Diplomatic complexity and long-tailed distributions: the function of non-strategic bilateral relations

States enact relations with both important partners and seemingly irrelevant countries. The non-strategic constitutes the larger set; a histogram could visualize them in a long-tailed distribution, with the x-axis denoting the partner countries, and the y-axis showing the interaction density. Investigating the function of this long tail, this paper premises that the international is characterized by complexity, meaning that the number of elements is so large that it is impossible to realize all relations simultaneously. States thus select their diplomatic partners based on power-rationales. The thereby inactive nodes nevertheless pose sources of danger, requiring occasional signals of amity—hence a long tail comes about. A repertoire of cheap and quick but unambiguously sovereign practices (such as Twiplomacy, gifts, or honorary consulates) can be spontaneously activated to fill otherwise neglected inter-state ties. Seemingly trivial gestures thus ensure peace among plural polities under the constraint of systemic complexity.


Introduction
The abundance of triviality Diplomatic practices abound with seemingly non-strategic interactions: for instance, Japan's Head of State confers a state award to a retired minister in Tajikistan, 1  Ukraine appoints someone as an Honorary Consul in Djibouti, 2 the de facto Foreign Minister of South Ossetia visits Nauru as part of an official trip, 3 a bilateral education cooperation is enacted between Austria and Oman, 4 and South Korea mobilizes a large sum of foreign aid for Tanzania. 5None of these events can find straightforward explanations by the usual theoretical determinants of international life, such as military might, economic interests or constructivist imaginations of a friend/foe-distinction.As will be illustrated below, states have at least some kinds of trivial diplomatic relations with approximately 160 countries each6 -but why?How to explain these allegedly non-strategic relations?
One may visualize these diplomatic ties in a diagram of a given state, with the x-axis showing the partner countries, and the y-axis denoting the intensity of interactions with the partner.Ordered by the intensity of interactions, one would get a long-tailed distribution: a few partner states obtain intense engagement with high frequency, another tier of polities is given intermittent but regular attention, and then comes a residuum of circa 160 states that merely receive the rare signal of amity.The antecedents that place a country into the high-frequency head of a given state's diplomatic distribution are well-discussed (e.g., Gartzke and Gleditsch 2022;Lebovic and Saunders 2016;Moyer et al. 2020): They are the nearest neighbors or otherwise spatially close, they exhibit dense trade ties, they enjoy great power status or similar signifiers of military might, they share historical commonalities in colonialimperial terms, and so on.Due to its obvious strategic value, the high-frequency head finds sufficient scholarly attention-the long tail, in contrast, remains in an unexplained blind spot.In most theories of International Relations (IR), that long tail is implicitly dismissed as mere noise not worthwhile of analytical investigations.And yet, diplomatic practices abound with seemingly non-strategic interactions; and if each of the world's states has their long tail of 160 countries in aggregate patterns Fig. 1 Recipients of Japanese state awards by country.Only every 7th country is labeled in the x-axis for better readability, and the y-axis is transformed into a square-root-based scale Fig. 2 Recipients of Lithuanian state awards by country.Only every 3rd country is labeled in the x-axis for better readability of trivial diplomatic practices, then the allegedly non-strategic must be a very common phenomenon.

Examples
And indeed, some random illustrations indicate that this pattern is visible across various examples, most of which even approximate a Pareto-distribution of 80/20, whereby 80% of all diplomatic interactions go to 20% of the world's countries (premising 190 of them-albeit the Figures in this section do not explicitly show countries when there is no single interaction recorded with them).
As a first example, Japan bestowed 2.615 honorific state awards to individuals from 179 countries between 2008 and spring 2021 (Fig. 1). 7The USA is the country with the most recipients (440), followed by Brazil (134) and France (118).When matched against a global stock of 190 countries, 80% of all award conferrals went to just 22% of all countries.As a second example, Lithuania uses the tool of state award less frequently than Japan, but it did confer 2.143 meritorious orders to foreigners between 1991 and 2021.While most bestowals went to the USA (356), Poland (242), and Germany (147), there were 56 other recipient countries with lesser numbers, again foregrounding a long-tailed distribution (Fig. 2).8    visits shows that 80% of all instances went to 17% of all countries.In an analogous US dataset (Lebovic and Saunders 2016) covering more than 750 presidential trips to 119 countries over a century (Fig. 4), the UK leads the list (having received 59 US presidential trips) ahead of France (46) and Canada (39); overall, the dataset likewise shows an approximation of a Pareto-distribution (with 80% of all state visits going to 24% of all countries).In the case of state visits from the People's Republic of China from 1990 to 2019 (Wang and Stone 2022), Chinese leaders had 405 official trips to 111 countries; the most frequent destination is Russia (22 visits), followed by Kazakhstan (14) and Germany (13)-overall, 80% of all trips went to 31% of all countries, thus again exhibiting a long tail (Fig. 5).
Other practices of diplomacy may likewise exhibit a long tail in the aggregate, such as official mentions of countries through mass media channels.This discursive dimension may be illustrated with three examples.First, scraping the articles published on the website of Poland's Ministry of Foreign Affairs (MFA)9 from 2018 to October 2021 leads to exactly 1.000 news postings.A rough analysis of the country names mentioned in the titles of these articles extracts 438 mentions (other than Poland itself) of 93 countries (Fig. 6).Belarus obtained the most mentions (29), followed by Lithuania (28) and Ukraine (26).Compared with the global backdrop of 190 countries, again the 80/20-rule becomes visible, as 80% of all mentions go to 22% of all countries.Second, the frequency of country mentions by the Chilean MFA Twitter account (@ChileMFA) as obtained from the Twitter API covers Fig. 8 Countries mentioned in official US documents on Foreign Relations.Only every 10th country is labeled in the x-axis 114 countries in 1.154 mentions from 2016 to 2022, led by China (87 times), the UK (81) and Canada (71), and it even shows a perfect example of 80% of all mentions going to exactly 20% of all countries (Fig. 7).The final illustration is the most extensive one-covering 3.795.254mentions of 193 countries in various documents concerning the foreign relations of the USA from 1950 to 2000 (Fig. 8), as collected by the FOIArchive (Connelly et al. 2021).The list is led by France (132k mentions), Japan (120k) and Germany (105k).This time, 70% of all mentions go to 28% of all countries, again exhibiting the long-tailed pattern.
These were just a few examples of long-tailed distributions among diplomatic practices.They are based on convenient samples that were not gathered systematically with an aim to be as comprehensive as possible, but rather to illustrate the theoretical claim with a handful of different cases.The fact that the illustrations comprise heterogeneous tools from various countries indicates that the long-tailed distribution reflects a fundamental, structural aspect of the diplomatic system.

The lack of existing explanations
How can one make sense of the prevalence of such bilateral linkages?Can one theoretically infer a generalizable function to these seemingly obscure diplomatic relations, rather than to brush them off as accidental noise?Common IR theories break their purview into two sides, placing specific variables (such as material power) typologically into the 'strategic' one as contrasted to the other, non-strategic, unmarked side.They then depart all their conceptual and empirical analyses from the former one, ex definitione leaving behind an explanatory residuum in the blind spot of the non-strategic, non-rational, exogenous realm.They then argue that even "unexciting international relationships" (Womack 2015: 1) which form the majority of diplomatic ties are ultimately explainable with rational cost-benefit analyses (as in the case of asymmetry theory), or that the world system's 'core' extracts resources from the global 'periphery' so that any other interactions are nothing but reflexions of this dominance.Whatever the phenomenon, it will be explained with a theoretical recourse to gains and costs, to hegemony and conflicts, to patrons and clients, to bandwagoning and balancing, to geopolitical interests and economic domination, to an animus dominandi and ontological security-suggesting that every aspect of international life nourishes itself from some kind of strategic rationality.As a counterreaction arises a semantics whose very function is to invisibilize the fact that the non-strategic exists outside the explanatory model-such as by labeling them as practices of 'soft power' or 'public diplomacy' that operate beyond powerbased rationales, or as mere 'habits' (Hopf 2010), or as accidental outflows from the psychic idiosyncrasies of specific leaders (Cornut et al. 2022).While such concepts may analytically diminish the irritations arising from the non-strategic realm, they do not aid in clarifying the phenomenon's systemic function and distinct forms.

Summary of the present work
This paper, in contrast, will attempt at elaborating the societal significance of diplomacy's long tail.It does so by drawing from modern system theory and its inherent propensity for functional analyses (Luhmann 1995: 52-58;Peña, 2015: 60).Given a system (here: the social system of diplomacy), it asks what function a systeminternal phenomenon (here: seemingly non-strategic bilateral ties) exhibits, that is, what system-specific problem may be addressed by that phenomenon.The present approach therefore does not start with a typology of presumably significant matters-such as military might or economic gains-based on which it ex ante either regards phenomena within diplomacy as analytically valuable or discards them as insignificant.Instead, the functional method premises that everything that occurs within a given system serves system-upholding functions by solving system-internally observed problems.It therefore offers a lens that does not discard the long tail of diplomacy as irrelevant prior to any analytical effort.This paper's argument, in brief, is the following.Diplomacy carries the function of ensuring the non-activation of physical force among a plurality of power-constituted polities (Constantinou 1996;Der Derian 1987;Sharp 2009;Youssef 2020: 224).However, it inheres the problem of complexity in the sense that the number of elements in the system is so large that no state can simultaneously enact relations with every other state (Luhmann 1995: 26-27). 10Consequently, there is the (improbable but nevertheless systemic) danger of neglected inter-state ties, which is latently destructive due to the power-constituted nature of all polities.While inevitable, every neglection could potentially fail in ensuring diplomacy's societal function of peace.As a solution, the diplomatic system keeps in reserve a repertoire of generalized practices (Goddard et al. 2019;McConnell 2018) that can be quickly and cheaply mobilized to occasionally nourish inactive diplomatic ties.Examples for such quick and cheap diplomatic tools would be honorary consulates, state awards, foreign aid, bilateral student exchanges or digital diplomacy.It is for this reason that countries typically do not merely enact foreign relations with an exclusionary circle of a select few of important partners, but instead exhibit a long tail so as to extend their external affairs toward the whole international community and its "fringe players" (Bátora and Hynek 2014)-despite the complexity behind managing such a large number of relations.The function of seemingly non-strategic bilateral enactments, therefore, is to minimize the systemic danger to world peace that may arise 10 Complexity theory contains diverse strands with various definitions of complexity stressing different aspects (like a system's internal variety of units, its openness toward environmental irritations, its unpredictability, its resilience against external perturbations, or the computational resources required to calculate an algorithmic outcome).The purely numerical definition used here is a parsimonious approach, highlighting a fundamental aspect common to all understandings of complexity.For general overviews on complexity in International Relations, see Kavalski (2007), Bousquet andCurtis (2011), andOrsini et al. (2020)-with numerous applications in recent years, such as on global pandemics (Kreienkamp and Pegram 2021), the emergence of international norms (Winston 2023), global financial crises (Oatley 2019), peacekeeping missions (Day and Hunt 2023), or power politics in Eurasia (Korosteleva and Petrova 2021).
out of neglected inter-state ties given systemic complexity; and diplomacy maintains a repertoire of quick-and-cheap-yet-clearly-sovereign practices that form the realization of this function.Non-strategic inter-state interactions are not meaningless, unexplainable, irrational noise; instead, they are crucial to fulfilling the diplomatic system's societal function of world peace.
The insights add to the literature on the seemingly mundane and everyday, the allegedly non-strategic and trivial aspects of diplomatic practices that are so ubiquitous across the whole system (Adler-Nissen 2013; Constantinou et al. 2021;Cooper and Cornut 2019;Pouliot 2016;Sending et al. 2015).This paper also demonstrates the analytical utility of modern systems theory and its functional approach (Albert 2016;Albert et al. 2010), without which the seemingly non-strategic phenomena either easily elude the analytical lens or are hard to grasp in coherent terms.
The following section develops the analytical premises with greater depth.After presenting the results of this theory-building exercise, the paper juxtaposes the finding with conceptual counterparts from the English School, and it closes with hypotheses for further research, including on the historical evolution of the long tail, on the broader validity of a Pareto-distribution of foreign affairs, and on a possible 'inflation' of peace that accompanies the ever-growing complexity of contemporary diplomacy.

Sovereign equality and the long-tailed distribution of diplomacy
The diplomatic system describes itself in terms of sovereign equality.Theoretically, all states are equally accessible to every other state through official channels.In practice, however, the states' capacities in conducting their external affairs are limited such that they focus most of their attention to a select few countries.This selection contains those who are deemed to be of highest strategic importance.
And yet, states are nevertheless frequently involved in diplomatic events with partner countries whose strategic values are less obvious.These occurrences then seem analytically trivial, superfluous, exogenous to a power-centered rationality.Theory may discard such diplomatic enactments as obscure and insignificant, so that the happenings end up being ignored-but nevertheless, the phenomenon persists.To some individual diplomats, the long tail perhaps occupies the majority of their work.
Analytical endeavors, often within the realm of Area Studies or Foreign Policy Analysis, may impute strategic patterns behind such events.Through case-by-case investigations, they find that such interactions inhere a situational validity, momentary importance, rational justification.They craft convincing narratives as to why they occurred.The interest here, however, lies in the systemic patterns in the aggregate, and not in the situational circumstances of each specific case.The individual event comes and vanishes, but what they lead to are general structural patterns resembling the long tail-and it is the latter that requires a plausible explanation here.The level of analysis in this paper, therefore, is not one of concrete events, but the abstract-systemic from whose viewpoint the elementary episodes seem merely 'random'.While Area Studies or Foreign Policy Analysis may 'de-randomize' specific parts of the long tail, they do not provide theories for the overall long tail as such.
Modern systems theory and its propensity for a functional analysis may aid in illuminating why the allegedly non-strategic ties persist.It conceptualizes diplomacy as a system that addresses the problem of plural polities.That is, the system of politics amasses intense capacities of physical violence with the function to enforce collectively binding decisions in a given territory (Luhmann 2002).However, historically, the political system did so not within a single center of power, but rather generated a multiplicity of such states (Tilly 1995).The problem behind plural polities is that inter-polity ties are inherently dangerous and threatening, precisely because of their potential to mobilize vast power forces against each other.It is in response to this problem that society internally differentiated a diplomatic system.And this diplomacy's function is to invisibilize the mistrust and enmity inherent to international politics by generating practices of trust and amity.Diplomacy enacts peace instead of yielding might; its societal function lies in nothing but in "offering restrictions on [a state's] power" (Ikenberry 2001 p. xvi).11An ideal system of diplomacy with infinite resources would constantly communicate signals of peace in every potential inter-polity relation.As the system's capacity is limited, however, diplomacy is forced to select only a few realizations of possible inter-polity relations at a given moment in time.In other words, the system is characterized by complexity in the sense that the number of system-internal elements is so large that not all of them can be bound together at the same time (as regards this numerical of definition of complexity, see Luhmann 2012: 78-80;Simon 1976).At any given instance, much of the system's potential remains in an unrealized state while only a few potential relations are activated.
One may view this systemic problem of complexity from the level of a polity: if a country took the semantics of sovereign equality seriously, it would select its diplomatic attention equally among every single partner state.The number of interactions (and their protocollary level) with state A would be the same as the number of interactions (and their protocollary level) with state B-and with state C, D, E, F, etc.A ministry of foreign affairs would be institutionally tasked with overseeing the practical implementation of this 'equidistant diplomacy' (Teo and Koga 2022) by ensuring numerical and formal equality (Kuhn 2023).
However, societal realities-other systems outside diplomacy-irritate the diplomatic system such that it is pushed to channel attention in an asymmetric fashion.The political system formulates a 'national interest' and passes it on to diplomacy (Kratochwil 1982); the economic system follows geographical feasibilities and generates skewed trade flows that regularly demand interventions from diplomacy (Dür et al. 2014); the systems of sports or culture spew forth huge international events to which diplomatic attention needs to be temporally directed (van der Westhuizen 2021); the system of law condemns a multilateral agreement as illegal and stipulates remedying actions (Helfer and Voeten 2014); the system of higher education clusters organizations of scientific excellence around specific locations with which diplomacy is tasked to negotiate exchange and joint research agreements (Yılmaz 2019)-and students join these efforts with grassroots activism and thus, contribute to diplomatic attention-channeling (Zemanová, 2022); and so on (Peña and Davies 2022).It is due to such external irritations that the diplomatic system's semantics of sovereign equality is hardly realizable (Krasner 2001).
Instead of exercising sovereign equality, diplomacy necessarily generates indifferences by selecting its attention.Consequently, and from a given state's viewpoint, not all countries are equally worthy of diplomatic engagement.In other words, diplomacy copes with the systemic problem of complexity through selections at the level of the state.

Programming 'right' and 'wrong' peace signals
To decide on which of the potential inter-state ties are to be realized, the system generates so-called programs (Luhmann 2012: 217).They program the system such that they provide an orientation as to what practices and which addressees are the 'right' or 'wrong' ones (in a political semantics, this right/wrong-distinction could be translated into strategically important/irrelevant).Foreign policy goals are the most salient programs in diplomacy.Passed on from the system of politics, they inject power-related considerations (politics) into the peace-determined system (diplomacy) (Nishikawa-Pacher 2023a).In other words, diplomacy programmatically uses political selections to reduce its internal complexity.For instance, if the foreign policy goal is one of energy security, it programs diplomacy in such a way that the state enacts diplomatic communications disproportionately with energyabundant partner states.The usual repertoire of diplomatic practices-such as highlevel state visits, great amounts of foreign investments, or ceremoniously signed memoranda of understandings-will then find their instantiations with potential suppliers of energy resources.Diplomacy knows of other kinds of programs, such as the system-wide semantics of 'great powers' or 'rising powers' or 'regional hegemonies'-they likewise steer how diplomatic attention is distributed.The volatile dynamics behind those semantics (Bhal 2023; Kupchan 2014; Larson 2018) already hint at the fact that programs can change over time.For instance, in earlier centuries, diplomacy may have been programmed according to the glory of ruling dynasties (Youssef 2021) or according to the religious attributes of polities (Ash and Dolan 2021; Diwan 2021).Whatever the programs at play, they serve to channel the limited resources of diplomatic attention so that only specific inter-state ties are actualized.The system thereby generates structures so as to steer itself through its own complexity and to focus its capacities.
Deviations from the programs are not impossible, but improbable.They carry the stigma of strategic irrelevance, uselessness, triviality.If diplomacy is programmed such that powerful actors receive more careful attention than non-powerful ones, then a state deviating from this program faces a burden of justification when it engages solely with remote and small states.Imagine that Russia would withdraw every single one of its ambassadors around the world, only to open a new embassy in Kiribati-the sole to be sustained for the next decades.Such a scenario is highly improbable, but not impossible (given the contingency of societal action; see Körösényi et al. 2016).In light of the 'stigmatization' of program-deviating actions (Adler-Nissen 2014; Kurowska and Reshetnikov 2021), one may thus hold that in the usual course of diplomacy, all inter-state ties not covered by 'foreign policy goals' (and other programs) therefore risk remaining in a passive, latent, hidden and neglected fringe.

The function of the long tail: ensuring peace in neglected ties
While programs offer a solution to the problem of complexity, it brings forth its own risk-the risk of neglection.Regardless of the programs in force, the system's underlying societal problem remains: that is, the inactive nodes continue to be power-constituted polities and thus, continue to pose sources of danger-even if they are not in the high-frequency head, even if they seem to be mere 'weak states' (Newman 2007) or 'small states' (Panke 2012) or 'micro-states' (Quester 1983) or 'remote', 'fringe', 'neutral', 'rebel', 'breakaway' territories.The problem persists: there are plural polities and every single polity is a source of danger.There is always an (implausible but not impossible) risk that hitherto inconspicuous polities mobilize forces against other states (Elias 2018).Or they may create systemic problems through means other than war, i.e., by 'the weaponisation of everything' (Galeotti 2022), or misusing any phenomenon to render it a liability to a foreign state (such as refugees, see  (Baldacchino and Wivel 2020: 2).And once incited, the conflicts that emerged in remote peripheries may succumb into a dynamic of spatial contagion to spread across the globe (Acuto 2014;Buhaug and Gleditsch 2008).While the diplomatic system is sensible enough to spare capacities via the inactivation of non-strategic nodes, it ultimately cannot eliminate the danger inherent to plural polities, and it cannot rule out that even small states create big problems (to paraphrase Keohane 1971: 161).
Society therefore needs to ensure that diplomatic peace extends to the remotest corner as well.The fringe players may remain in a passive latency, but the system of diplomacy nevertheless requires them to be occasionally nourished with low-level signals of peace and amity-lest diplomacy risks failing in fulfilling its societal function.As this systemic risk is distributed across the level of polities, every state is tasked to pay attention to seemingly non-strategic, non-powerful partners in spite of strategy-demanding, power-oriented programs.Politically formulated national interests, semantics of great powers and hegemonies, and other such systemic programs may aid in mitigating the risk of (localized or global) mass destruction that arise out of plural polities, but they do not solve them.They instead leave behind a residual risk with regards to all inter-state ties that are not covered by the programs.
It is because of this residual danger that the diplomatic system structures bilateral relations in the form of a long tail.Not 100% of a country's external affairs are strategic; perhaps 80% are, to use a generic assumption of a Pareto distribution.The system thus dichotomizes a 'strategic' realm (the high-frequency head) from a 'nonstrategic' one (the long tail) and ensures that both sides obtain their (unequal but fair) share of diplomatic peace signals.The function of the long tail is thus the same as the general function of diplomacy as a whole-namely, to consolidate peaceforegrounding practices that restraint plural polities lest they activate their amassed reservoir of destructive forces.
Its function specifically emerges from the background structure that complexityreducing programs (like foreign policy goals) are so power-oriented that they risk neglecting most polities.With the long-tailed distribution, diplomacy ensures that the otherwise unattended polities do not remain completely ignored.

The forms of the long tail: cheap and quick but sovereign
Given that the function of diplomacy's long tail is just the same as the function of diplomacy's high-frequency head-that is, they both serve to achieve world peace in world society-how, then, does diplomacy distinguish between the two?
While the function may be identical, their respective forms are different.In other words, the diplomatic system distinguishes one kind of practices that are reserved for the strategic but small, high-frequency head of partner states from another kind of practices that are reserved for the non-strategic, long tail of other countries (Dorussen et al. 2021).The former obtains 'costly' signals-well-funded resident embassies, frequent state visits at the highest level, publicly visible support in salient matters at international organizations, the pooling of wealth in supranational projects, the regular enactment of joint military exercises, membership in formal alliances, a multitude of officially endorsed people-to-people exchanges, etc.These are all resource-intense practices; they require broader political backing in the domestic realm or the scarce-but-valuable attention of the highest offices.The long tail, in contrast, cannot legitimately claim such high costs.It would seem 'wrong' (trivial, irrelevant, absurd) as the system is not programmed in this way.What, then, are the forms of diplomatic communications that can be used for the non-strategic long tail?
The diplomatic system needs a repertoire of practices with which it can continue paying disproportionate attention to the high-frequency head without completely neglecting the risk that arises out of small states.It needs small gestures, gestures that do not consume too many resources, a repertoire of practices below the threshold of astute, power-maximizing statecraft.The tools need to be cheap and quick to mobilize-cheap and quick at least relatively to the tools that commonly mobilize the high-frequency head of bilateral relations.They should not demand lengthy deliberations of a grand strategy, they should not invoke complicated procedures of decision-making, and they should not require palpable monetary costs paid by the public.Instead, they should be so minuscule so as to evade the attention of domestic veto players, possibly by lowering the protocollary level, or by only consuming a tiny share of a foreign ministry's budget.It suffices that the non-strategic diplomatic practices are justifiable with vague semantics of amity and friendship (Devere et al. 2011) and peace-that is, with the overall societal function of diplomacy-as long as they are quick and cheap.
In addition to being costless and rapid, the practices reserved for the long tail should also be unmistakably attributed to a sovereign, power-constituted polity.Otherwise, their reference to the diplomatic system would be too ambiguous; it would not be clear whether the communication is a diplomatic one or not.Thus, the anonymous sending of flowers to the partner Head of State would not be a suitable tool-it may be cheap and quick to arrange, but it would lack the sovereign semiotics inherent to the system of diplomacy (see Carrió-Invernizzi 2008).To ensure a clear attribution to the sending polity, the practices should occur through official channels, exhibit a state iconography, use a legally envisioned tool, or realize an otherwise internationally normed oughtness.It is only then that the quick and cheap practices are unambiguously sovereign.
To offer some ideal-typical examples: for the long tail, it should not be the minister of foreign affairs involved but the vice-minister, or not the vice-minister but the undersecretary, not the undersecretary but the head of a department.It should not be a state visit but a working visit, not a resident embassy but a honorary consulate, not the highest order of merit to be bestowed but the secondhighest one (Nishikawa-Pacher 2023b), not a large-scale investment treaty but a non-binding memorandum of understanding, not the joint nomination of a candidate for the General-Secretary at an international organization but the support for the nomination of a judge at a temporary international dispute settlement body, not a physical meeting to extend a cordial message but a mere congratulatory Tweet (Shih 2020: 179).
While this is not the space for a complete taxonomy of current usances in non-strategic bilateral relations, the former paragraph at least offered a few illustrative examples.They all convey a credibly sovereign, amical and yet largely irrelevant display of inter-state peace.They are quick-to-be-forgotten instances of a high-tempo but low-level diplomacy rather than slow but large-scale mobilizations of grand politics with notable effects upon whole populations.The minuscule, the everyday, the ritualistic, the inconspicuous, the trivial (Aalberts et al. 2020;Guillaume and Huysmans 2019;Pacher 2019;Visoka 2019), the cheap and quick and yet sovereign practice is the suitable form for the long tail of diplomacy.

Summary
This paper asked about the function and forms of a common phenomenon in diplomacy: States not only enact bilateral relations with obviously important strategic partners, but also with seemingly irrelevant and remote states.Numerically speaking, the latter (i.e., the non-strategic) constitutes a larger set than the former (i.e., strategic)-possibly in a Pareto distribution of 80% versus 20%-so that one could visualize it in a histogram as a 'long tail'.
Drawing from modern systems theory and its functional analysis, this paper first premised that there is complexity within the diplomatic system, for diplomacy cannot bind all of its internal elements with each other at any given moment.It reduces complexity by disproportionately realizing the power-oriented, high-frequency nodes of inter-state relations.But this approach, in turn, risks neglecting remote polities, and since every polity teems with the potential of massive power forces, the absence of diplomacy in so many inter-state ties increases the risk of unforeseen threats.To hedge against this (perhaps improbable but not impossible) danger, every state's diplomacy generates a long tail of 160 or so states to whom they send the occasional, rare but still essential signal of peace and amity.Thus, the function behind the long tail is to ensure that no state neglects any other state, however, remote or irrelevant they seem.As regards the form, one may distinguish two ideal-typical repertoires of diplomatic practices, namely a 'costly' one reserved for the strategic realm, and a 'cheap' one for the long tail.Examples for the latter include Twiplomacy, state award bestowals, low-level working visits, or other forms of inconspicuous practices that do not demand the attention of high offices or domestic veto players.

Further links to the literature: autopoiesis and English school
All this is not to say that cheap and quick diplomatic events immediately subdue all threats-even 'costly' ones may fail in doing so (Kim 2021).A single Tweet is not constitutive of durable world peace; but it signals a restraint of centralized power sources and offers an occasion for informational exchanges and displays of amity (Prorok and Cil 2021).The signals of peace across the long tail are small nodes to which future initiatives can refer to in long histories of bilateral amities (which can be constructed when required).Later, diplomatic actors can build new peace signals upon prior peace signals, Tweets upon Tweets, gifts upon gifts, agreements upon agreements (Kornprobst 2015).However, trivial they may seem, these signals of reassurances are thus potential enablers of global togetherness, international negotiation and life-enhancing occurrences for world society-even if they do not actualize this possibility, they at least create the generalized conditions for such projects, and thereby foster the autopoiesis of the diplomatic system.
The findings here do not necessarily need to be grounded merely in a modern systems theoretical approach, but they could resonate with other strands of IR as well.Think, for instance, of the English School (ES) of International Relations, according to which an 'international system' (defined as an inter-polity "arena where there was interaction between communities but no shared rules or institutions"; Dunne 2020: 144) transforms into an 'international society' with deeper social bonds and common values (Bull 1977: 13) through thickening interactions, as mediated through technological progress (Buzan and Little 2000).Quantifications of inter-polity ties could offer relevant indicators.While the ES originally stressed the inclusion of formerly fringe entities into the international society's membership (Bull and Watson 1984: 432), recent works have highlighted how new members remain factually excluded (Dunne and Reus-Smit 2017;Keene 2002;Linsenmaier 2018).The long-tailed distribution of diplomatic communication indicates both propositions as well.On the one hand, it may be regarded as a signal of inclusion into society due to low-level interactions with the formerly excluded; on the other hand, it may also be interpreted as quantified tokens of exclusion because they only receive fleeting interactions from the traditional powers.A clearer response could probably be given with robust findings on whether certain groups of states find themselves in the lower end of the tail in disproportionately many cases.Such data would indicate that the current world order indeed places some states into a lower stratum of a global hierarchy (suggesting a 'system' in ES terms) rather than to practically live up to the shared commitment of an equidistant amity with all other sovereigns (which would suggest a 'society').

Diplometrics
This paper limited itself largely to a theoretical level; while the introduction offered numerous illustrations of the long-tailed distribution, they were based only on a convenient sample.For future research, one could envision a metaanalysis of quantitative studies of inter-state ties so as to test the hypothesis of a long-tailed Pareto distribution more systematically across various states and time.Such 'diplometric' studies could investigate patterns of embassies and consulates, illuminate the uses of 'likes' and 'retweets' in digital diplomacy, analyze data of international state award bestowals, look at co-voting behaviors in multilateral settings, inspect structures of official state visits, filter mentions of partner countries in the press releases of Heads of States, scrutinize the budgetary allocation of ministries of foreign affairs, observe patterns of bilateral student exchanges, induce repertoires of practices in diplomatic ethnographies, and so on (Adler-Nissen and Drieschova 2019; Ayhan et al. 2021;Duque 2018;Kuus 2013;Lequesne 2017;Manor and Pamment 2019;Nair 2021;Pacher 2020;Zoodsma and Schaafsma 2022).

Evolutionary perspectives
There are numerous other venues that further research could tread on, such as by considering how the long tail-distribution came about in an evolutionary perspective (Neumann 2021;Youssef 2020).Empirically, the changing costs of diplomatic signals may offer a clue.In premodern societies, the costs of dispatching diplomatic communication were immensely high.Legates risked sacrificing their own life and limb for such missions (Roosen 1980).With technical progress, the costs of signaling became lower while the spatial radius of political danger rose (Deudney 2018).The hitherto obscure threat started to loom ahead, the remoteness moved closer, and polities now sense security issues not only from the immediate neighborhood but also from the 'spooky distance' (Der Derian and Wendt 2020).The necessity to attend to seemingly irrelevant polities attains greater relevance when every state, regardless of its geographical position, signifies a latent enmity.Diplomacy needs tools to do so quickly, and it is perhaps because of this that diplomacy developed a repertoire of quick, cheap, uncomplicated but clear and unambiguously sovereign signals of amity.With the evolutionary development of a greater scope of political power actions came the need for cheaper diplomatic peace tools.

The inflation of peace
This observation leads the focus away from the past history of society toward speculations on how diplomacy may evolve in the future.With society's growing complexity, there may accrue a greater need for practices that are quick, cheap and unambiguously sovereign.However, with more and more peace signals being omitted by foreign ministries to more and more states and to a greater global public (Melissen 2005), a further risk may arise: the risk of inflating peace.The diplomatic system's medium of peace may become so ubiquitous that it loses its credible efficiency among society at large.Once ubiquitous, a diplomatic Tweet or a low-level state visit will lose its condensed meaning of credible peace.The concept of inflation or deflation with regards to a societal medium other than money is a topic that has found nascent attention in modern systems theory (Parsons 1963), but that still awaits an elaboration with regards to international political settings (Baldwin 1971).It could be worthwhile to track the ever cheaper and quicker practices of diplomacy and to analyze to what extent the medium of peace may suffer from inflation.
In a certain sense, the historical rise of multilateralism may be an indicator of this inflation.Negotiating and voting together in international bodies, often many times a day, puts states into indirect amical relations to each other in a tempo so high that their patterns can hardly be monitored anymore.One could unbundle multilateral happenings into one-on-one relations-a trilateral talk could be seen as A enacting bilateral relations with B and C simultaneously (Bicchi and Schade 2022;Haugevik 2022), or Japan's aid-giving behavior via TICAD (Tokyo International Conference on African Development) may be seen as dozens of Japanese bilateral relations with each of the 50 + participating African states-but there might be collective practices of multilateralism that cannot be reduced to bilateral state-to-state interactions anymore (Pauwelyn 2003;Rixen and Rohlfing 2007).In fact, even the occurrence of a TICAD meeting does not mean that Japan treats every single partner state equally.There are indeed indications that new practices of digital multilateralism deepen existing inequalities (Vadrot and Ruiz Rodríguez 2022).Integrating multilateralism, supranationalism and other kinds of collective inter-state fora into the present paper's theory remains a desideratum for further research.
Whatever the outcome of such theoretical efforts, the circulation of peace around the globe even among improbable inter-state ties cannot be regarded but as an evolutionary achievement of the system of diplomacy.The long tail does not emit irrelevant noise, but it fulfills a basic function for world society.Whether it does so durably without generating new problems-such as that of inflating peace-is an open question.
Funding Open access funding provided by University of Vienna.

Declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
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Fig. 3
Fig. 3 Countries that received official visits by the Brazilian Head of State.Only every 4th country is labeled in the x-axis

Fig. 4 Fig. 5
Fig. 4 US presidential trips by the country visited.Only every 5th country is labeled in the x-axis for better readability

Fig. 6 Fig. 7
Fig. 6 Countries mentioned in the article titles at the Polish website of the Ministry of Foreign Affairs.Only every 4th country is labeled in the x-axis Bose 2022; or biological facts, see Denton 2019; or economic resources, see Farrell and Newman 2019; or water, see Grech-Madin 2021; or outer space, see Johnson-Freese and Burbach 2019; or artificial intelligence, see Qiao-Franco and Bode 2023; or culture, see Zhurzhenko 2021).Any state can thus unleash for any other state "unconventional security risks stemming from mass migration, terrorism, money laundering and environmental degradation"