaimed and visible wealth of Player Two, and it may of course have been affected by other considerations, such as popularity. In court, each agent would try to uncover the hidden portions of the other's wealth, or the difference between his proclaimed wealth and his true wealth, in order to avoid the trierarchy. Thus, when choosing an opponent for the antidosis one would select the agent for whom one had the most valuable private information.

OUTCOMES

In the static game, there will be a property swap only if offering the trade makes Player Two better off than risking a court case and only if accepting the trade makes Player One better off than risking a court case. This is only possible if T2 ≥ T1, or, in other words, if the cost of discharging the trierarchy is higher for Player Two than for Player One (See Appendix 1).

Additionally, for citizens to participate voluntarily and without a challenge, they must have expected that the cost of the trierarchy after a court appeal was less than or equal to zero or that there was simply no one to challenge with a positive probability of receiving a favorable outcome from the court. Only then would going ahead and performing the trierarchy leave them better off.

The mechanism of the antidosis therefore revealed that players with no chance of winning in court did not issue challenges, most likely due to their greater wealth, provided that the trierarchy was costly. Alternatively, the present value of the trierarchy might have been essentially zero because payments for it could be postponed and in the meantime it would bring in public honors.22

There exists also the possibility that the trierarchy would prove profitable, in addition to any purchase of political capital. It is suggested that contractors hired out to serve would take on the responsibility for a lump sum payment, indicating the potential for private gain through plunder or other similar tools. Accounts of large booty include a case in 355 when two trierarchs seized over nine talents from a merchant in Naukritis (Gabrielsen, Financing the Athenian Fleet). This profitability is certainly dampened in expected value by the considerable risk undertaken.

To summarize, trierarchs would “participate voluntarily” when the trierarchy was costless (or possibly profitable) or there was no eligible substitute. They would choose the antidosis otherwise. The challenged trierarch would make an acceptable offer for property exchange when his costs of the trierarchy were higher than the citizen originally chosen and when the offer would compensate for the possibility of an adverse court ruling. Though the citizen might still volunteer for the tangible gains of political power, the existence of the antidosis mechanism belies the strength of this incentive. I pursue this question of incentives quantitatively.

Long-Run Considerations for Trierarchs

In many cases, as far as our records indicate, individuals did not go to court, and they did participate without challenge in discharging their trierarchies. Of the 492 trierarchs for which we have records, only 110 are known with certainty to have gone to court for issues relating to public expenditures such as the trierarchy (see Appendix 2 for discussion of our knowledge of court cases and the trierarchy).23

There are some cases where the epigraphical record is unclear as to whether two appearances of a similar name are for one individual or two individuals in the same family. Davies's assessment of the record is used here (Davies, Athenian Propertied Families).

Ancient historians have offered the desire for timē or aretē as a significant explanation for the lack of court cases.24

Davies, Wealth; Whitehead, “Competitive Outlay”; and Wilson, Athenian Institution, p. 172ff.

But as other ancient historians point out and the mechanism just presented confirms, we need not rely on this explanation alone.25

Gabrielsen, Financing the Athenian Fleet, p. 11ff.

Note also that performing a trierarchy would reduce one's visible wealth and the probabilities of being assigned a future trierarchy both initially and through court hearings. Also, past unchallenged trierarchal participation was used often as a signal that a person was not as well off as his opponent because he had already spent so much money on the state:

For it is the duty of honest jurymen to give respite to those citizens, when they have need of such help, who, when prosperous, willingly perform public services… but as to those who consider lost whatever money they spend on the state, you should bring them to the list of [trierarchs].26

Demosthenes, 42.25.

This reference in the case against Phainippos, and similar ones throughout Demosthenes, Isokrates, and others, address such motivations. Evidently this unknown speaker had performed a past trierarchy and was using it at this time to avoid another. Here we witness two equilibria for the same man over time, and it is unfortunate that we cannot even identify him in order to check his claims or add to our understanding of his situation. I will use the data to identify the characteristics that made people seek court decisions and attributes that would convince them not to go to court.

Efficiency, Budget Balance, and Feasibility

Before I analyze the data, however, let us examine the trierarchy from a welfare standpoint. A mechanism such as the trierarchy elicits compliance with a principal's (here, the polis's) goals—and does so in spite of privately held information—by providing incentives for agents to contribute appropriately (as defined by their willingness to pay, or marginal rate of substitution) to the public good. Yet as theory predicts, however, it is generally impossible to achieve efficient provision, feasibility, and budget balance simultaneously in cases with several agents.27

Fudenberg and Tirole, Game Theory, p. 268ff.

Without the budget balance requirement, any efficient provision of public goods can be implemented, because the increase in social welfare from the provision can be redistributed amongst the agents to insure feasibility. But if budget balance is required, then feasibility fails; compliance with the mechanism that obtains efficiency must be imposed on at least some agents, who will not otherwise choose to participate.

By efficiency, I mean that the level of naval service provision maximizes the sum value of benefits to the community from such service; in other words, the addition or removal of additional trierarchs would lower overall social welfare generated by the naval defense. If the trierarchy is efficient, the sum of the citizens' marginal rates of substitution for naval services equals the marginal rate of transformation of resources for providing these services.

To achieve feasibility, all agents' individual rationality constraints must be met. In other words, the trierarchy must be one in which citizens are willing to participate. Both the antidosis and the distributions of monies from the state affect feasibility; with greater state funds dispersals, the citizen's cost of participating in the trierarchy is lowered and so participation is therefore more likely.

Budget balance requires funds expended must equal funds collected. Here, the trierarchs all must pay for their trierarchies rather than become public debtors for budget balance to hold. Again, it is in general impossible for all three criteria to be met simultaneously. Without state intervention, naval protection would be undersupplied, and the situation could only be remedied if the state subsidized the operation or coerced agents into paying (thereby violating feasibility). What tradeoffs did Athens choose, and with what repercussions?

Efficiency of the trierarchy would require that the individuals with the highest net returns to performing the trierarchies do so, in effect minimizing the cost (and maximizing the benefit) to the polis. The mechanism of the trierarchy was set up so that this efficiency should be achievable. That is, if the individuals with the most property and most land in Attica had the highest valuation from preserving independence and democracy and garnering the other benefits of performing the trierarchies, then the mechanism would work efficiently to provide naval defense at the lowest total cost to the state. This seems a reasonable interpretation of the general incentives Athenians faced. The mechanism does appear to place the burden not only on those who are the wealthiest but also those with the lowest cost of compliance.28

These individuals would have the highest valuations for quality within the ship for which they had responsibility so that the underprovision of quality would be minimized as well. This would be an important consideration as there was no fixed figure for expenditure for the trierarchy or any other liturgy. One's actual duties consisted of manning the trireme with rowers and more experienced seamen. The military personnel on board were at least partially fed and paid by the state. Because the Mediterranean was full of warships and oarsmen could be hard to find, the ships were often manned by non-Athenians. Competition for crews among city-states could be fierce and sometimes battle could be won simply by hiring away sufficient numbers of the enemy's crew. Such was the major expense of the trierarch (Rosivach, “Manning the Athenian Fleet”; and Gabrielsen, Financing the Athenian Fleet. At times ships might also be commanded by hired noncitizens (Jordan, “Metic Trierarchs”).

As stated, in theory optimal provision would require a system where the sum of the individual marginal rates of substitution for the navy over other goods was equal to the marginal rate of transformation (Samuelson's condition). However, considering naval defense as a type of discrete good, by which there is either sufficient protection from attack or there is not, the question of optimal provision of naval power becomes simpler to analyze.29

This ignores the gains from using the navy for other purposes, such as pirating or offensive actions. To consider more fully the offensive role of the Athenian navy in this time period, one could use the evolution of hegemonic power Athens influenced over the Aegean as a measure of the success and failure of naval provisioning over time.

The optimal quantity of ships sent into service each year could be dictated by the state if the ships could be manned. The fleet was large enough that any but the greatest of attacks was warded off. The need for ships also was not continuous; because demand peaked during periods of war, the state had to keep many ships idle for much of the year.30

The citizens did not let the ships sit completely underutilized, however, as there are several known cases of using equipment from one trireme for another, or even using equipment for personal needs.

The feasibility constraint requires that the expected payoff from participating in the mechanism is greater than zero.31

Using the expected payoff to a type relies on the Bayesian individual rationality constraint, which allows players' decisions to remain sensitive to the beliefs they have about each others' types and actions, rather than a stricter dominant strategy constraint (see Fudenberg and Tirole, Game Theory, pp. 270–71.

In our story, the theoretical problem of defining the expected payoff is complicated because the return to the naval services changed over the time period in question. First, the citizens were defending against an external foe, Persia. Then, in building a naval empire, both the demands for and the support of the navy increased (with both ships and tribute flowing from the empire). This was followed by warfare within Greece and even dissention within Athens regarding the form of government and rights, duties, and privileges of its citizenry. With a few brief exceptions, however, Athens did provide naval protection for its citizenry with self-rule until it was incorporated into Alexander's empire, and we interpret the expected payoff to naval defense as the additional monetary and nonmonetary returns achievable as long as it was self-ruled. As those payoffs changed, so too (as we shall see) did the mechanism.

One important concern here (which affected efficiency, feasibility, and budget balance) was that after an individual was assigned to his ship, he often did not know with certainty if he would be needed that year. The probability that he would be needed was a function of the political climate; if tensions were high between Athens and another seafaring nation, the demands on the navy would be much higher. Thus one might have been more willing to accept responsibility for a trierarchy in a peaceful year than otherwise. The evidence suggests that wars were indeed a big instigator for reforms within the trierarchal system.32

Cawkwell, “Athenian Naval Power”; and Gabrielsen, Financing the Athenian Fleet, pp. 173–217.

In these years of warfare, changes to the trierarchal mechanism were frequently proposed or incorporated, and public debts from trierarchies were collected with more rigor. A brief discussion of the wars and the reforms that resulted puts the questions of the budget balance and feasibility into perspective. Overall, it appears that the mechanism moved from one (in the fifth century) where the state supplemented funds so that the budget balance requirement did not matter to one (in the fourth century) where efficiency declined or public debts were incurred. The mechanism also evolved to become more forgiving by including syntrierarchies, or partnerships in which several individuals shared responsibility for a single ship. The partnerships helped spread the financial burden during the fourth century in an attempt to maintain the institution.

In 411, after the disastrous naval losses at Syracuse and at the beginning of the final stage of the Peloponnesian Wars, an internal oligarchic coup by a group known as the Four Hundred (it consisted of some of the richest Athenians) briefly overthrew Athenian democracy. By this point, Athens had lost virtually all of her empire, and the lengthy war had drained local resources as well.33

Thucydides 8.1.

State distributions to the citizens from tribute dwindled. Nevertheless, they continued to fight, and for a short period (410 to 404) regained both democracy and much of their Aegean influence. After the restoration of the democracy, trierarchs no longer had to take a trierarchy single-handedly. Syntrierarchies were now allowed, reducing the individual cost.34

Until further reforms in the mid-300s, syntrierarchies usually included two individuals. Individuals were allowed to choose their partners if they wished one, and so that the many compliance problems one might face with an unwilling partner could be avoided, most chose trusted family members for partners, upon whom they could most easily place sanctions for defaults.

Dwindling individual and state resources made it harder to balance the budget and made the government (particularly under the oligarchy) force individuals to participate; the government also changed in the distribution of the burden to improve feasibility.

At the conclusion of the war in 404, Athens' defeat resulted in another brief overthrow of democracy and significant reduction in the role of the navy. Spartan naval rule of the Aegean, however, never took substantial root and the Athenian triremes continued to be an important force amidst shifting allegiances throughout most of the fourth Century.

In 358 Athens was about to enter a war abroad with Philip of Macedon over Amphipolis, and some of the polis's richest island subjects overthrew Athenian leadership in the Social War. At this time, reforms promoted by Periandros were accepted, which diffused costs further, in order to make it easier to support a navy big enough for battle. The idea of these reforms was to spread the liability for the trierarchies out over a larger group of citizens in each year. Whereas before there had been about 300 trierarchs, one for each of 300 warships, now there were 1,200 trierarchs appointed for all 300 ships.35

Gabrielsen, Financing the Athenian Fleet, pp. 182–99.

The 1,200 men were grouped into 20 symmories with 60 members each, and the ships were assigned to the symmories.36

Ibid., p. 182.

In this manner, the financial burden was supposed to be more evenly distributed among the richest men.37

Ibid., p. 174.

The extant evidence, however, lends little support to the success of these reforms. A handful of individuals were still directly responsible for a single ship, and the extended liability that might have reduced the financial burden (including smoothing of costs across disparate ship quality and battle assignments) by sharing responsibilities across both ships and individuals was not fully operationalized.38

Davies, Wealth.

Two years later, after several defeats (for example, Macedonia, Rhodes, Chios), the Athenians pushed for, and succeeded in gaining, the collection of many old trierarchal debts. Some of these had been outstanding for 20 years. Apparently rules regarding trierarchal debts were relatively lax in peacetime.39

Gabrielsen, Financing the Athenian Fleet, p. 158.

The government was apparently failing to achieve budget balance in the provision of this public good in times of peace.40

The punishment for not paying other public debts was a doubling of the debt enforced by the confiscation of property. Trierarchy debts, while doubled, apparently were not enforced through confiscation. It is understood that the financing must have come from the eisphora (property tax), or increased taxes on foreigners and resident aliens (Gabrielsen, Financing the Athenian Fleet).

Here is where we see again the incompatibility of the mechanism with respect to simultaneous feasibility, budget balance, and optimal provision levels. If they had actually collected the debts in peacetime, then the number of individuals willing to participate in the mechanism would have been too small. When debts were not collected in peacetime, the present value of the cost of the trierarchy, Ti, was essentially zero, giving individuals more of a reason to undertake the trierarchy In war, by contrast, the valuation for the navy would be higher, and it would be easier to collect the debts in light of the threat to the democracy.

A half-generation later, in 340, again on the brink of war, Demosthenes tried to change the system by again spreading each individual's duties across ships, partly in order to enlist those who might not be able to pay for an entire ship but could pay for a fraction.41

Gabrielsen, Financing the Athenian Fleet, pp. 207–13.

An individual might then be involved in three syntrierarchies, with three different partners, instead of holding responsibility for a single full trierarchy. Thus, liability was more widely distributed and payment was perhaps fairer. The actual effect of the change in the law seems to have been to capture individuals who had successfully avoided all trierarchal responsibilities in the recent past.

Either these improvements were insufficient or else the threat of Alexander the Great was far greater than expected. The trierarchy ended in 322, with the defeat of Athens and its incorporation into the Macedonian empire.

DATA AND ECONOMETRIC ANALYSIS

Overview

I now turn to examining quantitatively the probability that an individual attempted to avoid the trierarchy's responsibilities through the antidosis. This probability is a function of the types of known wealth (land, mines, etc.) for the individual and the deme, additional liturgical service, and generational variables indicating when in the Classical period an individual would have been liable. I also analyze cases where an individual performs more than one trierarchy as a function of the same variables. I look for evidence that individuals with greater wealth and lower costs undertook more of the trierarchal burden. In identifying the aspects of wealth that promoted voluntary private provision of this public good, we are able to understand better how the Athenian democratic system could provide such a successful navy with such significant institutional constraints on its resources. And we can do so without casting aside economic reasoning or invoking unusual altruism among Athenian citizens.

The data set was compiled from three main sources. The first, Athenian Propertied Families, catalogues all of the extant evidence on wealthy families in Attica from 600 through 300.42

Davies, Athenian Propertied Families.

Organized by individual and family, this source furnishes personal information about individuals, including their names, demes of residence, numbers of known trierarchies, and other indications of their family wealth. Second, Robin Osborne's work gives us the ratio of known wealthy individuals to all individuals in each deme.43

Osborne, Demos. Strictly speaking, what Osborne gives is the ratio of wealthy individuals to the bouleutic quota for each deme. The bouleutic quota was the number of representatives sent to the boule by each of the demes. While the bouleutic quota bore a strongly positive relationship to the total citizen population of a deme (Whitehead, Demes, pp. 22–23; and Traill, Political Organization, p. 56), it is not a one-to-one relationship.

Finally, community demographic details, including where each deme is located within Attica and the deme's characteristics, are known through The Political Organization of Attica.44

Traill, Political Organization.

I first discuss the variables and investigate cross-tabulations of key components of the data to summarize the evidence. Two separate regressions are then used to analyze the characteristics that would move individuals away from the solution of using the antidosis or going to court and toward the uncontested contribution equilibria. The limitations of the data and potential sample biases are discussed for each variable.

The first regression investigates the probability that an individual went to court over a trierarchy as a function of his deme, the number of trierarchies he performed, whether or not he performed a trierarchy subject to Demosthenes's reforms in 340, the generation in which the trierarchies were performed, his other liturgical duties, his known public office holdings, the source of his wealth (land, silver mines, or workshops), his known associations with bankers, and whether his ancestor was known to have performed a trierarchy. Though we do not distinguish whether the individual initiated the court case or had it initiated against him, in either case the results suggest which characteristics would cause an individual to avoid uncontested participation in the trierarchy.

The second regression investigates the number of trierarchies performed by individuals using a Poisson regression because we cannot say much about individuals who were not trierarchs. It also controls for “exposure” in the epigraphic record. This regression complements the first by illuminating which individuals in the sample might be considered wealthiest, with the lowest costs, and which individuals were most influenced by altruistic preferences. If these actions can be explained as economic decisions, then the argument that aretē drove uncontested provision is not necessary.

Discussion of Variables

The limited epigraphical record raises questions of sample selection that are worth discussing here along with the institutional framework and the historical interpretation of the variables. As much as possible, this article strives to reduce the potential biases by relying on primary sources. Although the limited amount of extant data makes sophisticated econometric techniques difficult, we can use the Poisson regression to control, in a sense, for the available historical record when we look at multiple trierarchies performed by an individual, because we can condition the results on the exposure of known family members to recorded history.

Table 1 provides descriptive statistics for the dataset. The quantitative analysis is limited to the fourth century due to these data limitations. In the fifth century, it is understood that the state's distributions from the silver mines were greater than in the following century, so that the individual trierarchical burden was likely lower, and we would expect greater voluntary compliance.

Legal Action

Diadikasia, the dependent variable in the first regression, is a dummy variable recording whether or not we know today if the agent was involved in an antidosis case (Diadikasia = 1 for antidosis case). At least 110 of the 492 trierarchies of which we know were involved in a transfer of liability from one agent to another.45

Gabrielsen, “Diadikasia Documents.”

For two dozen of these, we know there was a trierarchical dispute settled in court from extant evidence, including trials described by Isokrates, Demosthenes, and others. These cases most likely concern wealthier trierarchs because they would have been more willing to hire an orator to make their case, and the orator (such as Demosthenes) wrote down his arguments. It is these written arguments that give use the most information about legal cases.

The remaining individuals require a bit more interpretation, as their place on the list of antidosis cases in our sample comes from their presence on the diadikasia documents of 380/79.46

IG II2:1928–1932.

The complications of this list are discussed in Appendix 2, but readers should note that no one disputes that the “B instead of A” format refers to a transfer of financial burden as required in the antidosis, and that the epigraphic evidence suggests the transfers were indeed court ordered.

Community

Trittyes, or thirtieths, divided each of the ten tribes (phylai) so that it contained communities distinguishable as coastal, urban, and inland. These need not have been adjacent for each tribe, and deme membership does not necessarily reflect habitation. Nonetheless, demes-men formed communities in which individuals most likely knew more about each other than they did about individuals outside the deme (with the exception perhaps of neighboring landowners), and as with other direct and indirect taxes, would be competing mainly within their deme to determine their service requirements. Incentives and opportunities for gathering better information about your fellow demes-men were greater than they were across demes or trittyes for other purposes (for example, deme-level liturgical services) as well, and so membership in these communities separates citizens into a variety of potential types. I investigate whether the type of community has an identifiable impact on the spread of the liturgical burden across types of citizens. A dummy variable (Coast) indicates whether a trittys was coastal rather than inland (Inland) or in the city (City), or of unknown location (Unk. trittyes). I investigate this demographic divide. For example, citizens residing in urban trittyes may have had better access to Athens, perhaps increasing political activity and the number of trierarchs from that community. Coastal trittyes and their demes may have been more susceptible to naval attack, and this may have increased the likelihood of trierarchs if they held greater individual interest in naval defense.

Number of Trierarchies

Trierarchies is a variable counting how many trierarchies we know for an individual. Syntrierarchies counts the number of joint trierarchies undertaken. Tri-total sums these contributions equally, while Syns is a dummy variable indicating whether any of the total is composed of presumably less costly syntrierarchies. Because many of the records have been lost or destroyed over time, there is no way of knowing for sure what percentage of the true number of trierarchs these represent. If all 300 ships went out every year for about 58 years (about 380 to 322), there should have been more than 18,600 trierarch-years. We know of 492 trierarchs, and about 650 trierarch-years, which would be approximately 3 percent. As all ships did not go out each year, the actual percentage is likely higher. When one looks at the spread of known trierarchs across the fourth century, there are more known for generations with wars than without. Thus we expect a fairly representative, though small, sample of the ships going out in any given generation.

There may also have been a shortage of trierarchs, as the naval records for various years list up to one half of the potential fleet as “unallotted,” or without trierarchs for the year.47

Gabrielsen, Financing the Athenian Fleet, p. 180.

This again highlights the impossibility of providing public goods privately in a way that meets all three conditions of optimal provision, budget balance, and feasibility. Conceivably the ships were not allotted because they were not needed, but because the shortage was seen as a driving force for Periandros's and other reforms, it seems more likely that efficiency was failing due to feasibility constraints under tighter budgets.48

Ibid., pp. 180–82.

For some cases, the actual year of service for a trierarch is unknown, and only a range of years is available. At least 97 of the 492 individuals in the sample performed more than one trierarchy. The maximum number of known trierarchies or syntrierarchies performed by an individual is nine. This is the dependent variable for the second regression. It would have been preferable to have a sample of nontrierarchs to compare with trierarchs, or to be able to compare based on the actual expenditures, but unfortunately neither of these were possible because these names come only from documents recording trierarchs and rely instead on statistical adjustments for truncated count data.

Demosthenes

If an individual performed more than one trierarchy in the same year after the implementation of Demosthenes's reforms, the cost of each is expected to be lower. A dummy variable (Demosthenes) indicating such participation is included because the law was purported to have caught many individuals who had been shirking their civic duty prior to the law. Thus, those individuals who performed trierarchies under this law were perhaps less likely to have gone to court because they had managed to keep

below the amount that would place them on the lists in the first place, but when the list was expanded to include more individuals they were brought into the system. At this point there were fewer people available to be challenged because they had also been assigned as trierarchs. This variable affects about 6 percent of the sample.

If an individual were performing more than one trierarchy, as in the second generation, one would expect that the Demosthenes law would have a positive effect, as it spreads responsibilities across ships.

Generations

Dummy variables Gen0, Gen1, Gen2, Gen3, Gen4, and Gen5 indicate the time during which the trierarchy was carried out. There are three generations of 33 years for which we know of trierarchs, and the other three distinguish individuals who served in more than one generation. Gen0 (omitted, 9 percent of sample) corresponds to the first generation, from 399–366. Gen1 (5 percent of sample) includes those who participated in both the first generation (Gen0) and the second generation (365–333, Gen4). Gen2 (26 percent) is the portion of the second generation known under Periandros's law, from 357 to 340. Gen3 (9 percent) marks those who participated in both the second generation and the third one (332–300). Gen4 (25 percent) represents the second generation, from 365–334 (if specific information does not put them more clearly in Gen2) and Gen5 (26 percent) the third generation, from 332 to 300. The expected signs and importance of these variables are in relative terms to the service of the first generation, a period in which there was little warfare. For court cases, theory alone gives us little guidance; it may be that there is a positive influence on the numbers of cases going to court in years that there are more trierarchs (such as during wars) but a negative influence in times of war when the demand for national security was higher and the willingness to pay increased. For the case of multiple trierarchies, participation across generations (Gen1, Gen3) should be a positive influence on the number of trierarchies as they imply at least two syntrierarchies, while the other generations might have a positive or negative influence, as the war years were also years of mechanism reforms that spread the cost burden.

Nonland Wealth

Nonland wealth is a dummy variable (Nonland) marking those who were known to have made money from renting silver mines from Athens or from the ownership of a workshop. Because the mines were technically owned by the state, they were not included in an individual's list of assets and therefore would be a good way to hide wealth from taxation. They were, however, more risky than land and there are reports of individuals being financially ruined by their mining enterprises.

49

Finley, Studies.

Also, the slaves one owned to work the mines would have been included in one's wealth so the enterprise did have some influence on one's visible wealth. One would expect individuals engaged in mining to hide more of their wealth but because they were hiding it legally (in other words if their mining assets were brought up in court their visible wealth,

, would not change), they would not fear court and might go more often. This variable includes about 11 percent of the sample.

Other Liturgies

A dummy variable (Other Liturgies) indicates whether the individual had provided other liturgical services. Unfortunately this variable is subject to severe underreporting because the records were not nearly as inclusive as those for the trierarchy. For instance, while several individuals a year would pay for a choregia, only the winner would be recorded. These choregia winners are the most common source of knowledge we have for this variable. The bias in this case is that the winners of the choregia are much more likely to have spent more money on their production, and are therefore arguably among the richer of the trierarchs.50

Davies, Athenian Propertied Families.

This variable is perhaps best interpreted as a wealth variable, and includes about 21 percent of the sample. It also implies potentially ostentatious spending and so we expect it to have a positive influence on the number of trierarchies and a negative influence on court appearances.

Public Office

This is a dummy variable (Public Office) indicating known service in public office. This suggests both interest and ability in politics. It is taken to indicate that the individual may desire political capital from his expenditures on the state. Like Other Liturgies and Bankers, this variable may be significantly underreported and does not differentiate between types of office due to a lack of information.

Banker Interactions

The dummy variable Bankers marks whether an individual was known to have dealings with a banker. Banking in general was a risky affair; unlike all other market transactions, banking occurred without witnesses.51

Cohen, Athenian Economy.

The lack of witnesses meant that banking was the most assured way to hide wealth, but also the easiest way to lose it. Because these banking associations are known, it may be that they were less for purposes of hiding wealth than for earning it. In this case, those trierarchs with known banking associations would be perhaps more likely to have been in court, as they had visible wealth of which some but not all fellow Athenians might know, making them the target of the antidosis.

An additional possibility is that the individuals were using bankers to hide wealth and they went to court anyway, thinking it safe, but their hidden wealth became known through the process. We dismiss this possibility by investigating the data. Of the approximately 468 known trierarchs, 20 had known associations with bankers.52

There are some cases where the epigraphical record is unclear as to whether two appearances of a similar name are for one individual or two individuals in the same family. Davies's assessment of the record is used here (Davies, Athenian Propertied Families).

Pasion, a banker and manumitted-slave-turned-citizen of the first generation, his descendants and their associates, account for 14 of these known cases, and another banker, Aristolokhos, accounts for another two. Two of the remaining four are known from Demosthenes's lawsuit against Aphobos regarding Demosthenes's father's estate, ten years before his first known trierarchy.53

Davies, Athenian Propertied Families.

We apparently do not know of these associations because they are revealed during an antidosis; rather, most involve rare cases of an Athenian citizen who was a banker, and whose banking wealth would have been known by his fellow citizens. These citizens may have had a greater interest in state spending as a way of purchasing political capital not attained through birth or land ownership, but with lower opportunity costs than most farming citizens, they may also have been better suited to low-cost provision. Thus a known association with a banker is expected to increase the likelihood of both the number of trierarchies performed and participation in an antidosis case. 54

Whether Pasion and his family's actions are actually different from other trierarch's or only appear so from the unusual presence of evidence, the manner of inclusion in the empirical analysis is the same and is required in order to avoid omitted variable bias.

Ancestors' Actions

If an individual had an ancestor who was a trierarch (Previous Family Trierarch), then others might perceive his wealth to be high. Such a person would stay out of court because it would be harder to prove that someone else was wealthier. The probability of losing in court was thus high, so one would make one's hidden wealth vulnerable to exposure with little chance of relief from the trierarchy. Alternatively, this sort of person might have been able to invoke his service as evidence of volunteerism and might therefore appeal to the court rather than simply paying. Because wealth did not change much from generation to generation, it is likely that an ancestral trierarchy signals significant wealth and likely additional trierarchies.

I also use Davies's work to tally the known members of a trierarch's family throughout the historical record, and use this to contextualize the number of trierarchies known for an individual.55

Davies, Athenian Propertied Families.

Because it is more likely that we know of multiple trierarchies in a family when we know more details about a family, this variable (Known Family) is used as the exposure variable in the regression.

Deme Wealth

Ratio Trierarchs to Deme attempts to gauge the perceived availability of substitutes from one's deme by calculating the ratio of all the known trierarchs for a deme to all known wealthy members of the deme during the classical period (600–300). Thus we have a relative view of the liturgical burden of the deme. One would expect the sign on this variable to be negative: if there are more wealthy individuals in the deme who are already participating, it will be harder to find a substitute.

Results of Regression on Trading of Financial Duties

The results of the logit regression on whether a trierarch was involved in a transfer of financial duties, most likely resulting from a court decision, are shown in Table 2. Hereafter, we refer to this transfer as going to court for expositional purposes. Overall, the greatest marginal effect on the probability that a person went to court was from known associations with bankers, which raised the odds 47 percent. This was statistically significant at the 99 percent level. Other factors of significance (at or above the 90 percent level), in descending order of effect, were being a member of generation 4 (365–333), which raised the odds by 24 percent (see Figures 2 and 3 for visual representation of the differences in trierarchy burdens and court cases across generations), the number of trierarchies (12 percent), holding of public office (10 percent), a previous family trierarchy (9 percent), and syntrierarchies (5 percent). Of the statistically insignificant variables, none would have particularly large effects if they were significant. It is somewhat reassuring that City does not have a large or significant effect because it seems likely that records are not biased toward Athens proper and may indicate that local knowledge of a neighbor's wealth was more important than proximity to the boule.56

Several other specifications with different regional variables all show similar lack of importance.

FIGURE 2 COMMITMENT VS. CHALLENGES: SINGLE GENERATION

As expected, individuals were less likely (by 14 percent, with a coefficient significant at the 10 percent level) to have gone to court if they were subject to Demosthenes's law (so that costs of compliance were considerably lower in expectation). In the second generation, it does appear that Athens was facing a budget crisis for funding of the trierarchy. Having tapped the richest families for a century and a half, Athens tried several reforms. Periandros's first attempt at reform in 358/57 set the eligible number of trierarchs at 1,200 per year and led to more and more individuals serving as syntrierarchs to spread costs and ease shortages, though for the most part individual trierarchs remained the norm.57

Gabrielsen, Financing the Athenian Fleet, pp. 182–99.

These reforms may have helped; while there is no significant effect on going to court for those under Periandros's reform (Gen2), there is a significant increase for those in the same generation who are not identified as being under the reforms (Gen4). In 340, Demosthenes's reforms again attempted to decrease the individual burden of the trierarchy while increasing the overall success at provision. These reforms may explain the 14 percent reduction in cases for those operating under Demosthenes's reforms (significant at the 10 percent level). They may also explain why the third generation (Gen5) and the individuals operating under Periandros's law (Gen2) seemed less likely to take cases to court than members of the second generation who were not necessarily acting under the reforms (Gen4).

FIGURE 3 COMMITMENT VS. CHALLENGES: CROSS-GENERATION

These results support the hypothesis that the reasons for performing a trierarchy were not simply prestige and power. The mechanism design of the institution had teeth; the antidosis was necessary for the provision of the public good. The increased probability of court appearances that accompanied an increased number of trierarchies might stem from two factors. First, there might be diminishing returns to providing trierarchies, so that additional calls for service would instigate greater efforts to avoid service. On the other hand, visible wealth in the form of past trierarchies might cause the community to expect more service. We investigate these possibilities with a second regression on the factors that caused an individual to perform more than one trierarchy.

Results of Regression on Multiple Trierarchies

The results of this Poisson regression on the total number of trierarchies and syntrierarchies are recorded in Table 3. Statistically significant incidence rate ratios (IRRs) greater than one indicate that the variable increases the likelihood of performing more than one trierarchy, whereas IRRs less than one indicate that it decreases it. In an effort to control for the holes in the historical record and for the fact that we do not see nontrierarchs, we use known family members to condition the results for the disparities in our knowledge of the family histories.58

If Ej is the exposure, the expected number of events Cj will be

where rj = exp(b0 + b1 * x(1,j) + … + bk * x(k,j)) is the incidence rate ratio.

Compared to the (omitted)59

The constant term contains the effect of being in Gen0, so that all subsequent generations are relative to this constant.

first generation (Gen0, 399–366), the members of other generations all perform statistically more trierarchies. There are two reasons why. To begin with, individuals in the first generation, following as they did at the end of the Peloponnesian Wars, might have performed many earlier trierarchies for which we do not have records in our sample. In addition, they may not have needed to perform trierarchies due to lower naval activities. Also unsurprisingly, “Generations” 1 and 3, which actually account for individuals whose service spans more than one typical generation of 33 years, perform trierarchies at higher rates, and these variables serve mainly as controls. Large impacts on the number of trierarchies also come from the reforms that ease the trierarchy burden: the presence of syntrierarchies in one's service record has an IRR of almost 1.8 and the IRR for subjection to Demosthenes's law is almost 1.4. Both are statistically significant impacts at the 99 percent confidence level.

The demographic variables generally support the idea that coastal trittyes invested more in performing trierarchies, with a statistically significant IRR of 1.19 as compared to city trittyes (the omitted category). Interestingly, the trittyes in unknown locations also increased the odds of performing multiple liturgies, with an IRR of 3.09.60

Only 4 percent of the sample has an unknown trittys location, and city appears underrepresented at 24 percent of the sample, if we assume that trierarchies are distributed evenly across the types of trittyes. However, city had one of the highest populations of non-Athenians and thetes (the landless, liturgically exempt, class of citizens) so there may be a smaller percentage of eligible citizens for the trierarchy. If the unknown trittyes are mostly city trittyes and we group them together, the magnitudes of the influence of coast and inland do not change much, but they lose statistical significance. On the other hand, the sample is 33 percent coastal trittyes (and 39 percent inland). If more of the unknown trierarchs come from coastal trittyes, as would support the idea that they had more at stake, then this strengthens the magnitude and statistical significance of the coastal trittyes.

The other significant increase come from known relationships with bankers (IRR = 1.4). As discussed previously, in large part this likely reflects actual noncitizen or new-citizen bankers performing multiple trierarchies in order to gain citizenship or prestige.61

Because we know so much about the case of the banker Pasion and his family (see Davies, Athenian Propertied Families) with respect to the trierarchy, we are able to link the significance of the banking association variable to this family's interests directly. The strong positive relationship between banking and trierarchies corroborates the suspicion that Pasion and his descendants were attempting to purchase prestige. This is strengthened by the use of the exposure model, which conditions the estimates on the level of knowledge about family members, so that the greater incidence within that family is taken into account in the estimates and still returns a result that suggests the behavior of the set of those known to have banking connections, dominated by that family, is significantly different from the behavior of other trierarchs and their families.

The performance of other liturgies and nonland wealth have no statistical influence on the number of trierarchies performed. The ratio of all the known trierarchs for a deme to all known wealthy members of the deme for the classical period also has no statistical significance. This may reflect the fact that the known wealthy members of the deme may also be family members, so controlling for known family members may mitigate this variable's impact.

Having previous family trierarchs greatly reduces the odds of performing multiple trierarchies. The argument that you should be relieved of responsibility because your ancestors' efforts have depleted your wealth apparently worked. Holding other public office also reduced the incidence rate for multiple trierarchies. If citizens used both the trierarchy and public office to garner public respect and the prizes that accompanied it, then the two appear to have been substitutes as well. This is also compatible with the possibility that the returns to the choregia and the trierarchy differed in terms of honors and socio-political capital, so that those seeking more glory were more likely to participate in the choregia and less likely to participate in the trierarchy. Combined with the information in the first regression, we can safely say that many citizens found alternatives to costly service if they could.

CONCLUSIONS

The trierarchy functioned as an institutional mechanism that provided for the private provision of an essential public good, the Athenian Navy. From its inception at the end of the sixth century, the mechanism worked toward the simultaneously impossible goals of providing a fleet of the optimal size, a balanced budget, and voluntary compliance. It met with sufficient success, however, to support the city-state's growing hegemonic influence in the Aegean Sea until Alexander the Great absorbed Athens into the Macedonian Empire.

Despite a paucity of data, we can combine the epigraphical and archaeological records and analyze individual's behavior quantitatively. Evidence on types of wealth holdings, court actions, community identity, and family choices show that the mechanism did not rely on non-economic incentives. Athenians, long credited with purely altruistic behavior or unusual glory-seeking, actually functioned as economic decision-makers. Even the political gains are quantifiable in holdings of public office.

The model is useful to economists as an example of a mechanism implemented in the real world but also provides some insights for ancient economy. Using an economic model and quantitative analysis together to investigate the motivations of the Ancient Greeks helps fill in some of the unknowns. The theoretical constraints required by the mechanism for feasibility, budget balance, and efficiency provide a framework for a broader understanding of the long-run success, and ultimate failure, of the trierarchy to provide naval defense. As the budget options of the state changed, the mechanism also changed. In the fifth century, when state distributions were significant and the individual burden was low, trierarchies not analyzed here show that feasibility and efficiency were easier to attain. As the individual burden increased, compliance became more coerced, and the navy ultimately failed to maintain Athens as an independent state.

The equilibria of the game suggest that economically self-interested individuals would not necessarily go to court, and the existence of the mechanism belies the traditional belief that Athenians sought mainly noneconomic rewards. The citizens did challenge their responsibility for the trierarchy when it was in their best interest, and they worked to avoid the cost. Visible wealth led to the need to comply, and the provision of naval services appears to have been carried out by those most financially able to do so at the lowest cost. The antidosis was a necessary part of the mechanism design, and long-run requirements for wealth preservation might result in even greater voluntary compliance with the trierarchy.

Appendix 1: Mathematical Expression of the Mechanism

We formalize the game, sketching the incentive compatibility constraints corresponding to the textual discussion. Table 1 provides visual representation of the mechanism.

GAME SET-UP

Citizens vary in true wealth, θi, and visible wealth,

.

Stage One: Generals assign trierarchies

Generals rank citizens (types) by visible wealth (

).

Selected types have

and are considered Player Ones. Unselected types have lower visible wealth (or other exemptions) and are potential Player Twos.

Stage Two: Player One (assigned a trierarchy) chooses to pay or challenge

Player One chooses between paying for the trierarchy (resolving the game) and challenging a Player Two (an individual not assigned a trierarchy) to the antidosis.

In the case of a challenge, the game proceeds to Stage Three. In a challenge, Player One asserts that his self-proclaimed worth is

(which may be greater than, less than, or equal to his visible wealth

) is less than Player Two's true wealth, i.e.,

. Without a challenge, the game ends and payoffs are simply their true wealth adjusted for the tax:

  • Player One: θ1 − T1, where T1 is the cost of the trierarchy to the trierarch, and
  • Player Two: θ2.62

    Player One will presumably choose the Player Two he believes has the highest wealth given both public and private information (in other words the person he has the highest chance of convincing to trade or against whom he is most likely to win in court).

Stage Three: Player Two (challenged) pays or trades property

In the case of a challenge, Player Two chooses between accepting responsibility for the trierarchy (resolving the game) or making a property exchange offer. If Player Two accepts the trierarchy, the game ends and payoffs are:

  • Player One: θ1,
  • Player Two: θ2 – T2, where T2 is the cost of the trierarchy to the challenged citizen.

If Player Two contests, then a property exchange offer is made. In making a property exchange offer, Player Two chooses to list the property that he is willing exchange (his visible wealth plus a portion of his private wealth,

) for Player One's self-proclaimed wealth (

).

Stage Four: Player One accepts or rejects Player Two's offer

Player One decides whether or not to accept Player Two's offer of exchange,

.

If he accepts, the game ends, property is exchanged, and he discharges the trierarchy. Payoffs to each player are then:

  • Player One:
    ,
  • Player Two:
    ,

Where x is the amount that Player Two is willing to increase his visible wealth in order to facilitate the switch. If Player One rejects the offer, the case goes to court (Stage Five).

Stage Five: The court makes a decision

With probability P1, Player One is found to be the in the right, and does not pay for the liturgy. Player Two is spared with probability (1 – P1). Note that P1 is a decreasing function of

and

, and an increasing function of

and

. The expected payoffs if the game reaches this final stage are therefore:

  • P1θ1 + (1 – P1)(θ1 – T1), and
  • Player Two: P1(θ2 – T2) + (1 – P1)θ2.

BACKWARD INDUCTION OF THE CONDITIONS FOR EQUILIBRIUM

Conditions for property swap to occur

In the static game, there will be a property swap only if the offer to trade is such that

, where

is the difference between visible wealth and self proclaimed wealth. Simplified, an exchange is only possible if

. This can be shown with a set of theorems that solve the game through backwards induction.

Theorem 1: Player Two will offer

Proof: Player Two will make an offer such that his payoff for acceptance is no less than his expected payoff from rejection. In accepting, he gives up his visible wealth plus a premium, x, in exchange for Player One's declared wealth. In rejecting, the case goes to court, and with probability (1 – P1), Player Two is found less wealthy and maintains his wealth (LHS), while with probability P1, Player Two is found the wealthier and must discharge the trierarchy, for an expected outcome depicted on the RHS of the equation

or simplifying,

Theorem 2: Player One will accept Player Two's offer only if

Proof: Player One's incentive compatibility constraint requires that accepting the trade (LHS) is better than the expected outcome of the court deliberations (RHS)

which simplifies to:

Lemma: Acceptable offers that Player Two can make to Player One are in the range where

Lemma: A necessary condition for an acceptable offer is that

63

In the case that T1 = T2 = T, there exists a unique acceptable exchange offer where

In the static game, it will also be true that citizens will not willingly participate without challenge unless the expected cost of the trierarchy after a court appeal is less than or equal to zero or there is no possible individual to challenge with a positive probability of receiving a favorable outcome from the court.

Theorem 3: Player One will not accept the trierarchy without challenge unless T1 ≤ 0 or P1 = 0

Player One's incentive compatibility constraints require that if he is to participate immediately rather than challenge a player, then

As shown above, to accept this offer,

is necessary. By substitution,

must be satisfied for volunteering to be preferred to such an offer. In the more likely case that an unacceptable offer is made, Player One's incentive compatibility constraints require that

, which also reduces to the condition that 0 ≥ P1 T1. QED.

Appendix 2: The Diadikasia Documents

Though there is considerable controversy over the exact meaning of the diadikasia documents, as Inscriptiones Graecae (IG) II2 1928–1932 are known, no one disputes that the “B instead of A” format refers to such a transfer as required in the antidosis. A variety of opinions have been offered.64

Davies, Athenian Propertied Families and Wealth; and Gabrielsen, “Diadikasia Documents” and Financing the Athenian Fleet, pp. 70–71.

These include the possibility that the documents refer directly to trierarchy cases for a given year, or that they involve a collection of debts from various responsibilities over a period of time. It is the acceptance of the financial burden, however, that is useful to our analysis. For the cases to be committed to stone, they must have been a notable cost to the new payee.

If the replacements listed on these documents went through the court process, then we can assume that the agent listed as the replacement lost the case. If the replacements did not go through the courts, but instead “voluntarily” accepted the debt, we must assume that they benefited more than they would have had they risked going to court. It would be wonderful to know for certain which case is true. Most presentations of the diadikasia documents do assume they reflect court-ordered decisions; this is consistent with the decision to record the event. In the possible case that they do not, however, we can still interpret the activity as a function of wealth and private incentives, and as a reflection on the institutions for public munificence. Whether the trade was due to a court decision or not, the existence of a trade implies that agents involved had not truthfully revealed their wealth in the initial stage of the game. Since we are not concerned in the empirical analysis with whether or not the agent in question actually won or lost in court, the crucial information contained by these diadikasia documents is that there was a recorded transfer of fiscal duty to the state.

Special thanks go to the anonymous reviewers, Robert Wallace, Joel Mokyr, Louis Cain, Alan Taylor, Tom Hillman, Thomas Lurquin, the Triangle Economic History Workshop, and the participants of the 2003 Cliometrics Conference for their encouragement, assistance, and advice.

References

LITERARY TEXTS

Carter L. B. The Quiet Athenian. Oxford: Clarendon Press, 1986.
Casson Lionel. Ships and Seafaring in Ancient Times. Austin: University of Texas Press, 1996.
Cawkwell George L. “Athenian Naval Power in the Fourth Century.” Classical Quarterly 34, no. ii (1984): 334-45.Google Scholar
Cohen Edward. Athenian Economy and Society: A Banking Perspective. Princeton, NJ: Princeton University Press, 1992.
Davies John K. Athenian Propertied Families: 600-300 BC. Oxford: Oxford University Press, 1971.
Davies John K.. Wealth and the Power of Wealth in Classical Athens. New York: Arno Press, 1981.
Finley Moses I. Studies in Land and Credit in Ancient Athens 500-200 BC. New Brunswick, NJ: Rutgers University Press, 1952.
Finley Moses I.. The Ancient Economy. Berkeley: University of California Press, 1985.
Fudenberg Drew, and Jean Tirole. Game Theory. Cambridge, MA: M.I.T. Press, 1992.
Gabrielsen Vincent. “Diadikasia Documents.” Classica et Mediaevalia 38 (1987): 39-51.Google Scholar
Gabrielsen Vincent. Financing the Athenian Fleet: Public Taxation and Social Relations. Baltimore: Johns Hopkins University Press, 1994.
Jordan Borimir. “Metic Trierarchs.” The Ancient History Bulletin 15 no. 3 (2001): 131-34.Google Scholar
Lyttkens Carl H. “Effects of the Taxation of Wealth in Athens in the Fourth Century B.C.” Scandinavian Economic History Review 40, no. 2 (1992): 3-20.Google Scholar
Lyttkens Carl H.. “A Rational-Actor Perspective on the Origin of Liturgies in Ancient Greece.” Journal of Institutional and Theoretical Economics 153 (1997): 462-83.Google Scholar
Millett Paul “Maritime Loans and the Structure of Credit in Fourth-Century Athens.” In Trade in the Ancient Economy, edited by Peter Garnsey, Keith Hop-kins, and C. R. Whittaker, 36-52, 186-89. Berkeley: University of California Press, 1983.
Osborne Robin. Demos: The Discovery of Classical Attika. Cambridge: Cambridge University Press, 1985.
Rahe Paul A. “The Primacy of Politics in Classical Greece.” American Historical Review 89 (1984): 265-93.Google Scholar
Rosivach Vincent J. “Manning the Athenian Fleet.” American Journal of Ancient History 10, no. 1 (1985): 41-66.Google Scholar
Shipton Kirsty. Leasing and Lending: The Cash Economy in Fourth-Century BC Athens. London: Institute of Classical Studies, School of Advanced Study, University of London, 2000.
Silverman David L. “The Trierarchy and Athenian Civic Identity.” Ph.D. diss., Uni-versity of California, Berkeley, 1994.
Traill John S. The Political Organization of Attica. Princeton, NJ: American School of Classical Studies at Athens, 1975.
Wallinga H. T. Ships and Sea-Power before the Great Persian War: The Ancestry of the Ancient Trireme. Leiden: E. J. Brill, 1993.
Whitehead David. “Competitive Outlay and Community Profit: ? in Democratic Athens.” Classica et Mediaevalia 34 (1983): 55-74.Google Scholar
Whitehead David. The Demes of Attica 508/7-CA.250 BC. Princeton, NJ: Princeton University Press, 1986.
Wilson Peter. The Athenian Institution of the Khoregia: The Chorus, the City, and the Stage. Cambridge: Cambridge University Press, 2000.
Aristotle. Athenaion Politeia: 21.2, 22.7
Demosthenes. 4. First Phillipic: 21, 36
Demosthenes. 14. On the Symmories: 16
Demosthenes. 21. Against Meidias: 78
Demosthenes. 42. Against Phainippus: 25
Herodotus. 7.144
Thucydides. 1.14, 1.74, 1.112, 8.1.
Inscriptiones Graecae
II2: 1604–1632
II2: 1928–1932
Carter L. B. The Quiet Athenian. Oxford: Clarendon Press, 1986.
Casson Lionel. Ships and Seafaring in Ancient Times. Austin: University of Texas Press, 1996.
Cawkwell George L. “Athenian Naval Power in the Fourth Century.” Classical Quarterly 34, no. ii (1984): 334-45.Google Scholar
Cohen Edward. Athenian Economy and Society: A Banking Perspective. Princeton, NJ: Princeton University Press, 1992.
Davies John K. Athenian Propertied Families: 600-300 BC. Oxford: Oxford University Press, 1971.
Davies John K.. Wealth and the Power of Wealth in Classical Athens. New York: Arno Press, 1981.
Finley Moses I. Studies in Land and Credit in Ancient Athens 500-200 BC. New Brunswick, NJ: Rutgers University Press, 1952.
Finley Moses I.. The Ancient Economy. Berkeley: University of California Press, 1985.
Fudenberg Drew, and Jean Tirole. Game Theory. Cambridge, MA: M.I.T. Press, 1992.
Gabrielsen Vincent. “Diadikasia Documents.” Classica et Mediaevalia 38 (1987): 39-51.Google Scholar
Gabrielsen Vincent. Financing the Athenian Fleet: Public Taxation and Social Relations. Baltimore: Johns Hopkins University Press, 1994.
Jordan Borimir. “Metic Trierarchs.” The Ancient History Bulletin 15 no. 3 (2001): 131-34.Google Scholar
Lyttkens Carl H. “Effects of the Taxation of Wealth in Athens in the Fourth Century B.C.” Scandinavian Economic History Review 40, no. 2 (1992): 3-20.Google Scholar
Lyttkens Carl H.. “A Rational-Actor Perspective on the Origin of Liturgies in Ancient Greece.” Journal of Institutional and Theoretical Economics 153 (1997): 462-83.Google Scholar
Millett Paul “Maritime Loans and the Structure of Credit in Fourth-Century Athens.” In Trade in the Ancient Economy, edited by Peter Garnsey, Keith Hop-kins, and C. R. Whittaker, 36-52, 186-89. Berkeley: University of California Press, 1983.
Osborne Robin. Demos: The Discovery of Classical Attika. Cambridge: Cambridge University Press, 1985.
Rahe Paul A. “The Primacy of Politics in Classical Greece.” American Historical Review 89 (1984): 265-93.Google Scholar
Rosivach Vincent J. “Manning the Athenian Fleet.” American Journal of Ancient History 10, no. 1 (1985): 41-66.Google Scholar
Shipton Kirsty. Leasing and Lending: The Cash Economy in Fourth-Century BC Athens. London: Institute of Classical Studies, School of Advanced Study, University of London, 2000.
Silverman David L. “The Trierarchy and Athenian Civic Identity.” Ph.D. diss., Uni-versity of California, Berkeley, 1994.
Traill John S. The Political Organization of Attica. Princeton, NJ: American School of Classical Studies at Athens, 1975.
Wallinga H. T. Ships and Sea-Power before the Great Persian War: The Ancestry of the Ancient Trireme. Leiden: E. J. Brill, 1993.
Whitehead David. “Competitive Outlay and Community Profit: ? in Democratic Athens.” Classica et Mediaevalia 34 (1983): 55-74.Google Scholar
Whitehead David. The Demes of Attica 508/7-CA.250 BC. Princeton, NJ: Princeton University Press, 1986.
Wilson Peter. The Athenian Institution of the Khoregia: The Chorus, the City, and the Stage. Cambridge: Cambridge University Press, 2000.

LITERARY TEXTS

Aristotle. Athenaion Politeia: 21.2, 22.7
Demosthenes. 4. First Phillipic: 21, 36
Demosthenes. 14. On the Symmories: 16
Demosthenes. 21. Against Meidias: 78
Demosthenes. 42. Against Phainippus: 25
Herodotus. 7.144
Thucydides. 1.14, 1.74, 1.112, 8.1.

EPIGRAPHICAL TEXTS

Inscriptiones Graecae
II2: 1604–1632
II2: 1928–1932
Figure 0

FIGURE 1 GAME TREE FOR TRIERARCH DECISIONS

Figure 1

TABLE 1 DATA SUMMARY

Figure 2

TABLE 2 PROBABILITY OF COURT ACTION (logit regression, dependent variable = Diadikasia)

Figure 3

FIGURE 2 COMMITMENT VS. CHALLENGES: SINGLE GENERATION

Figure 4

FIGURE 3 COMMITMENT VS. CHALLENGES: CROSS-GENERATION

Figure 5

TABLE 3 INCIDENT RATE RATIOS (IRR) FOR REPEATED LITURGICAL SERVICE