1 Introduction

In this paper I develop a theory of sovereignty rooted in political exchange (Buchanan 1987, Sect. IV; Shughart and Thomas 2014), specifically the bargaining over political rights by holders of political power broadly defined. I assume that the parties to these bargains are rational—they have ends that they seek, and they select the means they believe to be most appropriate to achieve their ends. However, the final results of these bargains may not be intended by the actors ex ante. They are emergent phenomena: to paraphrase Adam Ferguson, “{the result of human action, but not of human design.” The emergently ordered outcome of the distribution of rights-claims among political bargainers can be thought of as the political analogue, at the constitutional level, to the similarly emergent distribution of resources resulting from market bargaining processes.Footnote 1 Sovereignty is attached to command over particular political rights-claims; as such, to the extent that political power is divided, it may be the case that a single state has multiple sovereigns. My goals in developing this theory are twofold. The first is to understand better sovereignty in itself. The second is to understand how sovereignty, typically thought of in the context of monocentric political institutions, is in fact reconcilable with modern scholarship on polycentric governance.

Conceptions of sovereignty usually are under the purview of political philosophy or theory. Western political thought has seen significant changes to the conception of sovereignty, from the medieval order to modern liberal-democratic societies. The medieval conception of sovereignty predates the nation-state. In this conception, the sovereign (usually a king) was simply the final source of appeal, with a specific (and hence limited) set of rights and duties, in a rigid socio-political hierarchy. The sovereign was not above the law, and certainly was not a legislator (de Jouvenel [1957] 1997, III.12). As social, political, and economic forces favored the greater centralization of power in the early modern era, absolutist theories of sovereignty became more prominent, most notably the divine right of kings. Whereas divine right was seen as limiting a sovereign’s power in medieval Europe—the sovereign held office as a compact with God, and his continued authority depended in upholding the custom-based law of the land, as well as obedience to Divine Law—it was used to place the monarch above the law (rex legibus solutus) in early modern Europe. The monarch, as sovereign, could not be limited by any other authority, or else the limiting authority, and not the monarch, would be sovereign (e.g. Filmer [1680] 1991). These doctrines came into full fruition around the time of the Peace of Westphalia and the birth of modern nation-states. Of course, both of these theories stand in stark contrast to post-Enlightenment conceptions, which retain the linkage of sovereignty with the nation-state, but see legitimate sovereignty quite differently. Prevalent in the liberal-democratic regimes of the West, these variations locate sovereignty in Rousseauvian constructs such as the ‘General Will,’ or more saliently ‘the People,’ as exhibited in the Preamble to the US Constitution.

Each of these conceptions has some intuitive appeal. The medieval conception focuses on the structure of rights and duties that bind political elites; the absolutist highlights the importance of the quis custodiet? problem; the post-Enlightenment recognizes that any regime must have, at minimum, the tacit consent of a large part of the population in order to maintain its rule. However, each of these conceptions has noticeable drawbacks as well. For example, the medieval conception seems far too static; the absolutist seems to place too much emphasis on sovereignty de jure at the expense of sovereignty de facto; the post-Enlightenment seems difficult to reconcile with the iron law of oligarchy (Michels [1911] 1915; more recently Olson 1982), which suggests democratic self-governance is quite difficult to realize in practice, at least in large polities. These complications arise because the above conceptions of sovereignty are mixed together with theories of legitimacy. It is difficult to extract from these accounts claims about who actually exercises sovereignty, as opposed to who is supposed to exercise sovereignty.

I offer a solution to this ‘signal extraction problem’ in this paper. The account of sovereignty I will develop is purely positive; it will attempt to locate sovereignty in a hypothetical state of affairs unrelated to any particular ethical framework. I contend that sovereignty does exist, and that it is best understood as the result of -self-enforcing political exchanges both within and across polities. As will be seen, a sovereign is an individual or group of individuals, acting as a corporate party to a political exchange that does not rest on third-party enforcement. Importantly, since my conception of sovereignty is defined only with respect to a given hierarchy of political rights, a sovereign may or may not be bundled with a particular nation-state. This conception is reconcilable with dynamics in the underlying conditions that lead rational political elites to revise previously settled upon bargains.Footnote 2 While a better understanding of sovereignty is of obvious interest, it is not the chief benefit of adopting the framework advocated here. Instead, the chief benefit is greater explanatory power of social phenomena such as the relationship between sovereignty and statehood, the relationship between sovereignty and martial strength, the possibility of identifying sovereignty in environments otherwise thought to be ‘anarchic,’ and, contra Gordon (2002), a nontrivial conception of sovereignty that is reconcilable with polycentricity, i.e., multiple centers of political decision-making within a given social system and geographic territory (e.g., Polanyi 1951, and especially Ostrom 2010).

My account of sovereignty will look familiar to readers acquainted with Nozick (1974), who proposes an emergent theory of the state. Although Nozick’s purpose primarily is normative, his account of how a sovereign body might emerge out of political bargains is obviously relevant to my thesis. My theory is distinguished by recognizing that Nozick’s ‘natural monopoly’ theory of the state does not imply a single provider for public services. The economic notion of contestability (e.g., Demsetz 1968) also exists for sovereignty: because political property rights are costly to define and enforce, multiple individuals or corporate bodies will “own” different portions of a given bundle of political rights, such as contract enforcement, taxation, and judicial review. Different distributions of political power will result in different distributions of rights-claims among hierarchical corporate bodies. For example, the fragmentation of political power in Europe resulted in many competing sovereigns, while centralization of power in China resulted in political arrangements that resulted in something much closer to the familiar ‘one territory, one sovereign’ ideal (Ko et al. 2014).Footnote 3

The remainder of this paper is organized as follows: in the next section I ‘unbundle’ sovereignty, using the development of Western political institutions, and hence the distribution of political power, as a lens for viewing my conception of sovereignty. In Sect. 3 I discuss the relationship of sovereignty to constitutions, for the purpose of understanding how sovereignty develops from bargains within a given polity. In Sect. 4 I focus the analysis on the relationship across polities, showing that external balances of power matter as well. Sections 3 and 4 together highlight the essential nature of political exchange, and its role in determining sovereignty, whether that exchange takes place within or across polities. In Sect. 5 I formally state the nature of the relationship between sovereignty and self-enforcing political exchange. In the final section I conclude by discussing the implications of my theory.

2 Unbundling sovereignty: the importance of political bargains

The development of Western governance institutions from medieval private-law societies to modern liberal democracies depended heavily on the distribution of political power. This in turn resulted from bargains among political elites—those empowered to take part in the governance of a territory or polity. The political bargaining process that resulted in the development of modern Western polities shows the importance of locating sovereignty in mutually beneficial political exchange.

The most extensive account of the political bargains that brought the West from medievalism to modernity is Roger Congleton’s Perfecting Parliament (2011). The framework Congleton uses to make sense of political bargains is the ‘King and Council’ model. In this model, governance rights are divided between a single executive and a council of advisors. The breakdown of political rights between these two parties determines the de facto balance of power, which in turn can become embedded in governance institutions. A strong king and a weak council results in an absolutist state; a weak king and a strong council results in an ‘aristocratic republic’ as exemplified by Great Britain in the nineteenth century or Rome during its republican era. While sovereignty does not appear explicitly in Congleton’s analysis, it is clear between the lines. What is being contested by those party to political bargains, ultimately, is sovereignty: political rights attaching to the privilege of command in a given hierarchy. Owing to unintended consequences, the resulting distribution of political rights will almost certainly look quite different from what any party may have predicted ex ante.

The entirety of analytical focus in Congleton’s model is on political bargains between the king and the council, and the implications these bargains have for the distribution of political rights and, hence, political power. Theories of sovereignty that place power in a specific individual or corporate body are thus incomplete, because they stop short of analyzing who has what political rights and, hence, control rights, in governance. This does not mean that sovereignty does not exist, of course. It simply means that sovereignty must be inferred, rather than observed directly. A realistic theory of sovereignty must be reconcilable with the observation that de facto governance rights are divided as the result of political bargains and power balances.

The most important feature of the bargains between the king and council is that they must be self-enforcing. In other words, the political bargains must be in each party’s rational self-interest to uphold. This is because, in Congleton’s model, there is no higher authority to which either the king or council can appeal to enforce previous political ‘contracts.’Footnote 4 The most salient model for the purposes of understanding self-enforcing political bargains is the distribution of taxation rights between the king and council (Congleton 2011, Chaps. 5 and 6). Assume the king has full taxation authority initially. He can impose any level of taxes he wishes. Of course, the king faces a problem: If taxes are punitively high, his subjects will not exert the effort to produce a large output. The king’s ideal strategy would be to promise his subjects a low tax rate. Then, after his subjects produced a high level of output, he could renege on his promise and engage in confiscatory taxation. But his subjects are aware that the king has an incentive to lie, so to them, no promise the king makes is credible. This results in the possibility of a welfare-enhancing bargain for all parties: The king can credibly commit to a low tax regime by ceding some authority on tax decisions to the council. The council obviously is better off with veto power over taxation than without. The subjects also are better off, although they had no input into the political decision-making process, because they can now safely produce a high level of output, only some of which will be taken through taxes. Finally, the king is better off, since his credible commitment to a low-tax regime by ceding veto power to the council results in much larger tax revenue and, hence, increased material well-being. Importantly, the solution to this credible commitment problem is institutional. By ceding partial taxation rights to the council, the king’s and council’s bargain has changed the ‘rules of the game’ (North 1991). In this sense, institutions can be seen as mechanisms for ensuring credible promise keeping ex post (Acemoglu 2003; Parisi 2003; see also Williamson 1983).

Congleton’s account, which can be thought of as positive contractarianism, shows how the analysis of actual governance decision rights depend on a bargaining process. Neither an omnipotent king nor council is desirable, even from the perspectives of the parties themselves, precisely because of the resulting credible commitment problems. Despite the lack of explicit normative content, Congleton (2011, pp. 606–607) admits that viewing political development in his manner most closely complements a Whig theory of history. This may raise doubts concerning the reliability of the analysis, given the underlying ‘meta-narrative.’ Fortunately, another narrative of Western political development mirrors Congleton’s, but suggests very different normative implications.

de Jouvenel ([1945] 1993) also examines the development of Western political institutions through political bargains. Whereas Congleton sees a series of bargains that are mutually beneficial for each party, yielding a steady increase in well-being as the West approached liberal democracy, de Jouvenel views the same bargains with a high degree of skepticism. de Jouvenel traces the development of the modern bureaucratic state to bargains between kings and subjects struck at the expense of the nobility. The radical break from the ancien regime occurred when subjects realized kings had ceded so much authority that they no longer needed kings in their pursuit of political power. Commoners, after overthrowing the kings, assumed control over an already-existing administrative apparatus (Salter 2015a).Footnote 5 de Jouvenel was especially worried that these bargains, to him ill-conceived, threatened Western society’s ability to enjoy ordered liberty. The fact that de Jouvenel’s positive account is so similar to Congleton’s, despite a differing underlying normative vision, suggests my initial conclusion was warranted: Sovereignty, as it actually exists, must be located in the distribution of political rights arising from bargains among holders of these rights.

3 Sovereignty and constitutions

The bargaining process described by Congleton and de Jouvenel is constitutional bargaining. The bargains struck determine who has what political rights and, hence, how decisions within governance institutions will be made. This structure of power detailing which political elite possesses which decision rights with respect to the polity is the polity’s constitution. If the body of political elites constitutionally endowed with a right is itself the enforcer of that right, the body is sovereign over that right; to the extent that different bodies enforce their own rights, multiple sovereigns exist within the polity. Constitutional bargains are a crucial element in the determination of sovereignty, within a given polity. In order to illustrate this point, I must discuss briefly the differences between various kinds of constitutions, and how they are enforced.

Constitutions can be grouped into two broad categories: formal and informal. Formal constitutions are enshrined in a single document. They are blueprints for how political institutions will make decisions, at least ideally. The most obvious example is the Constitution of the United States. In contrast, informal constitutions are not enshrined in a single document. Sometimes they are embodied in many documents, such as charters and court decisions, which yield a set of ‘governance norms’ to which political elites adhere because coordination on such norms is in the interests of each party. The most obvious example is the constitution (the lower-case ‘c’ is purposeful) of Great Britain. It is possible that informal constitutions exist entirely in norms and tradition, as was the case in many European tribal societies.

The political ethos of modern liberal democracy holds that written constitutions are highly desirable. However, the scholarly literature on constitutional effectiveness suggests that skepticism is warranted. Written constitutions do not enforce themselves; to be effective, constitutions must be self-enforcing (e.g., de Lara et al. 2008; Leeson 2011; Mittal and Weingast 2011). While bringing a polity under a rule of law that is general, known in advance, and enforced non-discriminatorily (Hayek 1960) certainly is a worthy goal, that goal must be achieved by flesh-and-blood human beings. Always and everywhere, men govern men. The rapid change in political economy following the ‘public choice revolution’ (Buchanan and Tullock [1962] 1990) occurred when social scientists began to treat political actors as ordinary individuals who make decisions based on the information and incentives they face in the institutions that structure their behavior.

Formal constitutions, to the extent they are self-enforcing, are expressions of informal constitutions. In other words, self-enforcing formal constitutions represent coordination to a specific distribution of power that was reached in the institutional environment of the informal constitution. Formal constitutions can be useful as coordinating devices (Hardin 1982, 1989; Ordeshook 1992) but the actual enforcement is done by the structure of norms and distribution of political rights—the informal constitution. It is only a slight exaggeration to say that, to the extent that they match informal constitutions, the formal constitutions are redundant; to the extent that they do not, they irrelevant. Ultimately informal constitutions—meta-rules that govern interaction among exercisers of political rights—that tells us who can do what.

It is thus to the informal constitution we must look in order to understand sovereignty. It is critically important that informal constitutions, even where formal constitutions dictate extremely centralized or decentralized power de jure, specify a set of ‘soft’ constraints that yield a more nuanced balance of power de facto. Even a nominal autocrat “continuously lives under the Sword of Damocles and equally continuously worries about the thickness of the thread” (Tullock 2005a, p. 292). All government is divided government; all governance institutions occupy some intermediate point on the ‘King and Council’ spectrum. De facto limited government does not invalidate sovereignty; in fact, it helps us better understand its sphere of control. Joseph de Maistre, the quintessential Continental ‘Throne and Altar’ conservative, describes how divided government and sovereignty are reconcilable. Using the English constitution as an example, de Maistre ([1965] 2013, p. 112) writes, “However sovereignty is defined and vested, it is always one, inviolable, and absolute. Take, for example, the English government: the kind of political trinity which makes it up does not stop sovereignty from being one, always and everywhere. The powers balance each other, but, once they are in agreement, there is then only one will which cannot be thwarted by any other legal will, and Blackstone was right to claim that the English king and Parliament together can do anything”. de Maistre here obviously is using sovereignty in its legibus solutus sense, which is inappropriate for my purposes for reasons cited in the Introduction. However, de Maistre’s intuition is sound: Sovereignty is not limited but characterized by informal constitutions that themselves emerge from self-enforcing political exchanges. Again using England as an example, the informal constitution of the time was such that the king and Parliament had specific political rights that resulted from previous bargains. Each had a scope of action, i.e., political rights, that emerged as a result of these bargains. Other polities in other times almost certainly will have reached different constitutional bargains. For example, whereas even in de Maistre’s time majority of political rights rested in Parliament (although the House of Commons was not yet ascendant), France’s constitution during the reign of Louis XIV was characterized by an extraordinarily powerful—but not all-powerful!—king, with a weak nobility, and even weaker commons.

More recently, and of far greater significance for the theory and practice of public policy, is the theory of ‘scientific’ administration of Wilson (1887, 1956 [1885]). The motivation for Wilson’s work was locating the essentially existing source of sovereignty, in contrast to so-called ‘literary’ theories that relied on implausible mechanisms such as the ability of the separation of powers to yield constitutional enforcement. Commenting on Wilson’s project, Ostrom ([1973] 2008a, p. 23, emphasis added) writes, “[o]nce the center for the exercise of sovereign prerogative is identified, the structure of authority is unraveled and the symmetry of social life in that political order can be understood”. Having done this, the theory and practice of bureaucracy can be conducted along scientific, and ideally apolitical, lines. As argued by Ostrom ([1973] 2008b), political economy studies of bureaucracy, such as Tullock (2005b), have shown that the the assumption of administrative separation from the vagaries of politics to be unsound.Footnote 6 Nonetheless, the Olsonian model has been unsuccessful in displacing the Wilsonian model in the public administration literature (Aligica 2013). Why is this the case? I believe that a significant part of the answer is the public choice literature’s neglect of sovereignty. Sovereignty is real, and models of political economy must account for it if they are to have explanatory power.

The insight overlooked by the public choice literature is that to be sovereign, one must be sovereign over something, i.e., in the context of a specific polity with a history, tradition, legitimating institutions, and so on. It is those concepts that define the background constraints that structure political bargains, and thus help determine the informal constitution. Of course, to be sovereign also means to be sovereign over a given command structure, i.e., over a specific set of rights conjoined with duties associated with those rights. For example, while Louis XIV radically expanded the powers of the monarchy relative to that of the nobility and the Catholic Church, he never dared to assert the kind of spiritual authority proclaimed by Henry VIII. The bureaucratic control Louis XIV exercised over France, at the expense of the traditional warrior aristocracy, was far greater than the control he exercised over Church and Papal authority, although the latter was by no means insignificant. For this reason we reasonably may say Louis was the head of the hierarchy of command that exercised temporal authority, and, hence, sovereign with respect to this set of command-rights and accompanying duties. But he was not sovereign with respect to the hierarchy of command that exercised spiritual authority. While de jure that authority rested solely with the Pope, who protested formally Louis’s growing influence on Church affairs, de facto the authority of the Church, exercised on behalf of the Pope by French bishops, when combined with Louis’s assent, constituted sovereignty. In this sense, in Louis’s France, spiritual command was characterized by a form of sovereignty not unlike that which prevailed in England with respect to temporal matters.

As another example, consider the United States, whose particular Constitutional (formal) and constitutional (informal) arrangements were alluded to above. Following Ostrom’s (1997, [1971] 2008a, [1973] 2008b) interpretation, the Constitution of the United States was an attempt to create a government conducive to genuine self-governance. In theory, the government qua political organization is in command of the political rights-hierarchies outlined in the Constitution; the People are sovereign. In reality, to use Hayek’s (1973) terminology, the government of the United States is not an organization, but an order. It is a spontaneous outcome of political bargains, resulting in a constitution that differs significantly from the Constitution. Multiple organizations, as the result of bargains in the political process, find their political rights-claims self-enforcing. In some cases this is formal—the Internal Revenue Service has its own SWAT team, which it can use to enforce its claims against citizens. In others it is informal—while it would be absurd to suggest the Internal Revenue Service would coercively enforce its claims against the executive or legislative branches, it does not need to; because it is unlikely to be in an legislator’s or bureaucrat’s interest to ‘reign in’ the Internal Revenue Service, its claims to political rights are self-enforcing.Footnote 7 Because the distribution of political power renders the constitution different from the Constitution, a political blueprint for terminating right of command in the People has instead resulted in competing sovereigns whose actions, as the wide body of previous public choice scholarship shows, are not necessarily in the interests of those subject to the organization’s exercise of power.

4 Sovereignty and inter-polity relations

The above account describes how bargains within a polity yields a distribution of political rights, and hence political power, from which sovereignty can be inferred. However, this is only one part of a successful account of an exchange-rooted theory of sovereignty. Equally important are inter-polity relations, i.e., the bargains that take place between members of differing polities. As I will argue, there is no fundamental difference between intra- and inter-polity bargains. There are differences, but these are of degree, not of kind (e.g., Buchanan and Tullock [1962] 1990, p. 113). The locus of action still centers on political exchange between rational and self-interested individuals. In fact, the terms of political exchange in this environment will do much to determine precisely which sociopolitical arrangements constitute a polity, and which do not.

Self-enforcing exchange is still the relevant category of exchange. This is especially important in analyzing interaction between polities, since inter-polity relations, even among modern Westphalian nation-states, is essentially ‘anarchic’—there is no supra-national organization capable of enforcing its will on all parties (Leeson 2007bc). However, ‘anarchic’ is not synonymous with ‘ungoverned.’ There still exist institutions of governance between polities, and while it is far beyond the scope of the paper to analyze or even summarize them, we can still understand the subset of them that arise directly from the analysis of inter-polity bargains.

Perhaps the most useful paradigm for considering these kinds of political bargains is game theory, and specifically the infinitely repeated Prisoners’ Dilemma.Footnote 8 In this scenario, two polities—say England and France—are considering whether they will engage in Cooperation or Conflict. Cooperation can be thought of as any positive-sum strategy. In this context, the most salient interpretation is that England will respect France’s claims, and France will respect England’s claims, akin to the prevailing norms in pre-World War I international law.Footnote 9 Conflict means that England will not respect France’s claims, and will try to gain territory or other valuable resources at France’s expense, and vice versa. The diagram showing the payoffs to this game in each time period is shown in Fig. 1 below, with England as the row player, and France as the column player. By assumption, C > A > 0 > B, and 2A > B + C.

Fig. 1
figure 1

The prisoners’ dilemma

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The dominant strategy in a one-period version of the Prisoners’ Dilemma is well known: each party chooses Conflict, resulting in payoffs for both parties of 0. This is inefficient; total surplus would be higher at the mutual Cooperate equilibrium. But this cannot be sustained, because each player receives a private payoff from defection. In a repeated Prisoners’ Dilemma, however, the situation is quite different. Assume each player discounts future payoffs at rate \(\beta \in ({0,1})\). Also assume players are using ‘grim trigger’ strategies—if one party engages in Conflict, the other party punishes the first party by playing Conflict forever after. In this case, the mutual Cooperate equilibrium can be maintained, provided the future (discounted) payoffs from playing Cooperate exceed the immediate payoff of Conflict, or

$$\mathop \sum \limits_{t = 0}^{\infty } \beta^{t} A > C$$

Applying the rule for the sum of an infinite geometric series and simplifying algebraically shows that cooperation can be maintained if

$$\frac{A - C}{C} > \beta$$

In other words, as long as England and France are sufficiently patient, i.e., do not discount future payoffs to cooperation too highly, a mutually beneficial and self-enforcing Cooperate equilibrium can be maintained.

Thus the cooperative equilibrium in the repeated Prisoners’ Dilemma represents ‘live and let live’ approaches to inter-polity relations. In this case, England and France—each with their separate commands over specific political rights—agree to respect each other’s rights. Combined with sovereignty arising from intra-polity bargains, as in the example of England’s ‘King in Parliament,’ the inter-polity bargains determine the scale, over which the unit characterized by a given hierarchy of command, operates. The mutual Cooperate equilibrium implies England will not interfere in French affairs, and France will not interfere with English affairs. Each unit’s claims are enforced by that unit themselves, and are maintained between units by agreement, tacit or otherwise.

Of course, the mutual Cooperate equilibrium will not always prevail. As soon as the parameters of the game change, the profitable strategy may be subject to change as well. Suppose France suddenly discovers a new source of vast wealth, but this wealth has not yet afforded France the ability to equip a larger army or navy. In that case, the payoff to England of Conflict rises, since England now has the opportunity to loot France. But because France does not yet have the capacity to channel this wealth into martial strength, the expected costs to England of Conflict have not risen in tandem. If the increase in potential looted wealth is large enough, England would be willing to engage in Conflict with France, forsaking future cooperative outcomes for the possibility of increased wealth today. Such conflicts are rarely over the scope of the entire polity; the loser in a conflict generally does not experience complete subjugation by the winner. The conflicts in these cases are over specific political rights, perhaps most prominently the right to extract rents from economic resources within the scope of the polity. In all but the unusual case where a polity is fighting for its right to remain sovereign, what is in conflict is not sovereignty per se, but a marginal set of rights accompanying sovereignty. This ‘jockeying at the margin’ between polities determines how each party’s claim to sovereignty, as manifested in the termination of a command hierarchy over a specific set of political and economic rights, changes as circumstances alter to favor Cooperative versus Conflict strategies.

The above example assumed parity in martial might between polities. This is reflected in the symmetry of payoffs between the row and the column players. However, this can easily be modified by changing the payoffs of either the row or the column player. So long as the ordinal ranking of the payoffs remains the same, the Prisoners’ Dilemma logic still holds. For example, the column player’s payoffs could be modified from C > A > 0 > B, to c > a > 0 > b, where C > c, A > a, and B > b. This could represent repeated interaction between polities of differing strength. The weaker polity will receive lower payoffs from cooperating, and experience greater losses from conflict, than the stronger polity. But since the rank ordering of payoffs is unchanged, the Cooperative multi-period strategy can still be preferred by both players. Intuitively, even when England could dominate, say, Portugal, the opportunity costs associated with conflict are sufficiently high that it is still in England’s interests to respect Portugal’s claims. Thus mutual recognition of rights can still exist between polities of differing, and even vastly differing, strengths.

A final scenario requires changing the Prisoners’ Dilemma to another setup. In some cases with vast strength differences between polities, it is in the stronger’s interest to prey on the weaker. Provided both the strong and weak polity accurately perceive the costs and benefits of conflict, the ensuing relationship will be one of proprietor and client. The weaker is a suzerainty of the stronger. This can be represented in a number of game-theoretic scenarios, but perhaps the simplest is the Ultimatum Game. In this game, two players decide over the division of a fixed resource per time period. The first player proposes a split of the resource, and the second player has the option to accept or reject. If the second player accepts, both receive the agreed-upon payoff; if the second player rejects, both receive nothing. In this case, the stronger party takes the role of the ultimatum-giver, and the weaker is in the passive role of accepting or rejecting the bargain. Modify this game slightly to change the state of affairs that prevails when the weaker rejects the split. In this case, the players proceed to a new subgame of Hawk and Dove, sometimes called the Chicken Game. This game is characterized by large payoffs for the Hawk player when the other plays Dove, a zero payoff for the Dove player when the other plays Hawk, a moderate payoff for both players when each plays dove, and negative payoffs for both when each plays Hawk. This game is shown in Fig. 2 below.

Fig. 2
figure 2

The hawk-dove subgame

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The game is defined by B > C > 0 > A and b > c > 0 > a. Assume also that lower-case payoffs, the payoffs of the column player, are lower than those of the row player, while still satisfying the above ordinal inequality relationship. There is no pure strategy equilibrium to this game; each player wants to play Hawk while the other plays Dove, and vice versa; but conditional upon playing a Hawk, each player wants to play Dove. In this case, each player can avoid being exploited by randomizing—playing Hawk with probability p, and Dove with probability 1−p, where p is chosen to maximize expected payoff. Considering the entire game, the stronger polity, in the role of ultimatum-giver, would want to propose a split that maximizes his payoff, while presumably avoiding triggering the Hawk-Dove subgame.Footnote 10 To make the analogy even more concrete, even a more powerful polity cannot afford to completely abuse its vassal polity; eventually such abuse becomes so intolerable that the costs associated with fighting for independence are outweighed by the expected gains. In this case, the suzerain polity is not sovereign—its political rights are subject to enforcement or abrogation by a higher power—but the powerful polity is. Again, this holds only within the command hierarchy with respect to a given set of political rights, subject to the above constraints. De jure sovereignty never means de facto unlimited power. The resulting distribution of political power from the partially coerced political exchange is characterized, ideally, by no violent conflict. This is because political property rights are well-defined, and each party recognizes violence is not in its self-interest. However, once we introduce ambiguity—perhaps the weaker polity has access to private information that suggests armed revolt now maximizes its payoff—conflict becomes a possibility. Where conflict exists, the particular rights attaching to sovereign command are being contested. Political property rights are now poorly defined. The conflict will end when a new and clearer demarcation of political property rights, and hence a new and clearer demarcation of sovereignty, is reached.

5 Sovereignty: scale and scope

The analysis in the preceding sections allows me now to list the properties of a sovereign. A sovereign is a corporate bodyFootnote 11 whose claims to political, and any accompanying social and economic, rights are enforced by the corporate body itself. Likewise, any duties or liabilities that are implied by these rights are imposed by the corporate body itself. It is the highest authority within a given command hierarchy. Importantly, this formal definition of a sovereign is unrelated to the tacit understanding of sovereignty as it applies to Westphalian nation-states. Undoubtedly social, political, and economic changes in the early modern period resulted in a state of affairs where there were significant economies of scale to bundling governance services with contiguous geographical territory. But this fact is accidental to the explanation; there is nothing in my account of sovereignty that requires a sovereign to be sovereign over a modern nation-state. It is certainly possible for, say, an organized criminal organization—and more generally any group of stationary or roving bandits (Olson 1993)—to be sovereign, although nobody may regard their claims as legitimate in a moral sense.

Whether a corporate body is sovereign depends on the nature of self-enforcing political exchange within a polity (scale) and between polities (scope). In the above analysis I treated these categories separately. In reality, they are not separable—the terms influencing self-enforcing exchange within and between polities is constantly in flux, and there are obviously interdependencies between the two categories. But this complication does not imply that the categories are analytically inseparable. Treating one while taking the other as given was necessary to isolate the factors that cause the locus of sovereignty to shift. Ceteris paribus assumptions, while perhaps inappropriate in empirical work, are acceptable for the purposes of theory.

In one sense, the exchange theory of sovereignty resembles the medieval conception, in that each individual sovereign is characterized by a hierarchy of command relationships.Footnote 12 These command relationships specify rights and duties at each command level, and terminate in the sovereign. Since by definition the rights-claims (and accompanying duties-claims) must, eventually, be enforced by the party that claims them, their continued enforcement is a function of the relative payoffs the sovereign corporate body faces in conducting self-enforcing exchange. Thus this account has something of the absolutist conception of sovereignty as well. But it is important not to exaggerate this point; the sovereign is far from all-powerful. Internally, the sovereign corporate body’s power depends on the terms of self-enforcing exchange favoring its continued existence at the apex of the command hierarchy; externally, it depends on the terms of self-enforcing exchange favoring a continued mutual respect of rights-and-duties-claims by other sovereigns. Since the variables that define the scale and scope of sovereignty are co-determined, once the terms change, the distribution of power resulting from self-enforcing exchange will alter as well. This can result in one sovereign body claiming rights that previously accrued to another sovereign, body, or that were previously claimed by no party. In extreme cases, it can result in a sovereign body losing its sovereigns status, becoming a vassal polity. As an example of the intermediate case, the Glorious Revolution marked the end of a period where the sovereignty vested in the King of England covered an expansive set of rights and duties, whose enforcement terminated in the body of the king. The 1689 Bill of Rights is the formal expression of the informal distribution of actual political power, and hence the set of rights-and-duties previously within the purview of the monarch, that vests sovereignty in the King-in-Parliament (e.g., North and Weingast 1989). As an example of a more extreme case, the ongoing conflict in the Middle East precipitated by the rise of the Islamic State represents sovereignty in conflict. Nation-states headed by corporate bodies that had reasonable claims to exercise sovereignty suddenly saw these claims cast into doubt. In other words, there was both disagreement concerning which body possessed which rights, and ambiguity with respect to each party’s ability to enforce these rights. The conflict will continue until the actual power parity matches the perceived power parity; at this point, political property rights will be sufficiently well-defined that it will no longer be in each party’s interest to continue the conflict. This will be precisely the point where the distribution of political power, previously in flux, becomes known, and hence actual sovereignty becomes known as well. Rather than viewing this conflict as a failure by existing parties to continue to exercise sovereignty, the conflict is better viewed—positively, not normatively!—as the necessary process for discovering which body actually possesses the rights over which the conflict is fought.

Sovereignty is also not the intended result of a single will or group of wills. In this sense, it is emergent—the result of a complicated bargaining process over political property rights, with the final allocation being perfectly foreseen, let alone intended, by the parties to these bargains. Rational choice models of autocracy (e.g., Tullock 2005a; Wintrobe 1990) frequently reduce the distribution of a polity’s income or its de fa cto political power to a constrained optimization problem from the autocrat’s perspective. As a proponent of rational choice social science, I have no qualms with these models, which most fruitfully highlight the nature of the actual constraints facing an autocrat or would-be autocrat. These models do a good job of showing that ‘absolute’ power, to the extent ‘absolute’ is synonymous with ‘unconstrained except by physical laws,’ is chimerical. But they should not be taken to imply the will of the autocrat is the direct cause of processes as complex as the distribution of income or the allocation of de facto political power. In essence, sovereignty is a bottom-up order, not a top-down order. It can only be understood by observing how self-enforcing political exchange plays out over time. To paraphrase Buchanan ([1982] 2002), sovereignty is defined in the process of its emergence. It cannot be divorced from the bargaining process that creates it.

6 Implications and conclusion

I believe the positive account of sovereignty I presented is superior to traditional accounts that inadvertently mix conceptions of sovereignty with conceptions of legitimacy. However, this is not the only, or perhaps even the most important, contribution. In addition, I put forward three implications of the theory that I believe help us better understand some real-world phenomena. Each of these could serve as the thesis of a paper in its own right; here, I will limit myself to presenting the essential features.

First, as hinted at in Sect. 5, sovereignty is neither necessary nor sufficient for statehood. Wherever there is political exchange, and thus nested rights, there will be some point beyond which these rights must be enforced by the body that claims them. This means that non-state actors can indeed be sovereign, which allows us to extend the concept of sovereignty to pre-Westphalia political arrangements. It also allows us to locate sovereignty in post-Westphalia non-state actors as well. For example, the settling of the American frontier took place in a largely ‘anarchic’ environment. Pioneer-settlers, traveling to new lands outside the territorial jurisdiction of the United States, had to form endogenously their own governance institutions, for activities as diverse as caravan defense and dispute settlement over property rights (Anderson and Hill 2004). In these cases, the bodies that exercised control over any particular governance institution was a tiny, but true, sovereign, and existed in an environment of multiple sovereigns that were simultaneously cooperating on some margins, and competing on others. That life on the American frontier was significantly more peaceful and orderly than popular imagination suggests implies that multiple sovereigns, even to the extent that they share geographic territory, can co-exist peacefully. How scalable this result is, however, is open to question, and its resolution is ultimately requires extensive empirical work (see, e.g., Powell and Stringham 2009).Footnote 13

Second, military might is merely one of the determinants of sovereignty. Obviously greater military strength, all else being equal, will allow a body to enforce better its rights-claims. But many situations also exist wherein rights-claims held by various sovereigns largely are unrelated to military strength. This is so because conflict itself is not costless. Significant strength disparities can and do exist between sovereigns, because weak sovereigns may not be worth the effort of subjugating. This is even true today: microstates such as Monaco or Liechtenstein are obviously unable to defend themselves from serious external threats, but it would be a mistake to conclude that these microstates’ existence depends entirely on the sufferance of stronger powers. Given the significant economic ties between developed nation-states, military might is probably declining in importance, at the margin, to economic ‘soft power’ in influencing the choice calculus of sovereigns or would-be sovereigns.

Third, and probably most importantly, the theory of sovereignty developed here is easily reconcilable with the theoretical ideal, and practical existence, of polycentricity. This is because the ‘work’ is being done not by any individual sovereign, but the network of relationships between them. Continuing in the tradition of the Bloomington School, Aligica and Tarko (2012, p. 237) define polycentricity as “a social system of many decision centers having limited and autonomous prerogatives and operating under an overarching set of rules”. In particular, sovereignty as argued in this paper can be particularly fruitful for understanding the link between the literature on analytic anarchyFootnote 14 (e.g., Leeson 2007a; Powell and Stringham 2009) and theoretical conceptions of polycentric orders (see esp. Aligica 2014, pp. 52–56). In polycentric orders, there are many centers of decision-making, each with a degree of autonomy, and not subsumed into a hierarchy under any other authority. At first, given the reliance my conception of sovereignty made of hierarchy, these paradigms seem irreconcilable. However, there is in fact no conflict. In a polycentric order, there are multiple cooperating and competing hierarchies that are partially independent of each other’s decision structure. For example, the medieval Church was highly hierarchical, but it existed as one element in the polycentric legal order of medieval Europe, sometimes competing and sometimes cooperating with temporal legal orders of nobles, kings, free cities, and trade guilds (Anderson 1991; Baechler 1975; Berman 1983; Raico 1994; Stark 2011, Chaps. 14–16). Each hierarchy, terminating in a body whose rights-claims are self-enforcing, is sovereign over those rights-claims to the extent that political property rights are sufficiently well defined such that the claims are undisputed. The rules that structured the interaction between sovereign hierarchies itself was emergent, and co-evolved with the emergence of sovereignty itself.Footnote 15

As an example, consider recent scholarship on the governance mechanisms of stateless Somalia (Leeson 2007c; Powell et al. 2008; see also van Notten 2005). The government of Somalia collapsed in 1991, following three years of civil war. Although violent conflict continued into the mid-1990s, by the late’90 s Somalia had become relatively peaceful, with the exception of the attempted restoration of centralized government in 2006. De facto governance currently is polycentric, as the various clans competing for power have realized that sustained push for monopoly control currently is infeasible. The initiation of civil war in 1988 can be viewed as a contestation over insecure political property rights. The collapse of traditional state sovereignty then was not a disappearance of sovereignty, but a transfer to the various groups contending for political property rights, each to its ability to enforce its rights-claims. Attempts by the international community to recreate the nation-state resulted in significant upswings in violence, as political property rights again became contested. Ultimately the efforts to impose modern Western conceptions of governance on Somalia have failed since they require restructuring political property rights into an arrangement that is simply not incentive-compatible for the actual holders of political power. The attempt to ‘restore’ sovereignty is simply a refusal to recognize sovereignty.

Some may object that I am expanding the definition of sovereignty to be so encompassing as to be incapable of doing analytical work. If there is always a sovereign or group of sovereigns, the objection goes, then sovereignty cannot be a useful concept. Putting aside the questionable positivist flavor of this objection, I reply that my conception of sovereignty forces social scientists and philosophers to classify existing orders of interacting hierarchies as they actually exist. Rights and duties, which at some point must be self-enforcing or self-imposed, are an important part of human interaction, and exchange relationships in particular. The conception of sovereignty outlined here forces the theorist or historian to classify the pattern of political power as it actually exists, according to a theoretical category (sovereignty) that must be present somewhere. In particular, my conception forces analytical attention on the nature of political exchange between command hierarchies. Whether this exchange is free or coerced, and its implications for future distributions of sovereign claims at the margin, should be a chief focus of the student of political society, just as the analysis of exchange and the institutions in which exchange takes place (Buchanan 1964; Shughart and Thomas 2014) is a central concern of the student of economics.