by Ober, Josiah
In this game, the three players are the King (K), the walled democratic City-state (C), and an Elite citizen of that state (E). The King moves first, deciding either to threaten the City with attack (demanding that the City submit and thus pay high rents as the price of peace) or alternatively to negotiate a relatively low-rent agreement (Q) with the City; Q may be the status quo or some adjustment to the status quo but will be lower than the rent level that the King could demand if the City submitted unconditionally.1 If K chooses to negotiate a low-rent agreement, the game ends and the outcome is Q. If K chooses to threaten, C (that is, the democratic majority of the currently democratic city) decides whether to resist or submit. If C decides to submit, the game ends, and the outcome (S) is that C and E pay high rents to K. If C decides to resist (or, more plausibly, if C had formulated a general policy of “resistance if and when threatened” in advance of K’s decision), then E must choose either to support the existing democracy or to subvert the democracy, transforming the City’s regime into an oligarchy. If E chooses not to support democracy, K now decides whether to carry through on his threat or to back down. If K attacks, then with probability p′, K’s attack succeeds, and with probability 1 − p′, the now-oligarchic City, without the support of the democratic masses, beats back K’s attack. If E instead chooses to support democracy, K again decides whether to carry through on his threat or to back down. If K attacks, then with probability p < p′, the attack succeeds and with probability 1 − p > 1 − p′, the democratic City (Elites and democratic masses working together) beat back the attack.
TABLE II.1 King, City, and Elite Game: Payoffs to Each Player
NOTES: Explanations of the abbreviations in this table and in the game form.
AO = King attacks (city is oligarchic because Elite has defected).
AD = King attacks (city is democratic because Elite has cooperated).
BO = Bluff of the King is called by the City (city is oligarchic), King backs down.
BD = Bluff of the King called by the City (city is democratic), King backs down.
L = Lottery. If the King attacks, a Lottery decides the final outcome, based on p, p′.
N = City and King negotiate King’s rents/tax on the City at moderate rate Q.
S = City submits to the King without negotiation, King sets high rent/tax rate.
p = probability AD succeeds. 1 − p = probability AD fails.
p′ = probability AO succeeds. 1 − p′ = probability AO fails.
Each player’s choices are determined by expected payoffs for each outcome. The payoffs for each player for each possible outcome are listed in table II.1. The game is illustrated as a decision tree in figure II.1.
The payoffs to the players are calculated as follows:
S: C submits. In this case, K can demand that C weaken its fortifications (Herodotus 1.164, 6.46–47 for early examples; cf. Frederiksen 2011: 45 with n. 56), can set a very high tax rate, and can change the rate when and as he wishes. This is a very good outcome for K, who gets high rents at low cost, but inversely and equally bad for C and E, who pay those rents.
AD: K attacks and C is democratic. If, counterfactually, there was no cost to K in mounting the attack, and if his probability (p) of success in the attack were 1, then K’s payoff would be 15. But he must pay the costs of carrying out the attack, so his net (p = 1) payoff is 15 − 5 = 10. In this version of the game, we assume that p = 0.6: K has a better than even chance of success because of highly developed Hellenistic siegecraft. But p is substantially less than 1 because C is well walled and well defended. If K attacks and fails, his payoff is −10 because C will pay no rents and K’s failure will motivate other cities to revolt. K’s payoff is the average of the payoffs he can expect based on p being the probability of success and 1 − p being the probability of failure. Thus, K’s expected payoff for the lottery (L) is calculated as 0.6(10) + 0.4(−10) = 2. C’s payoff is calculated in the same way. If K’s attack succeeds, C’s payoff is −15; if K’s attack fails, C’s payoff is 10. Under the assumed probability (1 − p = 0.4), C’s expected payoff for the lottery is calculated as 0.6(−15) + 0.4(10) = −5. E’s payoff is indexed to that of C, but because E must pay higher taxes in a democratic City, E’s payoff is always 2 points lower than that of C if C is democratic.
FIGURE II.1 King, City, and Elite game.
NOTES: K = King. C = City. E = Elite. L = Lottery. N = Negotiate. S = Submit. BO = King backs down (city oligarchic). BD = King backs down (city democratic). AO = King attacks (city oligarchic). AD = King attacks (city democratic). p = probability AD succeeds. 1 − p = probability AD fails. p′ = probability AO succeeds. 1 − p′ = probability AO fails. Assumed value of p = 0.6. Assumed value of p′ = 0.8.
AO: K attacks and C is not democratic. Payoffs to K, C, and E are calculated in the same way as above. p′ (the probability that K’s attack succeeds if C is not democratic) > p (the probability that K’s attack succeeds if C is democratic) because the oligarchic city has fewer well-motivated defenders. Here p′ is set at 0.8, which yields an expected payoff to K of 6. C’s payoff is −10. Because C is not democratic, E’s payoff is identical to that of C.
BD or BO: K backs down. K receives a payoff of 0 because he receives no rents from C, but he does not face revolts in other cities. C receives a payoff of 5, being relieved of taxes but not having the spoils of victory. E’s payoff is, as usual, 2 points lower than that of C if C is democratic.
N: K chooses to negotiate. In this case, C and E may offer a tax rate Q as K’s payoff. C’s payoff is the inverse of K’s. E’s payoff is 2 points below that of C. K accepts C and E’s offer if Q is higher than his other available payoffs. C and E make an offer Q that K will accept if Q leaves both C and E with better payoffs than are otherwise available to them.2
The solution to the game is as follows: K would most prefer S, but C will submit only if the alternative is AO. AO is K’s second-best outcome. E, however, prefers AD and BD to AO. K’s best payoff (other than N) is therefore AD = 2. C and E can accept Q at any level <5 because a payoff of >−5 leaves both C and E better off than other available options. C and E thus offer Q at a rate between 2 and 4.5. Since this is >2, K accepts the offer, and N (negotiated settlement at level Q) is thus the Nash (subgame perfect) equilibrium solution.
We calculate the equilibrium of this game through the usual method of backward induction. At the penultimate node of the game, K must decide whether to attack or to back down. Given the payoffs under the assumed conditions of the lottery, he will always choose to attack over backing down. At one node back, E must decide between democracy and oligarchy. Although, all other things being equal, E prefers oligarchy to democracy, because K’s attack is less likely to succeed if C is democratic, E prefers AD to AO, so E chooses democracy. Backing up a node, C must decide whether to resist K’s threats or to submit. Because C prefers AD to S, C chooses to resist. At the first node of the game, K must choose between N, resulting in Q, the relatively low negotiated rent, or threatening the city in an effort to gain higher rents. K knows that if he chooses to threaten the city, the city will resist and will remain democratic, leading to the lottery AD. K knows that C and E will offer Q higher than his expected payoff in the lottery, so he chooses to negotiate: N.
The solution to the game, i.e., the King negotiates a low rent rather than threatening attack, depends on the expected payoff-based preference orderings of the players (table II.1). Those payoffs include their expectations about the outcome of the lottery and their shared belief that the King’s attack has a higher probability of failing if the walled City is democratic. The reasons for that belief are not mysterious: Aristotle had pointed out in the Politics that democracy was in general more stable than democracy (see Ober 2005a); recent work by historians of Greek antiquity has helped to show why that was true (Simonton 2012, Teegarden 2012, 2014a). Democracy, both ancient (Scheidel 2005b) and modern (Reiter and Stamm 2002), has been correlated with success at war as a result of higher mo
bilization rates and higher morale among soldiers. High mobilization rates have been correlated, for modern democracies, with more progressive tax rates, and that correlation can be explained by the assumption that citizen masses believe that, in times of high mobilization, elites ought to pay more (Scheve and Stasavage 2012). Elites evidently agree, insofar as democracies are not overthrown during or in the aftermath of periods of high mobilization.
There are at least six reasons to suppose that the stylized game presented here tracks the historical reality of the early Hellenistic period.
First, as Aristotle clearly implies in the passage cited in chapter 11, if we change the second player in the game from well-walled City to unfortified City, the nature of the City’s regime becomes irrelevant. The King can threaten the City with confidence because the unwalled City’s forces must confront the King in the open field. Given the King’s much superior army, the City will certainly lose. Since that is also (as Aristotle points out) a matter of common knowledge (“cities that indulge in that form of vanity are refuted by experience”), the unwalled City will submit and will have to pay high rents. Thus, in an unwalled city, the elite had less incentive to support democracy. Under the conditions pertaining in at least some Hellenistic cities, therefore, we see that democracy is related to fortifications in a specific way: Insofar as the conditions modeled in the game are relevant for elite choices and insofar as elite choices determine democratic stability, it is only when there are fortifications in place—or when a federation does the work of fortifications by increasing the scale of field armies—that democracy is stably sustained.
Democracy is not caused by fortifications or federalism, but, according to the logic of the game (which oversimplifies reality by assuming that the players are formally rational, expected-utility maximizers), either fortifications or federalism provide necessary conditions for stable democracy—at least insofar as it is a matter of self-interested elite choices about whether or not to revolt. On the other side, insofar as fortifications are ineffectual without defenders and democracy increases the effectiveness of defenders by increasing rates of mobilization and raising morale, then having democracy makes the choice to invest in fortifications (i.e., to pay taxes to support fortified defenses) a more rational one.
Defense of walls required many reliable men. To be effective in defense, those men must be well trained in the use of catapults and projectile weapons—as Aristotle notes in the Politics passage and as, in reality, were the Athenian 18- and 19-year-old participants in the ephebeia by the mid-330s (Aristotle Ath. Pol. 42.3: bow, javelin, catapult). They must, moreover, be capable of deploying effectively and must not be treasonous. This means, in the first instance, that the defenders should be citizens rather than mercenaries and that the citizens should have good reason to support the current regime. Each of these factors was emphasized by Aeneas Tacticus, the mid-fourth century writer on defense of cities (ch. 9).
Second, the payoffs change when the probability of the King succeeding in his attack changes: The higher (or lower) the probability that the King’s attack will succeed, the higher (or lower) the negotiated tax rate (i.e., the King’s rents) will be. This means that, unless King and City can credibly commit to disarmament (I assume that they cannot), King and City each will have an incentive to continue investing in siege equipment and artillery and military architecture, respectively. The democratic citizens of the City (who are assumed to prefer democracy to oligarchy) also have an incentive to continue to mobilize and to train for city defense. Each of these conditions is demanded by Aristotle in the quoted passage and is manifest in the history of Hellenistic military developments.
Third, if the probability that the attack will succeed or fail, which depends in part on whether the City is democratic or not, is changed, then the payoffs to Elites will change as well. If the probability of attack success increases significantly (e.g., if the democratic citizens refuse to train or mobilize), then the Elite may prefer an attack by the King under the conditions of oligarchy to an attack on the City under conditions of democracy and so will choose to subvert the democracy. Likewise, if the spread between the City’s payoffs and the Elite’s payoffs is increased significantly (e.g., if the democratic masses increase the Elite’s tax burden or decrease the Elite’s access to civic honors), then the Elite will once again choose to subvert the democracy.
Insofar as the mass of citizens prefer that the democracy not be subverted, they have a correspondingly strong incentive to continue to train and mobilize, to exercise restraint in setting the tax rate on the Elites, and to continue to offer honors to patriotic and generous elites. Masses and elites thus have good reason to stay in communication regarding expectations and duties. As we have seen (ch. 9), a sophisticated discourse of reciprocal gratitude did in fact develop and was sustained between elites and masses in democratic Greek cities.
Fourth, the probability of the King succeeding in taking the City if he does attack, even when the City is well walled and democratic, remains substantial. The likelihood that, were the King to threaten an attack, the threat would be real and that his siege would succeed, means that the City must always expect to pay some rents to the King. As the likelihood of the King’s attack succeeding increases, so too, as a general rule, do his expected rents, although the strength of that correlation varies with other factors. The negotiations between the City and the King over the level of taxation are, in sum, real negotiations—each side has something to gain and something to lose.
Yet, under plausible scenarios, there is an equilibrium solution that all can agree to—once again supposing that all players share common knowledge of the probability of the King’s chance for success, should he choose to conduct a siege.3 The idea that there is a solution that can be agreed upon is the background condition against which there developed the performative language of king–city communication that was explored in detail by John Ma.4 The background assumption that there is an equilibrium solution is an enabling condition of the performative language, although it is not, of course, adequate fully to explain the richness and variety of the diplomatic language and practices that structured relations of kings and cities.
Fifth, I have assumed in setting up the game that the information relevant to forming expectations about the result of the “attack lottery” (that is, if the King attacks, the probability that he will succeed) is symmetrical, and thus that all players make the same calculations of probabilities. But this assumption does not always hold in the real world. The City or the King may make a mistake in estimating probabilities (perhaps by overestimating its own strength) or may possess information that the other side does not have (e.g., a secret advance in siege technology or military architecture), leading to differing expectations about the probable outcome of the lottery.5
As estimates of probabilities become increasingly divergent, the equilibrium solution of “negotiate a reasonable tax rate” is destabilized. The likelihood that the King will attack increases: either because he rates his chances of success higher than does the City or because the City, overrating its own chances of foiling the attack, offers a tax rate that is below the King’s reserve price (i.e., the calculated value of his chances of victory). Mistakes are potentially very costly to either side. Both King and City therefore have strong incentives to keep lines of communication open and to share information. This situation is manifest in the diplomatic language studied by Ma. But it also explains the cases in which kings did choose to besiege cities.
Sixth, and finally, although the negotiated rent level is not the first choice of any of the players, that equilibrium solution arguably had positive effects on economic growth—perhaps more positive than any given player’s first choice would have had. Although, as noted (ch. 11), we do not yet have good data for measuring Greek economic growth after 323 BCE, it seems likely that the surprisingly robust growth (by premodern standards) of the Greek economy in the previous half-millennium was sustained in the Hellenistic period.
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NOTES
PREFACE
1. Centralized, autocratic “natural state”: North, Wallis, Weingast 2009. Empires and godlike kings: Morris and Scheidel 2009. Tribal identities and unaccountable leaders: Fukuyama 2011.
2. Recent work, led by scholars at Australian universities, notably Benjamin Isakhan, Stephen Stockwell, and John Keane, seeks to uncover a “secret history of democracy” by searching for “democratic tendencies” (limits to the absolute authority of elite rulers) and ephemeral or local “democratic moments” across a number of historical societies typically regarded as autocracies: Keane 2009; Isakhan and Stockwell 2011, 2012. This research is valuable insofar as it reminds us that the categories “democracy” and “domination” are ideal types and that the historical reality is more complex. But highlighting and celebrating “tendencies” and “moments” risks obscuring fundamental differences between autocracy and democracy as a system of collective self-governance by citizens, sustained over generations by a complex of formal institutions and a widely shared political culture.
3. Morris 2010.
4. Value of democracy: Ober 2007, 2012. Reasons for the preference may be instrumental (democracy brings desired outcomes) or intrinsic (democracy valued for its own sake).
5. Murray 1990.
6. Runciman 1990: 364.
7. Rejection of quantification: Hobson 2014.
8. Big history, at various scales: Diamond 1999; Morris 2010; Christian 2011.
9. Ginzburg 1980 is an influential early example of microhistory.
10. Conjunction of quantitative and qualitative approaches to social science: King, Keohane, and Verba 1994.