STILL

Systems Theory and International Legal Legitimacy
Systems theory, Natural law, and International Constitutionalism; an unlikely triangulation
By Zorba J Parer, November 2011
Submitted as satisfaction for MIL Independent Research; Microsoft™ Word Count 9,206
The legitimacy of international law, indeed the very existence of binding international laws,
is a recurring theme in international relations, and in domestic discussions of international
obligations with regard to domestic executive actions, and legislative behaviour.
This question is at the forefront of international debate due to the ever changing global
political situation, and recent actions by coalition forces, in particular as contra points; the
US led invasion of Iraq; and the NATO intervention in Kosovo. Other emerging incidents in
the Middle East and northern Africa involving domestic uprisings and the various levels and
types of international intervention also highlight the question of international law and the
legitimacy of international state and non-state actions.
Natural laws have been known by other names, but exist perpetually, due to the
fundamental nature of the universe. Whether these are given by God, or are an emergent
property of hydrogen after 14 billion years, does not detract from the fact that they exist.
When designing an airplane the engineer does not defy gravity; rather by understanding its
properties we use one natural law to overcome the other, in order to change the state of
the aircraft to one which appears to defy a natural law. It is only with the effects of gravity
that an aircraft can fly, it is indeed the careful observation of the way things are, and how
they interact, that gives us all the marvellous gadgets we have in our lives, here at the
dawn of the 21st
century.
This research examines natural law, algorithmic game theory, graph theory, network
theory, and systems theory, in order to seek tools for understanding the current state of the
international legal system.

This paper seeks to bring together a broad range of ideas to explore a single notion;
can the international state system be mathematically modelled, and the role of
international law observed in these models. These ideas are drawn out from
readings in international relations, law, philosophy, mathematics, science, game
theory, graph theory, and network theory. In a world of shifting sources of
authority1
, it is critical to ensure that those authorities are grounded in a reality
which is harmonious with humanity, lest the system become oppressive rather than
liberating.
1
“Shifting Boundaries : the Authority of International Law 1”, Mayo Moran, New Perspectives on the
Divide between National and International Law, Edited by Janne E. Nijman and Andre Nollkaemper,
Oxford Scholarship Online, January 2009.

This essay was seeded by Posner and Goldsmith2
; who suggested that customary
international law is simply game theory, where States’ interests determine the law.
Game theory has established a significant corpus of methods and tools3
which were
initially applied to economic models by the early developers. Legal scholarship on
game theory is primarily focused on tactical implementation in courts4
, disputes5
,
contract formulation6
, or limited decision support analysis, where there is a small
step from the world of business and economics.
2
“The Limits of International Law”; Chapter 1, A Theory of Customary International Law, Posner and
Goldsmith.
3
‘Algorithmic Game Theory’ Edited by Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V.
Vazirani,
4
‘Settlement Negotiations with Two Sided Asymmetric Information: Model Duality, Information
Distribution, and Efficiency’, Daughety, Andrew F. and Reinganum, Jennifer F. (1994), International
Review of Law and Economics, 283-298.
5
‘Settlement Bargaining and the Design of Damage Awards’, Spier, Kathryn E. (1994a), Journal of
Law, Economics, and Organization, 84-95.
6
‘Incomplete Contracts and Signalling’, Spier, Kathryn E. (1992a), Rand Journal of Economics,
432-443. ‘The Dynamics of Pretrial Negotiation’, Spier, Kathryn E. (1992b), Review of
Economic Studies, 93-108.

The Posner and Goldsmiths conclusion that customary international law is simply
game theory falls short of understanding the underpinning metaphysics,
philosophy, and theory at work in game theory and human society, and thus draws
them to the false conclusion that customary international law is not law at all. This
conclusion appears to be based on the fundamental notion of international law as a
positivist act, states giving tacit consent rather than states recognising the intrinsic
nature of the system and consenting from necessity. Tacit consent is usually written
in blood; the centuries of theory proceeding world war two failed to convince and
bind the League of Nations on the principle of a prohibition on aggression. It was
only after witnessing the deaths of over 50 million people in an industrialised total
war scenario, that the States finally gave tacit consent to sacrificing some state
authority in an attempt to prevent a repeat of the wholesale slaughter of humans.
This essay begins with an examination of metaphysics and philosophical basis of
modern international relations7
. Scientific Realism is examined here as an
underpinning metaphysical and philosophical basis providing a background of
concepts which can be drawn upon to interpret and defend definitions of natural
law. This approach also allows us to move away from debates on whether natural
law is a religious/moral dictate, or a sociological construct, and merely examines the
“is”.
7
“Scientific Realism and International Relations”; Edited by Jonathan Joseph and Colin Wright

Rational Choice8
provides a framework within which to construct why people choose
to behave, whether as state agents, or as individuals within any given society.
Understanding the basic variables for why people choose to act, provides a
theoretical basis for constructing equations which can provide a positive theory
which can be empirically tested.
Once the theoretical basis of this approach is established, I move onto examining
International Relations concepts of Anarchy and the relationship to International
Legal scholarship notions of Natural law. Anarchy is proclaimed by many
international relations theorists to be the organising principle of the current
international system9
. These theorists use almost the exact words in defining
Anarchy as Hobbes did in defining Natural law. The ancient and enlightenment
philosophers approached law out of anarchy or as they called it natural law, and
postulated that the metaphysics, physics, and biological imperatives, of reality itself
dictated certain universal, immortal, and irrefutable laws for humans, above the
laws of man.
8
“Rational Choice Theory and International Law: Insights and limitations.” Robert O. Keohane, The
Journal of Legal Studies, Vol 31, No.S1
9
“Anarchic orders and balances of power” by Kenneth Waltz, American Foreign Policy, Theoretical
Essays Fifth Edition, 2005.

Some of the enlightenment philosophers who held this view included Leibniz and
Newtown, who are more famously known as Natural Philosophers, or in modern
terms, Scientists. These two brilliant polymaths independently discovered and
established the mathematics of calculus. Calculus is the mathematics of things
which change with relationship to other variables. Calculus encompasses partial
differential equations, which model systems with many different variables, and form
the basis of many algorithmic game theory methods. Partial differential equations
became part of the modern zeitgeist with the emergence of Chaos Theory. Partial
differential equations are shown to offer us the tools to model the international
system, and Chaos Theory provides us the methods for predicting the future
outcomes of the system, within certain prediction horizons.
International relations and international legal scholars have increasingly looked at
what game theory can tell us about how states behave. Beginning at the top and
performing reductionist analysis on state decisions, and approaching from the
bottom and performing constructionist analysis based on sociological analysis of
individuals, and group behaviours. Either way it becomes clear that the future of
international law is domestic10
, i.e. individuals drive the body politic interests of any
given Nation, and are the ultimate subjects of any international laws.
The birth of Algorithmic Game Theory came from the work of economists who
applied the third law of thermodynamics to economic models, and were also later
applied to evolutionary modelling. What does thermodynamics have to do with
people, nations, or state interactions?
10
“The Future of International Law is Domestic” by Anne-Marie Slaughter and William Burke-White
from New Perspectives on the Divide between International and National Law, Edited by Andre
Nolkaemper and Janne Nijman (2007)

It is because a seemingly impossible number of interactions can have a statistically
predictable outcome, if the constituents can be categorised (a taxonomy of States)
and their behaviours modelled. In thermodynamics these equations relate to atomic
and molecular interactions seeking to exchange and consume free energy, in
evolution it is how plants and animals interact seeking to use free energy, and in
economics and international relations it is how people and institutions seek to
consume free energy. Morals underpin human behaviour, globally there are many
moral perspectives which are forever changing, and the ultimate teleology of any
human social group is survival. Ultimately survival in the animal world is defined
evolutionarily by a species ability to obtain energy.
The mathematics of all these systems is governed by partial differential equations
which result in wildly different predictions based on the smallest changes to the
historical conditions of the equation, even though they are absolutely deterministic.
Thus while it is possible to make predictable outcomes on equilibrium and
optimisation within closed systems (a beaker of chemicals, an island of animals, a
village market), large open systems prove much less predictable (global weather
patterns, flame propagation in a bush fire, share market prices, human society in 20
years), and many of these systems were thought to be mathematically impossible to
predict numerically due to the impossibility of measuring and tracking every input
condition. With the advent of Chaos Theory, hope was born for predictable
outcomes for such systems. By calculating every possible input variable and plotting
the outcomes in a multidimensional space, we begin to see patterns emerge, and
once chaotic, seemingly random, systems begin to reveal deep sources of
information.

METAPHYSICAL AND PHILOSOPHICAL BASIS OF
RATIONAL, SCIENTIFIC, INTERNATIONAL LAW
The classic philosophers of law (Cicero, Aristotle, Augustine, et alia) through to the
Enlightenment and Renaissance scholars (Aquinas, Grotius, Spinoza, Hobbes, Kant,
Wolff, Vattel, et alia) have all at least attempted to clearly define their metaphysical
position. These positions then informed the basic assumptions they used to develop
their philosophies.
Since Hume threw the “naturalistic fallacy” spanner into the works, and produced
his remoulded realism model11
, the importance of maintaining a metaphysical
foundation has waned. However I will start at the beginning in order to obtain a
thorough understanding of the subject.
The very Victorian Sir Traverse Twiss considered international law to be an obvious
merging of natural and positive legal schools, under the banner of a scientific
approach to international law12
. It is the metaphysics of science that guides the
modern concepts of truth, and thus in any current discussion of laws or policy in
government our rational actions are guided by scientific reasoning.
11
“British International thinkers from Hobbes to Namier” edited by Ian Hall and Lisa Hall.
12
“Two introductory lectures on the science of international law”, Twiss, Travers, Sir, London 1856,
British International Law

Metaphysics is, by one definition, the study of being qua being, and in that sense
here it is the study of the essence of international law, or the essential underpinning
immutable forms of international law. Metaphysics provides a canvas upon which to
discuss the epistemology (how we know what we know) of international law. By
examining the basics, we move beyond semantic discussion of positivism and
naturalism, law and rule, and we can see that the major themes running throughout
the legal scholarship derive quintessentially from their metaphysical assumptions.
Whether this is Kant’s Perpetual Peace, tied to his metaphysical “Transcendental
Idealism” or Hobbes and his version of Realism, we gain a clearer understand there
thoughts and conclusions, if we understand their metaphysical positions.
This essay examines international law scientifically, which is to say, from position
that it is an a priori condition which becomes evident with the interaction of n>1
nations of people. International law exists, whether there are many or no nations of
people. However it remains unseen until such time that two or more groups of
people, having different governing social arrangements13
, interact, only then does
the law becomes observable. This then ascribes them a fundamental potency14
which becomes manifest when the n>1 nations interact.
13
“Between Authority and Interpretation – On the Theory of Law and Practical Reason” By Joseph
Raz, Oxford Scholarship Online: May 2009, Chapter 4
14
“Nature’s metaphysics – Laws and Properties” by Alexander Bird; Oxford Scholarship Online:
September 2007.

Metaphysically these laws exist without people or nations or any material form, they
simply have no effect. Similarly the laws which govern the interaction of oxygen and
hydrogen exist; however in a closed system without oxygen and hydrogen they have
no effect. Adding those elements to the closed system enacts the laws of chemistry
which results in a reaction between the two elements, giving off energy, and
resulting in equilibrium with some amount of water, and some excess of either
hydrogen or oxygen.
Claiming that international law is an a priori condition does not give it any claim to a
beneficial teleological purpose. The research and discussion here centres around
what is; in a form that ought to provide guidance to international legal thinking.
Natural international law from this perspective simply is; what we ought to do
requires us to make choices with regard to that law.
Without a corpus, (a population within which to function) law can still be said to
exist in the abstract (Platonic Form) sense, it simply has no visible effect on
existence15
. The positioning of law in this metaphysical construct rather than any
other varied position16
, allows us to distinguish between ‘Good’ and ‘Bad’
international law; law which is per se authoritative and legitimate. By combining a
constructive approach to defining international legal system within an deductive
mathematical framework, and using a statistical mode of thinking to examine
customary international law, we can seek evidence of natural international laws.
15
“Between Authority and Interpretation – On the Theory of Law and Practical Reason” By Joseph Raz,
Oxford Scholarship Online: May 2009
16
See for example “The Method is the Message” with Steven R. Ratner, 93 American Journal of
International Law 410 (1999), The American Society of International Law

Philosophy
The philosophy of science is firmly entrenched in modernity which on the
international plane has led to the application of scientific realism17
. The philosophy
of science is fundamentally inductive, and so too is the philosophy of international
law. Scientific realism requires inductive reasoning, the repeatable, evidence to
validate perceptions and assertions. The truth of a law of science is a combination of
the inductive (veritatem per demonstrationem18
) demonstrations of science,
combined with the deductive logical reasoning (verum per deductionem19
) of
mathematics. When these two elements are combined correctly, we find
predictable, repeatable, patterns in the universe; natural laws.
Realpolitik offers the perspective that international patterns emerge with the State
interest as the motive force behind action, the policy adopted by the State is based
on the necessity of the situation at hand arising from unregulated interactions. The
test of success in Realpolitik, of a policy is whether it preserves and strengthens the
State.
Taken in the literal sense, Realpolitik becomes fascism; the individual exists to
preserve and support the state. The outcome of fascism has been innumerable
shown to undermine the state, and lead to state extinction.
17
See “Scientific Realism and International Relations” Edited by Jonathan Joseph and Colin Wright, for
a treatment on SR and IR.
18
Latin always sounds more convincing!
19
Ibid.

Born out of Dickensonian experiences, Bentham and Hume expounded the notion
of utility and human happiness as the proper goal for rulers to focus upon delivering
to their people20
. This has been largely successful, although it was tempered in
favour of happiness for the aristocracy and socially enfranchised.
Morality and Legitimacy
Finnis provides three basic principles of morality which he holds to be irreducible, to
drive a legal structure21
, paraphrased here;
(i) Integral Human Fulfilment (Do Good, Love thy neighbour, a whole of
ends in systematic conjunction, greatest good/happiness of the greatest
number)
(ii) Protection of Human Good (Do no Evil, consequentialism,
proportionalist, utilitarian, aggregated moral theory)
(iii) Equality in Treatment (Reciprocity, do unto others as you would have
them do unto you)
20
“The Benthamite Constitution – Decline and Fall?” by Neil MacCormick, Quenstioning Sovereignty –
Law, State, and Nation in the European Commonwealth, Oxford Scholarship Online: January 2010.
21
“Natural law: The Classical Tradition” By John Finnis, The Oxford Handbook of Jurisprudence and
Philosophy of Law, 2002

This moral structure clearly places the individual as the focus of law, and what ‘good’
laws should strive to do. This approach requires a commitment in belief to these
morals through abduction; the observation of truth as a pattern amongst the data,
too complex for the test of constructive deduction, and to obfuscated for repeatable
induction. Abduction as a method for humans to make rapid decisions is of clear
benefit, however if valid they should hold up under the pain staking scrutiny of
deductive (albeit bounded) proofs, against which to compare the inductive (albeit
limited) evidence.
Keohane on the other hand provides the following Six Specific Criteria (again
requiring a leap of abduction on the basis of liberal democracies supremacy) for
legitimacy of global governance22
;
(i) Minimal Moral Acceptability (Respect for human rights; at least physical
security, liberty, subsistence);
(ii) Inclusiveness (Institutions open to all members, although not equality
amongst members);
(iii) Epistemic Quality (Institutional integrity and transparency)
(iv) Accountability (Three elements (1) Standards of measure (2) Provision of
information to compliance agents (3) Compliance agents ability to
impose sanctions)
(v) Compatible with democratic governments (Global rules must not
constrain constituent populations from choosing their own path)
22
“Global Governance and Legitimacy” by Robert O. Keohane (2011), Review of International Political
Economy, 18:1, 99-109.

(vi) Comparative Benefit (Global institution must be better than no
institution, or alternative local arrangements)
From this it is taken that legitimacy of an international organ, in the liberal
democratic sense, is that it receives the popular support of the body politic. It does
not however provide a basis of legitimacy in the sense of whether the governance
structure provides a positive outcome for the body politic. The liberal democratic
test of a successful policy is the preservation and strengthening of the individuals
within a state, which against the needs of maintaining the state structure may lead
to a failed or weakened state; see Greece 2011 and maybe the USA 2009 credit
crises. Therefore a global governance structure by these terms, may be legitimate in
a popular support manifesto sense, whilst being ineffective, and ultimately lead to
the inability to support individual citizen interests, therefore failing in its ultimate
teleology.
I suggest that the inductive test for success is that the state continues with the
existing identity; that the executive is not overthrown (revolution by spin, vote, or
gun), and the state institutions remain intact. This definition then presupposes that
the state continues to be supported by the populous, and remains sufficiently
supportive of the populous to maintain their support.
We have host of current examples of states failing, either through financial
mismanagement, Greece, or through popular uprising and revolution, Libya, Egypt,
Syria, et alia, or through breakaway state formation, Slovenia, Croatia, et alia. We
also have many contemporary examples of failed states which have not been able to
re-establish, Somalia, Zimbabwe, and the Congo.

There are also plenty of examples today of weakening states, USA, Russia, and
strengthening states, China, Brazil, India. Also many states emerging from total
institutional annihilation, beginning their journey from day zero; Germany and
Japan (post WWII), Cambodia, Vietnam, Burma (Post cold war), East Timor, Iraq,
and hopefully one day Afghanistan (Global consolidation war), Egypt, Libya, Syria
(Arab Spring).
Are there structural international legal elements which are causing, or contributing
to, the changing condition of these states? Are these simply the results of poor
domestic policy, international relations, egoistic state behaviour, or individual
antagonists? Are they temporary weaknesses, which are precursors to a
strengthening, based on a necessary cost of fundamental restructuring?
Natural law
Finnis provides this taxonomy of classic natural law forms of order23
;
(i) orders which are what they are, independently of our thinking, that is,
nature, laws of nature, and correspondingly the natural sciences and
metaphysics;
(ii) the order which we can bring into our thinking, and correspondingly the
standards and discipline of logic;
(iii) the order which we can bring into our deliberating, choosing, and acting
in the open horizon of our whole life, and correspondingly the standards
of morality and the reflective discipline of ethics;
23
“Natural law: The Classical Tradition” By John Finnis, The Oxford Handbook of Jurisprudence and
Philosophy of Law, 2002

(iv) the order which we can bring into matter (including our own bodies)
subject to our power, as means to relatively specific purposes, and
correspondingly the countless techniques, crafts, and technologies.
This taxonomy is useful in understanding the central theme of this particular essay;
the international laws of the first order as described above. The international laws
which stand immutable and unchanging, which if you choose to stand against them
will destroy you, whether you believe in them or not. The other elements go
towards the success of any particular society in recognising the immutable, and
aligning themselves into harmony with the natural order, the Dao24
.
The first form of the above taxonomy reflected in the ‘modern’ law of nations,
natural law thinking as seen in the work of Christian Wolff25
:
§3. Of what sort the law of nations is originally
Since nations are regarded as individual persons living in a state of nature, moreover, as men
in a state of nature use nothing except natural law, nations also originally used none other
than natural law; therefore the law of nations is originally nothing except the law of nature
applied to nations
§4. Definition of the necessary law of nations
We call that the necessary law of nations which consists in the law of nature applied to
nations. It is even called by Grotius and his successors, the internal law of nations, since it
evidently binds nations in conscience. It is likewise called by some the natural law of nations.
§5. Of the immutability of this law
Since the necessary law of nations consists in the law of nature applied to nations,
furthermore as the law of nature is immutable, the necessary law of nations also is
absolutely immutable.
24
“Law and Morality in Ancient China: the silk manuscripts of Huang-Lao” By Randell P. Peerenboom
25
“Jus Gentium Methodo Scientifica Pertractatum” by Christian Wolff, Translated by Joseph H. Drake
Oxford: at the Clarendon Press, 1934

The role of international law within the international relations realism framework
was largely claimed to be non-existent26
(in the Positive sense of law authoritatively
issued through a governing executive) by the international relations theorists27
.
Against the backdrop of the classical definitions above, based on Grotian definitions
of natural law, and thence the Law of Nations, the international relations scholars
seem like they were missing the point. While it is true that a power can set out any
form of rules within their power to enforce, the cost of enforcement in the face of
underlying prevailing natural orders will imperil the continuance of the nation28
.
Grotius defined two methods for divining international law, which have been used
by international legal scholars since his time; one a constructionist approach,
ascertaining the law by constructing rational logic from the physio-psycho-
sociological attributes of humans29
; the other a reductionist approach by observing
the normative, accepted, behaviours of sophisticated socio-political groups30
. Both
of these approaches are fundamentally inductive, requiring the study of humans as
they are, or observing the behaviour of states. These Grotian definitions mark the
departure of international legal philosophy from notions of God given rights of the
Feudal nobility, and the emergence of the science of international law viewing the
states power flowing from the will and capabilities of the subjects.
26
“International Law and International Relations Theory: A New Generation of Interdisciplinary
Scholarship” by Anne-Marie Slaughter; Andrew S. Tulumello; Stephan Wood. The American Journal of
International Law, Vol. 92, No.3. (Jul., 1998), pp.367-397.
27
Ibid
28
“The Economics of Lawmaking” by Francesco Parisi and Vincy Fon, Oxford Scholarship Online:
January 2009.
29
“arguing from the nature of and circumstances of mankind”
30
“by observing what is generally approved by all nations, at least by all civilised nations.”

In his two introductory lectures on the science of international law (1856) Sir Travers
Twiss points31
to the international legal taxonomy of Dr Richard Zouch; natural law
being founded on the tacit consent of nations32
, and positive law being that which is
based on the express agreement of nations33
. This clearly connects the 16th
century
Oxford professor’s definition of natural law to the modern customary international
law definition.
Wolff34
provides the following distinction between the species of international law:
§ 22. Voluntary law of nations35
§ 23. Stipulative law of nations36
§ 24. Customary law of nations37
§ 25. Positive law of nations38
31
“Two introductory lectures on the science of international law”, Twiss, Travers, Sir, London 1856,
British International Law, page 30.
32
Commonly referred to in modern terms as Customary International Law.
33
Also used in this way today, with the additional note that some positive law, when widely endorsed,
may be seen to have achieved a status of customary international law.
34
“Jus Gentium Methodo Scientifica Pertractatum” by Christian Wolff, Translated by Joseph H. Drake
Oxford: at the Clarendon Press, 1934
35
“With Grotius we speak of the voluntary law of nations, which is derived from the concept of the
supreme state, therefore it is considered to have been laid down by its fictitious ruler and so to have
proceeded from the will of nations. The voluntary law of nations is therefore equivalent to the civil
law, consequently it is derived in the same manner from the necessary law of nations, as we have
shown that the civil law must be derived from the natural law in the fifth chapter of the eighth part of'
The Law of Nature'.”
36
“There is a stipulative law of nations, which arises from stipulations entered into between different
nations. Since stipulations are entered into between two or more nations, as is plain from the meaning
of 'pact', since moreover no one can bind another to himself beyond his consent, therefore much less
contrary to his consent, nor acquire from him a right which he does not wish to transfer to him;
stipulations therefore bind only the nations between whom they are made. Therefore the law of
nations, which -arises from stipulations, or the stipulative, is not universal but particular.”
37
“The customary law of nations is so called, because it has been brought in by long usage and
observed as law. It is also frequently called simply custom, in the native idiom das Herkommen
[usage]. Since certain nations use it one with the other, the customary law of nations rests upon the
tacit consent of the nations, or, if you prefer, upon a tacit stipulation, and it is evident that it is not
universal, but a particular law, just as was the stipulative law”
38
“That is called the positive law of nations which takes its origin from the will of nations. Therefore
since it is plainly evident that the voluntary, the stipulative, and the customary law of nations take
their origin from the will of nations, all that law is the positive law of nations.
And since furthermore it is plain that the voluntary law of nations rests on the presumed consent of
nations, the stipulative upon the express consent, the customary upon the tacit consent, since

Vattell’s work39
on the subject (whilst somewhat derivative, he has independently
considered the issue) provides some further clarification on the “Necessary” law of
nations:
Since, therefore, the necessary Law of Nations consists in applying the natural law to States,
and since the natural law is not subject to change, being founded on the nature of things and
particularly upon the nature of man, it follows that the necessary Law of Nations is not
subject to change.
Since this law is not subject to change and the obligations which it imposes are necessary and
indispensable, Nations can not alter it by agreement, nor individually or mutually release
themselves from it. It is by the application of this principle that a distinction can be made
between lawful and unlawful treaties or conventions and between customs which are innocent
and reasonable and those which are unjust and deserving of condemnation.
Things which are just in themselves and permitted by the necessary Law of Nations may form
the subject of an agreement by Nations or may be given sacredness and force through practice
and custom. Indifferent affairs may be settled either by treaty, if Nations so please, or by the
introduction of some suitable custom or usage. But all treaties and customs contrary to the
dictates of the necessary Law of Nations are unlawful.
The framework espoused by Waltz40
fundamentally incorporates the concept of
natural law, through his firm positioning of Anarchy as the organising principle. One
of the difficulties is in the common definitions of ‘Law’ as a positive, authoritative,
act, by a legitimate law making body. Without rulers, parliaments, or other law
making bodies; law still exists.
moreover in no other way is it conceived that a certain law can spring from the will of nations, the
positive law of nations is either voluntary or stipulative or customary.”
39
The Law of Nations or the Principles of Natural Law” Emannuel de Vattel, Translated by Charles G.
Fenwick 1916
40
“Anarchich Orders and Balances of Power” by Dr Kenneth Waltz; pp.60-83, American Foreign Policy,
Theoretical Essays, fifth edition, 2005.

Waltz provides a sound working definition of ‘Law’ in his introductory text41
; “Laws
establish relations between variables, variables being concepts that can take
different values”. Organising principles in this context and laws as rules between
variables suggests that the rules are mutable, whereas the organising principle is
not. The rules in anarchy are the natural laws42
, those laws which are immutable.
The states which follow the immutable laws, within a sufficient degree of tolerance,
survive. Those which flout them, diminish. These ideas suggest a self enforcing
mechanism, with origins in human nature.
Where economics have long studied the effects of the micro on the macro, Waltz
suggests that even if a macro-political theory could be constructed, nations would
not act on them as they are the only actors capable of affecting the global macro-
political situation43
, and effects would still require reversion to the micro-political
order. While dismissive of a mathematical solution to the macro-political system, in
his balance of power theory he offers several useful lemas.
In taking the first of the Grotian approaches following von Wolff, Vattel and Kant,
down the constructivist approach, beginning with man in nature. Fundamentally we
are governed by our nature and our choices. From first principles we examine a
person alone in the wild. The first choice the person makes is to survive or die, to die
may seem easy but still the person has a set of rules they will need to follow in order
41
“Theory of International Relations” by Kenneth Neal Waltz, Chapter 1, “Laws and Theories”,
published 1979
42
Laws which govern the interactions between the variables.
43

to achieve this outcome. So too in nations; the body politic in choosing to work
together, self constitute44
.
The Balance of Power theory as defined by Waltz has two underlying notions; States
choose to exist; Anarchy organises their actions. Beyond this initiating principle,
states may choose to collaborate, and in doing so they subject themselves to
additional natural laws. So from this approach we see that the authority of natural
law is driven from the state choice, and back to the ultimate authority of dissolution
as driven by the individuals within the constituent state; for example the citizens
involved in the overthrow of states during the Arab Spring.
In taking the second Grotian approach, we would ask what actions have states taken
which were successful, and why? This reductionist approach is founded in the
inductive method of demonstrated success or failure. This is taken as a fundamental
principle in many approaches to espousing liberal democratic, and other socio-
political theories. The strength of the approach is that clear examples of successful
international legal tenants can be relied on, the weakness is that the difference
between a successful socio-political model (even within the same family of
structures such as democracies, state controlled, republics, monarchies) and a failed
one, are subtle and the critical fault line lost in the depths of the details of cultural
tendencies, geographic necessities, external influences, and other formative socio-
political variability.
44
“Self-Constitution – Agency, Identity, and Integrity” by Christine M. Korsgaard, Oxford Scholarship
Online: September 2009.

Ultimately for international institutions, organs, and laws, the legislative
acknowledgement and support, by state sponsors, is secondary to their primary
existence. Most, if not all, successful international institutions, regimes, and
frameworks constituted themselves out of necessity through a variety of
international actors, prior to any state acknowledging or creating a congress,
conference, regime, or other institutional embodiment.
In this very brief dip into philosophy, I have taken a direction of analysis to
international law requiring an inductive approach based on examining past
behaviours of states to find the behaviours which are successful, and those which
end with state failure, without a resort to leaps of moral faith. Our global
community necessarily bridges significant differences in fundamental moral and
ethical assertions requiring an objective approach to the topic.
To develop true ‘philosophy of science’ laws, they must be combined with deductive
methods of mathematics, and so requires also a commitment to the philosophy of
mathematics. All physical behaviours can be observed and reduced to mathematical
formulae; using mathematical methods these can be manipulated to provide useful
information about the behaviour of the system. Mathematics can be used to find
optimal solutions, which can be related back to the physical system.

The Beginning
Nations can choose to survive, and they choose to interact with other nations;
history shows that nations which interact with each other are more successful (as
measured in the Realpolitik sense) as they gain access to resources and capabilities
unavailable in their own domains. This comes at some cost of national identity and
ethnic homogeneity45
, in some cases (colonial interactions) this means the total
subsuming of the nation under a much more powerful nation, with the subsumed
culture changing the social and cultural fabric of the conqueror.
In other cases this has resulted in some agents (tribes, individuals, corporations, etc)
within the nation benefiting, at the expense of others. Once nations learn how to
effectively benefit from the transactions between nations, they have tended
towards empires with external nations forced to inclusion and benefit, or seeking
inclusion and benefit. Although eventually all empires to date have contracted as
the various elements seek to control the central power structure, veiled as making
remedy on their claim as conquered, their moral superiority, outright coups by
force, or other manifestations of revolution46
.
45
The USA occupation of Germany and Japan, through the personal interactions of soldiers with
citizens, to relationships, both intimate and platonic, which resulted in an increase in German
language, and an adoption of Kaisan management systems in the USA. The conqueror in exposing its
citizenry, absorbs a degree of the conquered.
46
“The Government of Self and Others; Lectures at the College de France” Michael Foucault, edited by
Frederic Gros, English translation published in 2010 by Palgrave Macmillan.

The international legal system is self constituting47
. From this perspective,
International Law does not exist where nations either have no knowledge of the
existence of other nations, other nations do not exist (n = 1), no nations exist (n=0),
or the nations have no ability to interact. Where more than 1 nation exists, and they
have knowledge of another nation, the rules which govern the behaviour between
those two variables begin to act, and the international system self constitutes.
As an aside this leads to a conclusion that if international law were truly monist, it
would not exist. That is to say, if everyone enshrined international law into their
domestic law automatically, then we would be a global nation, and international law
would cease to exist. Waltz asserts48
, this would not eradicate conflict it would
merely change all wars into civil wars. Waltz also predicts49
that a single global
governmental authority solution would not be sufficiently diverse to accommodate
the vast array of cultural, ethnic, and social conditions required to enfranchise all
individuals within the system, leading to increased violence as different factions vied
for control of the centralised authority. This prediction may in fact be playing out in
the form of Islamic transnational terrorism.
Legitimacy, Normative Behaviour, Authority
47
“Self-Constitution – Agency, Identity, and Integrity” by Christine M. Korsgaard, Oxford Scholarship
Online: September 2009.
48
49
Ibid

There are many definitions and theories of legitimacy. In the context of this research
I am looking at the legitimacy of international law. This is the legitimacy of the
previously discussed a priori rules which exist between variables under particular
circumstances. How do we recognise them as legitimate? One of the ways legal
scholars have recognised legitimacy is based on consistent state behaviour. If all
nations which continue to prevail follow a set of rules, then these could be claimed
as legitimate. This falls down when we see revolution leading to an overturn of long
held consistent state behaviour, in favour of new sets of consistent state behaviour.
For the purposes of discussing the legitimacy of international law I will take it to
mean that people all agree that the laws are binding, and if they disagree, the law
prevails irrespective of their belief. This high threshold is set to examine there exist
any international laws which can be demonstrably binding. From these we can then
examine what other rules ought to flow out of the basic principles.
In keeping with the philosophy of science, a law is only legitimate if it coincides with
reality. As an absurd example; a law which prohibits people from obeying gravity,
while authoritative (penalties for all), has no legitimacy. As a less absurd example; a
speed limit of 100 around a corner which can only be taken by a sports car at 35, is
excessive. That is to say it permits a speed which will ultimately lead to tragedy, and
a per se penalty not only for the individual injury, but also to society in cleanup
costs. In the other extreme a law which unreasonably prohibits the individual from
achieving reasonable ends is also not legitimate; a speed limit of 2 on a perfectly
straight road, with no obstacles or traffic.

A legitimate law in this sense is a fountain of wisdom from which the unfamiliar
stranger may drink and know they will be safely slaked of thirst. An illegitimate law
is one born from excess, restriction, or discord.
A legitimate law must also be coherent, and internally defensible. I will use here a
clear definition from Nomics50
.
Nomic Preservation (NP) … m is a law if and only if m would still have held under any
counterfactual (or subjunctive) supposition p that is logically consistent with all of
the laws (taken together).
NP … m is a law if and only if in any context , p-> m holds for any p that is logically consistent
with all of the n’s (taken together) where it is a law that n (that is to say, for any p that is
logically consistent with the first-order laws).
In the law against gravity example, it is not coherent with the nature of the system.
All humans live on earth, gravity applies everywhere on earth, all legitimate laws
accept that the law of gravity is a necessary law with supreme jurisdiction not
subject to negotiation.
Customary law forms through spontaneous adherence by members of the
community51
. So it is with customary international law; sometimes these customs
emerge slowly, and others emerge rapidly after dramatic global shocks.
Customary international law, in this context changes with the circumstances of the
environment, and the capabilities of the state members. As technology advances,
new challenges are presented which require the formation or adaptation of
customs. So how can it be considered immutable? In this sense the natural law is a
50
“Laws and Lawmakers Science, Metaphysics, and the Laws of Nature” Marc Lange, Oxford
Scholarship Online; September 2009.
51
“The Economics of Lawmaking” by Francesco Parisi and Vincy Fon, Oxford Online, January 2009.

maze where the hedges change over time; customary international law is the map
which must align itself to the changed map, if it is to remain useful.
The spontaneous selection of strategies demonstrated by long usage of agreed
principles in international law, suggests that these laws follow the natural (most
efficient) course of action. The river does not flow uphill. By examining customary
laws which have long been held as valid, it ought to be possible to deduce the
underlying mathematical principles in play on the international plane.
Constitutionalism
The above discussion indicates that International Law self constitutes under these
conditions:
A – the existence of nations52
; people constituted under a set of homogeneous
governing laws (rules, norms, or otherwise); i.e. a group of people harmonise and
choose to become a coherent nation.
AND
B – The existence of n>1 nations
AND
C – The interaction of n>1 nations
If we take it for given that the world we live in now (2011) is made up of many states,
with executive powers granted through some mechanism to a central state
authority; then what power should they give to a central authority? What head of
power should reside in the central global government, such that the states have
sufficient power without needing to wrest it from the central authority? Indeed is
52
I use the term nation rather than state as many non-state actors which meet the definition of
nation, but are not, or can not be, a recognised state need to be considered in the analysis of the
global governance structure. These nations have internal rules governing behaviour and come in
many forms; religious, ideological, and commercial.

the current trend toward conglomeration a stable configuration for large groups of
humans?
Constitutionalism as a project can be seem as the study and analysis of fundamental
norms, the type of actors, and the institutions and procedures through which legal
and political decisions are made53
. So here I will approach the constitutionalism
project, via algorithmic methods grounded in an inductive/deductive philosophy of
science/mathematics, based on a concept of legitimacy grounded in coherent and
consistent reasoning, with the ultimate authority the individual’s choice in
participation.
Game Theory and AGT
Modern game theory was the brain child of John Von Neumann, in his examination
of zero-sum games and the non-existence of blended-strategy equilibria. This initial
proof rapidly expanded into a wide range of primarily economic models of expected
utility and decision making analysis. It has been extensively applied in variety of
fields, and importantly for this essay; international relations and biology.
53
“Global constitutionalism: Mapping an Emerging Field” Antje Wiener, self published background for
conference, Constitutionalism in a New Key? Cosmopolitan, Pluralist and Public Reason-Oriented
Berlin, Jan 2011

The application of game theory to international relations has varied in its
application; indeed where it has been applied, the scope tends to be limited and
does not consider all the complexities of the open form extensive nature of the
international system or the variations in payoff ratios54
. The typical approach is to
use the Prisoners Dilemma, or other relatively simple game model to extrapolate
conclusions in limited circumstances with regard to international legal or
international relations cases, based on analogies. These simple form games do not
provide sufficient variables to accurately capture the complexity of options open to
the various state and non-state actors, and tend to be used as supporting rhetoric.
Others have taken the approach that assumes the validity of customary
international law, and examined the conditions which make it possible55
. The second
approach used in examining lex mercatoria posits the following game rule conditions
necessary for the formation of lex mercatoria [paraphrased]:
(i) Voluntary reciprocal duty (Players choose to participate with each other)
(ii) Reciprocity must be equitable (Payoff ratios are equivalent)
(iii) Ongoing relationship (Multi-shot game)
54
See for example “The Economics of Lawmaking” by Francesco Parisi and Vincy Fon, Oxford Online,
January 2009, “The Limits of International Law; Chapter 1, A Theory of Customary International Law”,
Posner and Goldsmith.
55
“Customary Law as a Social Contract: International Commercial Law” By Bruce Benson,
Constitutional Political Economy, Vol. 3, No. 1, 1992.

In a multi-shot game the agents participating learn from the previous games.
Reputation of past choices is retained, such that a consistent inequitable payoff will
result in the disadvantaged agent disengaging, trading inequitably, or following
some other non-optimal strategy. The technological and sociological conditions of
various nations gave rise to the international merchant, which constituted the
international trade cosmopolis. Unconstrained by formal positive laws, or external
enforcement mechanisms, the successful merchants were those that followed the
natural rules of the game. These rules were then, over time, codified into the lex
mercatoria.
One form of evolutionary game theory is the application of game theory in the
study of animal populations. Success and failure depends on the energy available to
different species dependent on their unique capabilities derived from random
mutations of their genome. These methods can be recast to look at any system
which can be seen as having multiple species (entities with unique inherent
capabilities), interacting in the same system (closed or open, but necessarily
connecting the species), over a period of time. It is a fairly small leap to see the
international system of states in this light.

The application of game theory, and evolutionary game theory, has met with some
success, but has so far failed to provide a set of concise tools to explain the
normative behaviours seen on the international plane. The complexity of trades
(economic, reputation, military, et alia) at the international level make defining a
universal utility variable difficult. Additionally, by observing the system from a
particular perspective (defining in the context of socially preconceived variables) we
find ourselves trapped by “Hume’s fallacy” of inferring an ought-statement from a
conjunction of is-statements56
, which in many cases results in a use of game theory
to bolster the foregone position of the writer. One promising theory57
suggests that
Entropy can be used as the utility function, which ‘ought’ to rid us of “Hume’s
fallacy”.
Algorithmic Game Theory (AGT) is a useful tool in examining strategic behaviour by
abstracting rational decisions and deducing the payoffs, which has emerged from
game theory applied to computer networks58
and other systems of greater
complexity. There is a significant body of knowledge on the subject59
which provide
a great number of tools for analysing many different problems. Based on the
previous discussions here, there are a number of AGT methods which appear to be
applicable.
The various types of algorithmic models depend on the system under inquiry. So
what kind of system is the international system?
56
Plato.stanford.edu/entries/game-evolutionary/
57
“Natural Games” By Jani Anttila and Arto Annila, Physics Letters A, Volume 375, Issue 43, p. 3755-
3761, Elsevier, 8 September 2011
58
“An Algorithmic Game Theory Primer” Tim Roughgarden, June 21, 2008
59
“Algotithmic Game Theory” Edited by Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani.

Defining the International System
Classical Natural Law
Let us begin by listing what a set of ‘constructive’ variables might look like using the
classic natural law taxonomy:
(i) orders which are what they are, independently of our thinking, that is,
nature, laws of nature, and correspondingly the natural sciences and
metaphysics;
There are 193 members of the United Nations.
There are 153 members of the World Trade Organisation.
Nations of the world choose to interact with each other. The international system is
“constituted” by a series of interactions on multiple levels, in multiple dimensions,
by a variety of nation types; states, corporations, ideologues, et alia.
(ii) the order which we can bring into our thinking, and correspondingly the
standards and discipline of logic;
The international system orders it’s “Thinking” through treaty making, in
accordance with the standards of the Vienna Convention on treaty interpretation,
and application of rational state behaviour.
Nations have unique socio-political thinking based on historically defined and
evolving standards and discipline of logic. Despite this diversity of national thinking,
the order of thought of states in the international system is based on the rules of
international diplomacy and discourse.

(iii) the order which we can bring into our deliberating, choosing, and acting
in the open horizon of our whole life, and correspondingly the standards
of morality and the reflective discipline of ethics;
The international system order for deliberation, choosing, and acting happens in
many different forums, and is based on a diverse range of morals and ethics. Within
the international system there is a formative notion of common morality around the
idea of jus cogens. However the international system currently recognises that each
state must choose its own path.
Nations have unique standards of morality and ethics which define which treaties,
conventions, congresses, regimes, and institutions where they participate. The
choice nations make is primarily based on the species of nation to which they
belong.
(iv) the order which we can bring into matter (including our own bodies)
subject to our power, as means to relatively specific purposes, and
correspondingly the countless techniques, crafts, and technologies.
The international system functions at this level with little required central influence
required.
Nations have unique natural (mineral and biological) resources allocated by virtue of
their geography. These are the raw, unformed, resources which no man may claim
as the produce of his labour, in the John Locke sense.

Nations have human potential; the potential identified by Rousseau as the core of a
nations being, supreme in sovereignty. While we might say that two individuals are
equal, very few individuals are equally capable. Just as a wheel chair bound Hawkins
is capable of amazing insights, he is not capable of winning an Olympic medal.
Nations have unique human capacities (scientific, technological, craft, art, physical,
et alia) dependent on historically defined, and evolving education and potency
maintenance standards. What a nation makes of its human potential.
The international system itself is in a physical sense closed. It currently cannot
obtain physical resources from outside the earth, although it potentially could.
However it is open in a pure resource sense; new technologies can always be
created, enabling a more efficient method of energy acquisition and utilisation, the
raw resources of earth are still being discovered, and new means of re-using waste is
constantly emerging.
Variables and Constraints of the International System
Given the above conditions, variables, and constraints, any model needs to be
representative under the following conditions:
• Multiplayer, > 1000 individual agents (defined as nations; groups of
individuals working together using an internally established set of rules/laws)
• Multi Shot; Reputation informs decisions, behaviours change over time
• Agents base decisions on deontological structures; utility sought is highly
dependent on national cultural beliefs

• Information is incomplete; agents know the rules of their own nations, but
have only imperfect, to no, knowledge of others
• Information is not symmetrical; different nations have different levels of
knowledge of the world
• Energy is measurable; GDP, investment, ownership (physical and
intellectual), natural resources (raw materials), capability resources (ability to
transform raw materials), IP generation (ability to create more efficient
capabilities)
• System is open; new energy is always discoverable
• System is survivalist; nations can feed off other nations if it is a more
efficient access to energy, and starve another nation
• Natural resources are unequally distributed; trades are necessary to
maximise available resources
• Capabilities are unequally distributed; trades are necessary to maximise
productive efficiency
• System is dependent on many variables which change over time and with
relation to each other; non-linear system
• Nations are highly interconnected; overlaying decision networks
• System is stoichiometric; law of big numbers applies and statistical
properties exist.
Graph Theory

Graph theory is part of the basic “language” of algorithmic game theory. Graphs
represent the nodes and connections within a given system. The global network of
states can be represented by 192+ nodes with an edge connecting each state with
an embassy, commercial or other connection. Further, national nodes (cooperative
groups of individuals using a uniform and unique set of rules for interaction) can be
represented with this model, allowing for visibility of non-state international agents.
Different flows can occur between the different nodes; resources, products, capital,
people, information, et alia. Different dimensions can be attributed to each of the
nodes, symbolising their participation in exclusive networks which may influence
their decision on any given matter. These dimensional networks can be historical,
ideological, religious, political, cultural, or any other national aspect.
The use of graph theory representation has been used to consider issues as broadly
separated as certification as a general model of governance60
, to the fundamental
metaphysical structure of the world61
. The use of graphs allows us to capture many
dimensions of a given node, and the multitude of transactions between the nodes.
The global system of today is highly defined by the UN institution of state
recognition; however there are also a multitude of other transnational actors which
affect the overall state of play. The UN recognition could be represented as an
exclusive network, which alters the behaviour of nodes connected to the exclusive
network.
60
“Structuring Transnational Fields of Governance: Network Evolution and Boundary Setting in the
World of Standards” By Tim Bartley and Shawna Smith.
61
“The Mathematical Structure of the World: the World as Graph”by Randall R. Dipert, The Journal of
Philosophy, Vol.94, No. 7 (Jul 1997), pp. 329-358

Non-government organisations can create social momentum over particular issues,
religious groups can mobilise their constituents, and corporations can freeze
regulations. While individuals can have an influence, it is only seen on the
international level when they are magnified through an institution. A person
standing on a sidewalk yelling is unlikely to have an enduring effect on Aboriginal
traditional land ownership. However a person, given access to the courts, and
quietly demurring to international law, may make a difference.

Each of the edges (connecting lines) has a weighting factor applied which represents
a transaction cost associated with the particular transfer. Laws as rules between
variables sit as weighting factors on the connections. Heavy trade tariffs between
nodes will increase the cost, and hence the weighting factor, associated with
transacting between the two nodes. The literature on routing algorithms is
extensive62
, as this has been a major driver in computer networking. Indeed the
complexity of information routing in the computing world far exceeds the
complexity of the international socio-political-economic system.
In constructing the international state model we need to account for every type of
transaction which occurs. This model would need to include individual relationships,
corporate associations, non-government organisations, treaty regimes, diplomatic
notes, et alia. These transactions create a bias between nodes, which over long
periods of time increases or diminish the transaction costs associated with particular
types of connections. Due to the difficulty in calculating outcomes with huge
numbers of inputs, an initial look would tend to use statistical data to sum up inputs
from minor variables.
In mapping out the history of the world as a series of transactions, we can see that
certain behaviours at the state level result in a lowering of transaction costs
between nodes. The nodes with the most connections, and the lowest transaction
costs, will ultimately dominate. The amount of capital a particular nation has can be
compared to trade, knowledge, or social flows which it can generate through
connection increases.
62
“Algorithmic Game Theory” Edited by Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani,
Cambridge University Press

A national node’s behaviour can impact the weighting of a particular variable. The
aggression of a nation upon another nation is likely to result in a diminishing of
trade between the two nations, and with other nations in general. The reduction in
trade is based on the nature of trade, i.e. stability is required to safely transfer goods
between ports. An increased risk due to warfare will reduce the amount of
individuals willing to transact. Even warfare can be seen as a transaction between
two nodes; in peace the cost of the transaction is zero, in war it goes up.
Transactions do not only involve financial consequences, they also transfer
information, ideas, culture, ethics, morals, social behaviours, product preferences,
and more. The interaction of nations transfers people, genetic lines, and creates
familial bonds. The different varieties of connections come with different legal
identity depending on the nations that are interacting.
Graph theory is a great tool for gaining insight into the system. For the purposes of
identifying natural laws from a data set of customary international law, we are
looking at the multi-shot game over very long periods of time. A nation, or group of
nations, could potentially work against the prevailing winds of natural law for a very
long time before they exhaust their energy reserves.

Non-Linear Equations applied to the International System
Non-linear mathematics is the foundation of modern engineering control theory,
used in everything from aircraft63
to automobiles. In examining the international
system as a system64
, we can examine international laws as the control inputs to the
system. Before we can do that, we need to understand how the system functions
without any control inputs.
Non-linear equations model systems with multiple variables which change with
relation to each other. One compelling argument provides an amoral mathematical
model based on restating thermodynamic equations65
;
(1)
This equation shows a change over time (dt) of entropy (S) using Bayesian
probability (P) due to energetic exchanges in kB (energy -> assets, money, IP,
labour, et alia) over time (dt) between two asset pools Nj and kB. For any particular
nation we can equate to national asset pools, kB, and the asset pool available from
the international system. So any connection to the outside world adds available
assets to drive the potential difference, it can also bi-directional and scalar (non-
dimensional form of cash or assets or IP into energy units). Each edge represents an
additional connection to a source of energy and is summed in equation (1) to
63
“Derivation and Definition of a Linear Aircraft Model” NASA Reference Publication 1207, August
1988
64
“Systems Thinking, Systems Practice” Peter Checkland, John Wiley, 1981
65

represent the total energy reserve available to a nation.
Intellectual
Economic
Social
Et Alia

The international system is an open energy system, on the basis that we have not
exhausted out natural resources, and discovery and innovation always allow new
sources of energy to be added. In an open system Ajk [equation 1] is the free energy
available to the system and is determined by multiplying the number of assets by
their value in energy units. This could be monetised by making energy equal to
currency, but floated currency itself is a form of energy with variability in this model.
Also the value of the asset is defined in the exporting nation, a greater value in the
importing nation provides a driving function for the transaction to occur, so long as
the increase in value exceeds the transaction costs.
This way of looking at international transactions sits neatly with the remedies the
World Trade Organisation provides in disputes. It is also demonstrable in the way
executive governments negotiate terms in Free Trade Agreements, and other
cooperative agreements, exchanging one form of asset or assistance (military
agreements, cultural exchanges, intellectual exchanges, et alia) for a different form
of perceived equal value. It also allows for information as knowledge and due to the
statistical nature of the model, the form of the knowledge becomes largely
irrelevant (whether it is strategic knowledge, technological, medical, or other). So
long as there are statistically diverse forms of a particular asset type, they can be
modelled as a single form; energy.

In working through these equations it is shown that the international system
represents a non-Hamiltonian system with three or more degrees of freedom,
where the driving forces and the energy flows are inseparable66
. This also leads to
the conclusion that if this model is correct a Linear model could be derived and
control theory methods used to show control inputs.
In looking at the international legal system we should see that customary laws
statistically follow natural laws, and represent the rules within the system context
which provide the optimal approach to achieving the maximum entropy within the
international system.
Further work in natural networks67
shows that networks themselves have a tendency
to drive towards the maximum entropy. Therefore networks of states and nations
would have a tendency to form connections which maximise energy gains from the
system. While there may be connections which do not lead to optimal energy
consumption, over a statistically relevant set of actions (500 years of international
interactions), the emergent rules should provide the paths which lead to optimal
energy gains.
66
67
“Natural Networks” by Tuomo Hartonen and Arto Annila, Not yet published [arXiv.org > physics >
arXiv:1106.4127]

The current macro-economic models used to handle our global economy are based
on the idea that the system is stoichiometric, that it is statistically defined due to
the law of large numbers interacting in complex ways, what systems theorists call
‘unorganised complexity’. However as we drive towards a goal of defining more and
more international laws, the system may become ‘organised complexity’. Still a
non-linear complex system, but with emergent properties which are no longer
stoichiometric.
Systems theorists working in computer science have found that classical electro-
mechanical stoichiometric failure models and methods cease to work in complex
computer systems, because there is too much structure while the systems remain
non-linear68
.
68
“STAMP a new approach to accident analysis” by Nancy Leveson, MIT Press, 2011
Random
Discrete
ComplexSimple
Unorganised Complexity
Stoichiometric – Macro-economic
Organised Complexity – Global
government
Organised –
Simple

Conclusions
Classical natural law theory provides us with a view of the law which is immutable
and eternal; as valid today as it was two thousand years ago, based on intellectual
consideration of historical observations. Using modern analytical methods and
mathematical tools we can examine the international laws naturally emerging from
international interactions. This method allows us to examine the rules in play which
are unrelated to our moral or ethical perspective, or particular teleological purposes.
These rules require ratification through positive international, only for the purpose
of not having to re-discover them continually. This way of defining Natural law is
significant, not because it proves here what is or isn’t a legitimate law, but that it
provides a method for weighing the legitimacy of international law without
presuppose the rightness of any one ethical or moral deontology.
The use of deductive methods to examine the international system as a network
allows us to construct a framework to which we can apply scientific laws of
thermodynamics. This coupled with the inductive process of examining past
international behaviours provides us a method by which to determine the rules
(laws) which result in the optimal access to free energy within the system. Further
survey efforts looking at customary international laws and networks, using entropy
as the driving utility function is required to demonstrate this method.

This view of the international system suggests that customary laws emerge only
after a statistically relevant passage of time, which has resulted in the agents within
the system learning the natural laws which result in maximum payoff. The authority
of these rules prevails so long as the system remains stoichiometric, over a
statistically relevant time frame. Movement away from the natural laws by any one
nation will result in inefficiencies and losses for that nation and with other agents
access the energy sources more efficiently, will lead to degradation and potential
collapse of that nation.
The legitimacy of an international law can be determined by understanding the
interactions of the international system as a network with a natural tendency
towards maximum entropy. International laws which disrupt the statistical nature of
particular interactions will cause a breakdown in the ability of the system to move
towards maximum entropy, and will be rejected by the system.
This breakdown and rejection process, when viewed the first person perspective can
be deadly. Breakdowns occur as national scale breakdowns in economy, social
structure, or pacific stability. An international legal system constituted on the
principles of natural law, enshrining only those laws which are clearly definable as
optimal interactions for achieving maximum entropy while maintaining a level of
randomness necessary for stoichiometric process, would be per se legitimate, and
ought rightly be enshrined in a formal international constitution providing a head of
power above the nation state.

My prediction would be that very few, if any, new additions to the international
treaty system would be required. Based on this research I would also predict that
continued pressure from the global community to build additional transnational
laws to foster ethical, moral, or social movements related to specific national
preferences will ultimate undermine the global governance system leading to
organised complexity and a need to totally rework the fundamentals of the global
system. Nations should be wary in seeking to develop transnational laws unrelated
to the necessary functions between them.
In closing, this paper has shown that the international system can be
mathematically modelled (albeit imperfectly), and that natural international laws
can be observed through historical statistical analysis. It also suggests that rather
than there being any limit to what nation states can enact as international law, that
there are limits on what they ‘ought’ to enact as international law. The modelling of
the international system shows that laws defying natural law, are as doomed to
failure as laws defying gravity. Enshrining natural law as a legitimate set of
constitutional limits in international law will limit excursions in national, and
transnational, behaviour which courts catastrophe.

STILL

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