Modelling International Groups: The Relation Between Goals, Power, and Effectiveness
 |
| Le Palais des Nations, in Geneva (AWM) |
I first developed this model in late 2008, refining it in 2010 and 2012. I heavily revised it in 2018, the year that Canada hosted the G7 Summit (I thank Jim Haley for his helpful comments). The views expressed here are entirely my own. . A PDF version is available here.
Abstract
The effectiveness of an international group depends on the
relationship between the member countries’ shared goals and their overall
power. A group can only be effective if these two factors are aligned: goals
that do not correspond to power are merely aspirational and powers unlinked to
goals are useless.
A group should only expand its membership if two conditions
are met: first, the new country must generally accept the group’s existing
goals. Second, the new country’s powers should help to achieve the group’s existing
shared goals. This framework helps to explain certain phenomena, such as why
superpowers are reluctant to join groups, how changes in one country’s policies
can affect an entire group’s effectiveness, and why adding powerful new members
can make a group less effective overall.
There are four major implications for the current state of
global governance. First, the G20 is likely to remain ineffective, as it
operates based on consensus. The G20 should be refocused as a discussion forum,
a task to which it is ideally suited. Second, although the current US
administration opposes many traditional G20 policies, the US remains an
essential G20 participant. Third, the G7 should focus on issues where its
members have the power to bring about change themselves and abandon more
ambitious goals. Finally, if the G20 were reformed so that it no longer
operated on consensus (for example, by restricting veto power), it could be
much more effective—assuming its members accepted such a change
Introduction
Suit the word to the action, the
action to the word.
Hamlet, III.ii
Hamlet, III.ii
The Trump administration’s “America First” policy has led to
new tensions in international governance, evident at major international
meetings since early 2017. From disputes over climate change at the G20 Summit
in Hamburg (July 2017), to arguments over trade protectionism in the lead up to
the G7 Summit in Charlevoix (June 2018), the United States has expressed
fundamental disagreements with policies long-endorsed by these forums.[1]
In one sense, this is deeply strange: over 2016-18, the
membership of neither the G7 nor the G20 changed. There was been no major new
international economic or security crisis. Several countries saw changes in
leadership (such as Italy and France), but this is a normal part of the
international meetings cycle. Instead, a change in US political leadership (and
without corresponding change in underlying US economic or military power) was sufficient
to prevent consensus.
The effect of this ideological shift reveals an important
aspect of the structure of international groups: when decisions require
unanimous consent, a loss in like-mindedness can hobble a group’s effectiveness—even
when overall power of the various members remains unchanged. By examining how goals,
powers, and effectiveness are interrelated, we can draw broader conclusions
about the strengths and weaknesses of not just the G7 and the G20, but any
international group. This in turn provides insight into possible ways to
strengthen international groups.
Defining Goals, Power, and Effectiveness
In brief, individual countries have various policy goals and
various powers; successful statecraft requires aligning the two. For example, Athens
may wish to conquer new territory. If it possesses a well-trained military, it
can use this aspect of its power to bring about this goal, thereby effectively
implementing policy. In contrast, Melos—the object of Athens’ ambitions—may
wish to avoid invasion. However, if Melos lacks a powerful military, it will lack
the power to bring about this goal and be ineffective.
Countries are effective only when goals and powers match:
goals that cannot be achieved are merely aspirational and powers unlinked to
goals are useless. (Athens could also use its military to attack the
much-larger Persian Empire; though this is within Athenian power, it is opposed
to Athens’ goal of self-preservation.) Some countries will be more effective
than others, either due to having broader powers or narrower goals. For
example, in this sense, between 1920 and 1939, the USSR became more effective
both by strengthening its industrial base (allowing for greater military
mechanization) and by adopting the doctrine of “Socialism in One Country” and
rejecting worldwide revolution (this being a difficult goal.)
Goals, power, and effectiveness can be defined as follows:
- Each country has individual goals, gi. These are both active (policies it wants to pursue) and passive (policies it can accept, if others implement them.) Goals can be changed in the short term and at relatively little cost.
- Each country also has individual powers, pi. These encompass the ability to act in any way, for positive or negative effect. Powers are relatively static and change only in the long term.
- Whenever goals and powers overlap, the country is capable of an effective action, ei. Goals that do not align with powers and powers that do not align with goals are irrelevant.
- Effective actions are associated with some positive utility, u(ei).
Figure 1: Goals, Power, and Effectiveness 
Group Effectiveness
By forming groups, countries can pool their individual powers
to achieve shared goals. For example, the resources of the Gulf Cooperation
Council (GCC) include Saudi Arabia’s oil and Bahrain’s natural gas, giving the
GCC significant influence on international energy issues.
When countries join a group, the effect on goals is more
complex. Most major international groups are characterized by three features: they
are veto-based (operating by consensus), senatorial (each member has one
representative or vote, regardless of its size), and utility maximizing
(countries join groups because they hope to become more effective.) These
features hold at the UN Security Council, the G20, the G7, the Asia-Pacific
Economic Cooperation forum (APEC), most free trade agreements, and a host of other
military alliances, treaties, and informal groupings. The three rules reflect a
balance between powerful countries’ unwillingness to surrender veto power and
smaller countries’ desire for equal representation.
Of note, certain international groups violate the first two
rules,[2]
such as the UN General Assembly (which is not veto-based), the European Central
Bank (which is not senatorial, as only a subset of members participate in board
decisions), and the International Monetary Fund (which is not senatorial, awarding
votes based on economic weight, nor veto-based.) Despite this, it is telling
that the most powerful international groups, as well as most groups that meet
at the level of leaders, are veto-based and senatorial.
Returning to Venn diagrams, given the additive nature of
power, a group’s overall power is the union
of the individual powers of the member countries. In contrast, when veto power
exists, common goals are the intersection
of the individual goals of the member countries.
Figure 2: Overall Power and Common Goals (Three Countries)
These relationships allow us to model the effectiveness of
an international group. Crucially, the effectiveness of a group is not the same
as the combined effectiveness of the individual members. Instead, groups entail
combinations of goals and powers that allow countries to achieve actions that
are not possible for any of them unilaterally.
The Lend-Lease agreement in the Second World War provides an
example: over 1942-45, the UK had airfields within range of Germany, while the
US had the capacity to build numerous aircraft. Through Lend-Lease, the two
countries achieved their common goal (attacking Germany) by combining their powers
(using US-made planes using UK airbases.) This would have been impossible for
either country to achieve unilaterally (i.e., their individual goals and powers
did not align in these respects.)
A group’s effectiveness is thus the intersection of its common goals and its overall power. This is
distinct from the union or intersection of the effectiveness of the individual members.
(For a proof of this, please see Annex 1.)
Figure 3: Group Effectiveness (Two Countries)
There is a further and more cynical implication of this
relationship: disputes over aspirational goals do not undermine effectiveness.
Even if countries dispute goals that are beyond their power, this in no way
affects their ability to enact other goals that are common and within their power.
In this light, the alleged disagreement between Roosevelt and Churchill at
Yalta over Stalin’s intentions in Eastern Europe was irrelevant, as neither the
US nor the UK had forces stationed there that could have countered Soviet
domination. Despite this disagreement, the rationale for Lend-Lease remained.
Membership Dynamics
Joining a group involves tradeoffs: due to the exercise of
veto power, members must forbear from carrying out certain effective actions
they could otherwise achieve unilaterally. To return to the Lend-Lease analogy,
the terms of the agreement made it impossible for either the UK or the US to
seek a separate peace with Germany.
Joining a group is only desirable when the utility of the
group’s effective actions exceeds the utility of unilateral actions. (As a
corollary to this, superpowers have little incentive to join groups, as they
are highly effective on their own.) The tradeoffs can be illustrated as
follows. (Again, please see Annex 1 for a fully annotated version of this
diagram.)
Figure 4: Tradeoffs in Effectiveness
Applying the Lend-Lease example to Figure 4, with Country 1
as the US and Country 2 as the UK, “C” represents “build numerous warplanes” and
“E” represents “use airbases within range of Germany.” “A” and “F” represent
“sign a separate treaty with Germany,” while “D” could represent “engage in
naval warfare against Germany” (advantageous to both countries, whether done
jointly or unilaterally.)
Over time, groups are also affected by changes in their
member countries. When a country adopts the group’s goals (a form of
international “socialization”) the group’s effectiveness increases. The reverse
case, as illustrated by the Trump administration actions in the G7 and G20,
reduces effectiveness.
Though changes in individual power occur more slowly, they
too alter group effectiveness. For example,
advances in US intelligence gathering capabilities have benefitted its “Five
Eyes” allies. Conversely, Indonesia’s gradual decline as an oil exporter
has reduced OPEC’s global market share.
Figure 5: Socialization and the Balance of Power
Expansion and Expulsion
A critical question for any group is whether to alter its
membership, either by welcoming new members or expelling existing ones. Focusing
on the alignment between goals and power is essential to understand the subtle
effects of changes in membership. While power is always additive (adding a country can never reduce overall power) and
common goals are never additive (adding a country can never broaden the scope
of common goals), group effectiveness can either increase or decrease.
Merely seeking to balance like-mindedness and power is
imprecise: what is required instead is strategic consideration of how the
country’s specific goals and powers will influence future group effectiveness.
Though Country A disagrees with the rest of the group on several issues, could
it help to achieve a crucial shared goal? (During the Confederation of Canada,
Prince Edward Island partly resisted union, but eventually was won over.) Though
Country B supports all the group’s initiatives, is it merely free-riding, offering
little new power? (Japan’s joining the alliance against Germany during the
First World War allowed it to seize German colonies in the Pacific, with
limited effects on the European theater.)
The formation of the United States presents an immensely
successful example of sovereign governments forming together with the explicit
goal of pursuing common goals. Capital-rich northern states joined
agriculture-rich southern states, allowing greater economic growth than either
could achieve alone, as well as facilitating mutual defense.
In contrast, Russia’s participation in the G7/G8 was a
failure. Russia was invited into the G7/G8 at the 1997 Denver Summit, despite
did not sharing many of the old G7’s existing goals or priorities. Even so, it was hoped that participation in
the group would socialize Russia, encouraging it to embrace G7 views. When
Russia invaded Crimea in 2014, the original G7 members recognized that there
was an irreconcilable ideological gulf, and Russia was expelled. Although Russia
wielded significant power over core G8 issues (such as nuclear disarmament and
counterterrorism), because it did not share the old G7’s goals, the G8 was
ineffective overall.
As a final consideration,
countries may join multiple groups to achieve discrete goals, even when the
larger groups oppose each other. For example, in return for sharing
intelligence with both countries, Pakistan receives support from China and the
US. Groups may understandably wish to discourage this type of behavior: indeed,
most Free Trade Agreements (FTAs) contain provisions against “transshipment.” For
example, while Canada has agreements with the United States (NAFTA) and the EU
(CETA), there is (as yet) no US-EU FTA.[3] Hence, it is forbidden
to tranship goods tariff-free from the US to the EU via Canada.
Figure 6: Multiple Groups
Conclusion & Implications
This analysis provides a new way to think about the
relations between goals, power, and effectiveness. It is not enough simply to gather
powerful countries together, nor to seek ideological uniformity before all else;
such groups are either powerful but indecisive, or unified but powerless.
Instead, a group’s effectiveness is determined by its power to implement its
shared goals. Aspirational goals and useless powers are both irrelevant.
When expanding a group, the essential factors are whether
the prospective new member’s individual powers will help to achieve the group’s
existing shared goals, and the degree to which the new member accepts those goals.
Framing the problem in this way can provide clarity on
certain phenomena, such as why superpowers are reluctant to join groups (they
have a high degree of unilateral effectiveness), how changes in one country’s
policies can affect an entire group’s effectiveness (by the scope of common
goals), or why adding powerful new members can make a group less effective
overall (through veto power.)
Admittedly, the model has limitations, notably the
assumptions that all members wield veto power and that representation is senatorial
(one country, one vote.) Furthermore, the assumption of utility maximization is
limiting, as it discounts the possibility that countries may join groups for
other reasons (such as a way to maintain dialogue.)
These principles have several implications for the current
state of global governance:
1. Absent an
immediate international crisis, the G20 is likely to be ineffective in terms of
enacting shared policies. Despite
this, the G20 can serve a useful purpose as a discussion forum. The G20
acted boldly and decisively during the Global Financial Crisis, launching $1
trillion in coordinated stimulus in 2009. At that time, all members shared the
goal of avoiding a global financial collapse and they jointly employed their
collective power. Since then, the G20 has struggled to achieve universal
agreement on major issues, limiting the group’s effectiveness. Given that the G20
operates on a consensus basis, it is not realistic to expect major new “deliverables.”
Instead, the G20 should be reimagined as a forum for discussion and the sharing
of views, a task to which it is ideally suited.
2. Despite
current squabbling with the United States, it is extremely unlikely that the
G20 will expel or disengage with the US. American participation still is a net
positive for G20 effectiveness. As did the G7 expelled Russia, so to could
the G20 theoretically expel the US. Yet despite the current US administration’s
opposition to the G20 consensus on climate change and trade, US participation
raises the G20’s effectiveness in many other areas, such as countering
terrorist financing and money laundering. Only if US power ceased to be
relevant to the G20’s priorities would there be serious talk of suspension or
expulsion.
3. The G7
should restrict its activities to areas where its members can bring about major
change on their own. It should cease to present itself as a global steering
group. The G7 should focus on those areas where its seven members have the
power to bring about change, such as in the realm of development assistance. Though
its seven members may be like-minded on many issues, G7 lacks the power to address
issues like exchange rate policy. (Of note, G7 disagreements on global issues
are not problematic, because the seven members lack the power to address such issues
in any event. From a strategic perspective, the US veto on supporting climate
change will have no impact on the G7’s overall effectiveness in other areas.)
4. Relaxing
constraints on veto power and representation can make a group more effective,
by increasing the scope of common goals. There are numerous ways to achieve
this, such as:
A final and farther-reaching implication arises from this
model. As changes in power take time, expanding the set of common goals is the
quickest and simplest way to increase a group’s effectiveness. Aside from
persuasion, this can also be brought about by changing the rules governing the
group:
- Restricting veto power to certain members (UN Security Council)
- Restricting representation to certain members (European Central Bank)
- Making decisions by votes, either with weighted votes (International Monetary Fund) or one country, one vote (UN General Assembly)
- Requiring members to accept certain goals as a condition of membership in the group (the European Union)
- Regular review of membership (UN Security Council, in part), with the aim of admitting countries that will increase effectiveness and expelling current members that reduce it
If the G20 were to embrace any of these rules, its effectiveness
could increase significantly. At the same time, it is unclear whether countries
would be willing to join such a group: veto power and senatorial representation
are widely adopted because they are attractive to leaders.
The UN Security Council provides the most promising template
for G20 reform on these lines: it is a widely-respected international group
that operates with a limited veto and majority voting (based on one country,
one vote), and it conducts regular reviews of its membership. With prospects of
major Security Council reform dim, a transformed G20—repurposed as a “Global
Economic Council”—could take up stewardship of the global economy, as the G20 so
ably did in 2008-09, before it lost its way.
Annex 1: Detailed Analysis of Tradeoffs in a Group
This diagram illustrates the full set of possibilities when
two countries form a group. Goals and powers can be divided into sixteen areas,
one of which is empty (null.) Each area can be explained individually.
Note that in previous diagrams, for the sake of simplicity
and clarity, areas 4 and 14, and extensions to areas 5 and 7 were not shown.
But to show the full range of possibilities, the Venn diagram requires these
regions (i.e., a country’s powers should have a “panhandle”, instead of being
rectangular.)
Country
A (red)
|
Country
B (blue)
|
→Group
|
|
Goals
(circles)
|
(1,
2, 4, 5, 6, 7, 8, 12)
|
(6, 7,
8, 11, 12, 13, 14, 15)
|
(6, 7, 8, 12)
|
Powers
(polygons)
|
(2, 3, 5, 7, 8,
9, 11, 14)
|
(4, 5, 8, 9, 10, 11, 12,
15)
|
(2, 3, 4, 5, 7, 8, 9, 10, 11,
12, 14, 15)
|
↓Effectiveness
|
(2,
5, 7, 8)
|
(8, 11, 12, 15)
|
(7, 8, 12)
|
Underlined: part of effectiveness
Italicized: shared
with the group
Area
|
Explanation
|
Area
|
Explanation
|
|
1
|
Goals
of A that it can never achieve (not alone and not in the group, as B would
veto them)
|
9
|
Irrelevant:
Useless powers shared by A and B (they do not correspond to A or B’s goals)
|
|
2
|
Effectiveness of A
that it must surrender (it can achieve this alone, but it is vetoed in the
group)
|
10
|
Irrelevant:
Useless powers of B (they do not correspond to A or B’s goals)
|
|
3
|
Irrelevant:
Useless powers of A (they do not correspond to A or B’s goals)
|
11
|
Effectiveness
of B that it must surrender (it can achieve this alone, but it is vetoed in
the group)
|
|
4
|
Irrelevant: powers
of B that correspond to A’s goals, but not B’s goals
|
12
|
Effectiveness that
B can achieve alone, and which A has as a goal. (A can only achieve this by
joining the group.)
|
|
5
|
Effectiveness
of A that it must surrender (it can achieve this alone, but it is vetoed in
the group)
|
13
|
Goals
of B that it can never achieve (not alone and not in the group, as A would
veto them)
|
|
6
|
Shared goals of A
and B that they can never achieve (not alone and not in the group.) The group
should expand its powers into this area.
|
14
|
Irrelevant: powers
of A that correspond to B’s goals, but not A’s goals
|
|
7
|
Effectiveness
that A can achieve alone, and which B has as a goal. (B can only achieve this
by joining the group.)
|
15
|
Effectiveness
of B that it must surrender (it can achieve this alone, but it is vetoed in
the group)
|
|
8
|
Effectiveness of A
and B that is possible both alone and in the group
|
16
|
Null (empty)
|
Thus, Country A gives up its effectiveness in areas 2 and 5,
but it gains effectiveness in area 12. Similarly, Country B gives up its
effectiveness in areas 11 and 15, but it gains effectiveness in area 7. For the
group to be effective, both the following must be true:
UA(12) > UA(2,5)
UA(7) > UA(11,15)
Further implications are that Country A has an incentive to
minimize areas 2 and 5, which it can achieve by persuading Country B to share
these goals. Country B has a similar incentive with regard to areas 11 and 15.
Moreover, the group should also aim to expand its powers into area 6, as these
are goals that both countries share, but which neither has the power to achieve
unilaterally or in the group.
Finally, note that utility may not be evenly distributed
across all areas.[4] For
example, although area 12 may appear small in the above diagram, it could have
an extremely high utility for Country A.
Annex 2: Mathematical Appendix
(Note: Due to time pressures, the mathematical
expressions below are presented as JPEGs. They are included in line in
the text in the PDF version.)
Below is a more formal treatment of the model, as well as an
alternative definition of effectiveness (2j).
For (3d), see [6]
For (4e), see [7]
[1]
The first-ever G20 Leaders Summit was convened by George W. Bush, in Washington
in November 2008. In the coming months, member countries would take a strong
stance against protectionism.
[2] Finding
groups that do not exist for utilitarian reasons is more difficult. The
Anglo-Portuguese Alliance, in effect since 1733, is an imperfect example: this
agreement has greater symbolic than practical significance.
[3]
Such as the long-mooted TTIP
[4]
Consider a third dimension, with utility extending perpendicularly from the
plane in a non-uniform way. This is analogous to surface integration.
[5] In
words, the effectiveness of the group is the union of the effectiveness of the
individual member countries contingent on the common goals of all other member
countries. Taking a two-country example,
By distribution,
By 2h, when there are two countries, k1 = g2 and k2 = g1, thus
This is seen in Figure 3 and also in Annex 1.
[6] In effect, the decrease in unilateral effectiveness due to the
requirement to abide by the goals the group 
must be offset by the gain in utility from
acting jointly with other countries 
etc.
must be offset by the gain in utility from
acting jointly with other countries etc.
[7] Because ki, the set of common
goals excluding country i, cannot
include any goals that are specific to country i, i.e., any of the elements of gui.