intra-EU28 trade, intra-EU15 trade isbased on trade in goods and services during the period of 1998-2000.However, the trade concerning the 10 new and 3 candidate countries,the data is based only on merchandise trade in 2001 for trade among
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Thomas Cottier / Satoko Takenoshita
tion of WTO contribution, which is proportional to the share oftrade in goods and services, intra-EU trade is included. As shown inTable 1, the current proportion of contribution of EU28 is over40%. This inevitably leaves the EU with a disproportionately highvoting weight. In order to deal with this problem, the Hypothesis 2is provided as an estimated case in which the EU is treated as oneentity. Considering that the EU constitutes a single custom area andthat the voting behaviour of the EU is completely homogeneous andcontroversial votes cannot be made amongst EU members, it isreasonable to assume the EU as one entity, by excluding intra-EUtrade. It is in this respect that calculations made in our first paperare amended and further developed.E. Calculated Voting WeightIn quantifying the formula, three models are tested under each hypothesis:x model a) without basic votes (V = bCs + cYs + dP + eLs);x model b) with basic votes (V = a + bCs + cYs + dP + eLs);x model c) with basic votes and exclusion of population variable(V = a + bCs + cYs + dP)Hence given the weight of each variables described above, themodel a and c will have 1500 whereas model b with 1750 votes intotal.Table 2 shows the regional representation of the voting weight.Under Hypothesis 1, whose calculation is based on the current allocation of contribution, the proportion of voting weight for the EU isas high as about 30 percent. This means that the sole EU is endowed with de facto veto power if the majority rule of three quarters were to be applied. Under Hypothesis 2, on the other hand,these effects are mitigated and eliminated by excluding intra-EUtrade for the purpose of allocating budgetary contributions. Hypothesis 2 is divided into two modes in treating the EU28. Model band model c provides the basic votes to the EU as one entitywhereas the model b’ and model c’ provides them with basic votesnew/candidate countries and between new/candidate and EU15 countries. Although trade in services exhibits increasing trend, the proportion of trade in services for those 13 countries are considered to bestill small relative their total trade. The actual EU28 contribution as awhole will not be too different from or slightly lower than our calculation.
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205
times 28 EU Members. The difference between the two modes isthat the EU has slightly less voting weight than the US under models b and c. The situation is revered for models b’ and c’ where theEU exercises slightly more rights than the US.19In comparing the two Hypotheses, there are two notable differences. Firstly, the distribution of voting weight is more favourablefor developing countries in Hypothesis 2. Secondly, the differencein proportion of representation between the US and the EU is muchreduced in the Hypothesis 2. Under Hypothesis 1, the EU is endowed with a voting weight almost double compared to the US. Incontrast, the Hypothesis 2 balances the voting weights of the twoeconomically influential countries. Hypothesis 2 also provides amuch more balanced representation of interests between industrialand developing countries compared to Hypothesis 1. Furthermore,Hypothesis 2 allows to avoid veto powers even when 3/4th majorityis required since the vote of the EU is limited up to 20% of the totalvote. Under Hypothesis 1, this is not the case and would allow theEU to control critical votes in a decisive manner.It is interesting to note the effects from the variables of basicvote and population. Both variables generally provide a highershare of votes to the group of developing countries as a whole. Yet,the gain in voting weight from the insertion of these variables variesamong different regions. In particular, the population variable almost exclusively favours Asian countries, since about 60% of totalworld population is domiciled in that region. The inclusion ofpopulation increases the voting weight of Asian region by six percent for both hypotheses (model b versus model c). As to otherregions, the population variable negatively affects the votingweight, except for Africa. The basic vote, on the other hand, has theeffect to increase voting weight for all developing countries in thedifferent regions, except for Asia (model a versus model b).
19
Of course, US-EU relation as well as industrial-developing relationin voting weight is subject to change over time, depending on thefuture development of different variables.
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Thomas Cottier / Satoko Takenoshita
Table 2: Regional Representation from Calculated Voting Weight(Calculated Vote Share in Percentage)Hypothesis 1Model
a
b
c
IndustrialCountries
58.60
53.97
59.75
USA
16.67
14.41
15.89
EU28
28.73
27.44
30.24
Japan
7.53
6.58
7.28
DevelopingCountries
41.40
46.03
40.25
Africa
7.20
10.18
9.95
Asia
21.73
20.75
14.49
Europe
0.73
1.14
1.34
Middle East
2.13
2.69
2.87
Americas
9.60
11.26
11.62
Hypothesis 2Model
b
b’
c
c’
52.46
46.07
48.80
50.83
53.71
USA
18.71
16.12
16.19
18.01
17.97
EU28
18.58
16.00
18.71
17.08
20.11
Japan
8.26
7.23
7.21
8.07
8.02
DevelopingCountries
47.54
53.93
51.20
49.17
46.29
Africa
7.86
11.50
10.58
11.54
10.62
Asia
24.90
24.15
23.57
18.35
17.77
Europe
1.26
1.99
1.72
2.13
1.94
Middle East
2.53
3.13
2.86
3.40
3.14
Americas
10.99
13.15
12.47
13.74
12.83
IndustrialCountries
Source:
a
Calculations by the authors.
The composition of the ten countries with the largest vote isshown in Table 3. Importantly, it shows that a high proportion ofvoting weight is distributed among countries from different regions.Although the first three positions are taken by a group of industrialcountries – the US, the EU and Japan – in all the models, they are
Towards Supplementary Weighted Voting
207
mostly followed by China. When the population variable is takeninto account, India is ranked at the fifth position. The remaininggroup consists of Brazil, Canada, Hong Kong, Korea, Mexico, Singapore and Taiwan. Hence, the voting weight – unlike in the Bretton Woods system – is not concentrated in industrial countries, butmore balanced and shared with countries from the regions of Asiaand Western Hemisphere as well.The voting weight of China deserves particular attention. Bycombining the voting weight of mainland China, Hong Kong, andMacao, China will have a larger voting weight than Japan and ranksthird. Considering the growing trend of China’s GDP and trade, it isprobable that China in the future will exercise a counterweight tothe US and the EU.Table 3: Ranking of Ten Highest Vote Countries from CalculationHypothesis 1Model aCountry
Model b
Votes
Country
Model c
Votes
Country
Votes
EU28
431
EU28
480
EU28
453
US
250
US
252
US
238
Japan
113
Japan
115
Japan
109
China
93
China
95
China
35
India
60
India
62
Canada
34
Canada
34
Canada
35
Hong Kong
25
Mexico
26
Mexico
27
Mexico
23
Hong Kong
24
Hong Kong
26
Korea
22
Brazil
24
Brazil
26
Singapore
19
Korea
22
Korea
24
Taiwan
19
Hypothesis 2Model aCountry
Model b
Votes
Country
Model c
Votes
Country
Votes
US
281
US
283
US
270
EU28
279
EU28
281
EU28
256
Japan
124
Japan
127
Japan
121
China
98
China
101
China
42
India
62
India
64
Canada
42
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Thomas Cottier / Satoko TakenoshitaHypothesis 2Model a
Country
Model b
Votes
Country
Model c
Votes
Country
Votes
Canada
42
Canada
44
Hong Kong
32
Hong Kong
31
Hong Kong
33
Mexico
27
Mexico
30
Mexico
32
Korea
27
Korea
27
Korea
29
Singapore
24
Brazil
26
Brazil
28
Taiwan
23
Model b’
Model c’
EU28
327
EU28
301
US
283
US
269
Japan
126
Japan
120
China
100
Canada
42
India
64
China
41
Canada
43
Hong Kong
32
Mexico
32
Mexico
27
Hong Kong
32
Korea
26
Korea
29
Taiwan
23
Brazil
27
Singapore
23
Source: Calculations by the authors
The models tested do not yet separate the effect of openness,but of population and basic votes variables, as we are mainly interested in exploring the impact of these parameters. The effect ofopenness in general is noted in the section of variable C.3. In orderto demonstrate the impact clearly, we would need to make anothercalculation without openness – but it is intuitively clear from Table1, that the openness variable strongly favours developing countriesas their economies are generally less restricted than those of industrialized countries.F. AssessmentIt is submitted that the models designed for weighted voting systemunder WTO amount to a realistic and fair picture of voting rights’allocations. In so doing, the basic requirements of simplicity, transparency, robustness to changing economic climate and Member’srelative power, balanced representation and avoidance of vetopower were sought to be fulfilled. In particular Hypothesis 2, in
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209
which intra-EU28 trade is excluded in allocating the contribution,demonstrates a better balance of representation between groups ofindustrial and developing countries as well as representation between the EU and the US. Further, unlike Hypothesis 1, Hypothesis2 provides a better option for majority voting as individual blockingvotes by individual countries are avoided. Hence we conclude thatHypothesis 2 is more suitable in fulfilling the requirements for legitimate weighted voting system. Regarding the choice of variables,the insertion of a population variable may be questionable as itseffect are exclusively limited to the benefit of Asian countries, eventhough the variable is suggested to enhance the impact and idea ofdemocratic representation. The introduction of basic votes proveseffective in providing more representation to the group of developing countries in general, covering most regions.Evidently, the choice of model and negotiations to achieve ashared perception on factors and voting rights allocations amountsto a major challenge. The experience within Bretton Woods andwithin the European Union shows that this is a difficult task, but notan excluded and unrealistic one.IV. Assessing of Voting PowerIt is important to note that the allocation of voting rights does notexclusively determine the impact of different Members on decisionmaking process. Effective voting powers cannot be defined in astatic manner, but depends on many additional factors, such as thepower of the pen (persuasion), conduct and coalitions. Statisticalmodels developed in a domestic context are employed in this section with a view to further refine the analysis.Based on the calculated voting weight, we suggest an assessment of voting powers for different majority rules. In so doing,Shapley-Shubik20 and Bahnzaf21 Power Indices (hereinafter SSI andBI, respectively) and the Inclusiveness Index22 are used for assessing the voting power of individual Members, while Decision Probability Index23 is used for assessing the efficiency of the votingbody in achieving a successful passage of legislation.20212223
See Shapley / Shubik (1954).See Straffin (1988).See König / Bräuninger (1998).See Coleman (1971).
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Thomas Cottier / Satoko Takenoshita
A. SSI, BI, Inclusiveness and Decision Probability IndicesThe voting power (as different from voting rights or shares) is defined as ‘the chance [it] has of being critical to the success of awinning coalition’.24 It is the probability that a country is crucial(pivotal) in making a decision which turns a loosing coalition into awinning one. In assessing the power allocation, Widgrén providesthree determinants of the outcome of the voting power: majorityrule, assigned weights of the various countries, and voting behaviour.25 The difference between SSI and BI stems from assessing thevoting behaviour determinant which is built on different assumptionof homogeneity and independence, respectively, in these two models.The Shapley-Shubik Index (SSI) is formally defined as( s  1)!( n  s )!Ii ¦n!S M i,where S denotes a randomly chosen coalition, Mi is the class ofminimum winning coalitions with respect to country i, n the numberof countries and s the number of countries in the coalition S.It assumes a random ordering of voters and perceives that onlya minimal winning coalition is required in passing a piece of legislation, as the remaining unexercised votes are not relevant as soonas a majority is achieved. This simulates coalition building and SSIis suggested to be more appropriate for a voting situation wherethere is strong coalition building and voters communicate with eachother to a considerable amount.26On the other hand, the Bahnzaf Power Index (BI) assumes avoting situation where each voter is independent and communication among voters is non-existent. The power is measured by thenumber of probabilities that the voter is able to alter the outcome bychanging his or her vote. Hence the order in which voters join acoalition is not an important factor. BI is defined as:n 1
§1·¨ ¸¦SM i © 2 ¹SSI is more appropriate for the power assessment under theWTO context, as decision-making is the outcome of repeated nego-
Ei
242526
Shapley / Shubik (1954).Widgrén (1995), 114.Straffin (1998).
Towards Supplementary Weighted Voting
211
tiations and bargaining. Thus, our analysis on voting power will befocused on SSI. BI will be presented as a reference in Appendix Cwhich shows the voting power of all individual countries.The Inclusiveness Index assesses the absolute chance that aparticular Member will be part of and incorporated in potentiallycollective decision-making. The index can be used as a quantifiedexpectation of a Member as to the legislative gains from potentiallegislation. In formal terms, the Inclusiveness Index is expressed as:¦ v( S )S  N ,iSZ i (v )¦ v( S )SN
Finally, the Decision Probability Index assesses the ability ofthe voting body to reach a successful passing of legislation. Theindex reflects the number of all winning coalitions, divided by thenumber of all possible coalitions, and is expressed as:¦ v( S )SNP (v )2nThe Decision Probability of the current consensus rule isP(v)=1/(2120), treating the EU28 as one voting entity. Hence theprobability to reach a successful passage of legislation is infinitelyclose to zero.B. Quantified Power IndicesUsing the indices above, our weighted voting models are tested forthree majority rules – simple majority, 2/3rd and 3/4th majority requirements. Further, each majority rule will be tested for doublemajority rules with which a second condition – simple majority rule(50% plus one) in terms of the number of membership – is imposed.As majority ruling requiring simple majority can be achieved basedupon mere voting rights with 3 to 6 members (depending on themodels tested) if the top largest voting weight-holders form a coalition, 7 to 19 members are required for 2/3rd majority and 13 to 37members for 3/4th majority, the introduction of a double majoritywill provide protection for smaller countries by increasing the possibility of being included in making a determining decision.In quantifying the power indices, Monte Carlo technique is being used as the use of algorithms for computation of these power
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Thomas Cottier / Satoko Takenoshita
indices becomes extremely complex with 120 voters (the current148 WTO members, but counting the EU 28 as one single entity).271. SSI and BIUnder the current consensus rule, each country is theoretically pivotal in decision-making hence both SSI and BI is 1.00 for all Members and normalized SSI and BI yields 1/120 or 0.0083 for eachMember. An introduction of weighted voting system inevitablyreduces the voting power of most Members at below 0.0083 formore than 100 countries.Table 4 presents the regional distribution of voting power. Forexample, under 2/3rd majority rule under model (a) of Hypothesis 1,a Member who is pivotal in a voting situation is 64.5% likely to befrom the group of industrial countries, whereas 35.5% from thegroup of developing countries. On the other hand, with 2/3rd majority rule under model (a) of Hypothesis 2, the probability is 55.7%for industrial countries and 44.3% for the group of developingcountries.In general, Hypothesis 2 provides a more balanced distributionof voting power between the two groups of countries than Hypothesis 1. The difference between Hypothesis 1 and 2 again reflects theconcentration of voting power of the EU28. Not only would Hypothesis 1, as discussed above, allow for a concentration of votingweight with the EU28 in comparison to the US; the voting power ofthe EU28 would be much higher than that of the US (see Table 5).Under Hypothesis 1, the EU is given about twice as much votingweight as the US, while the voting power of the EU is 2.5 time asmuch as the one of the US under this model Hypothesis 2, on theother hand, smoothes out such large difference in power by balancing the two. It is interesting to find that an introduction of double majority rule makes almost no change in the power relations.
27
The figures presented in this paper are results from 3 million trialsalthough the figures showed significant level of convergence after 2million.
Table 4: Regional Distribution of SSI Voting Power(Consensus, Simple, 2/3rd, and 3/4th Majority Rule)ConsensusIndustrial (10)* 0.083Devel. (110)
0.917
Africa (40)
0.333
Asia (23)
0.192
Europe (7)
0.058
M. East (8)
0.067
SSI: normalized figure
Americas (32) 0,267
* EU28 is treated as oneHypothesis 1
Model aSM
2/3
Model b3/4
SM
2/3
Model c3/4
SM
2/3
3/4
Industrial
0.636 0.645 0.670 0.594 0.598 0.622 0.654 0.673 0.676
Developing
0.364 0.355 0.330 0.406 0.402 0.378 0.346 0.327 0.324
Africa
0.062 0.062 0.056 0.089 0.089 0.082 0.085 0.081 0.080
Asia
0.193 0.185 0.176 0.184 0.182 0.173 0.125 0.118 0.117
Europe
0.006 0.006 0.006 0.010 0.010 0.009 0.011 0.011 0.011
Middle East
0.019 0.018 0.017 0.024 0.024 0.022 0.025 0.023 0.023
Americas
0.083 0.083 0.075 0.099 0.098 0.092 0.100 0.095 0.093Hypothesis 2Model aSM
Industrial
2/3
Model b3/4
SM
2/3
Model c3/4
SM
2/3
3/4
0.560 0.557 0.566 0.492 0.492 0.493 0.544 0.542 0.548
Developing
0.440 0.443 0.434 0.508 0.508 0.507 0.456 0.458 0.452
Africa
0.072 0.072 0.071 0.107 0.107 0.107 0.107 0.107 0.106
Asia
0.223 0.235 0.228 0.229 0.230 0.229 0.171 0.172 0.169
Europe
0.012 0.012 0.011 0.019 0.019 0.019 0.020 0.020 0.020
Middle East
0.023 0.023 0.023 0.029 0.029 0.029 0.031 0.032 0.031
Americas
0.101 0.101 0.100 0.123 0.123 0.123 0.127 0.128 0.126Model b’SM
Industrial
2/3
Model c’3/4
SM
2/3
3/4
0.523 0.522 0.528 0.575 0.572 0.587
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Thomas Cottier / Satoko TakenoshitaHypothesis 2Model b’SM
Developing
2/3
Model c’3/4
SM
2/3
3/4
0.477 0.478 0.472 0.425 0.428 0.413
Africa
0.098 0.098 0.097 0.097 0.098 0.094
Asia
0.222 0.223 0.219 0.164 0.165 0.159
Europe
0.016 0.016 0.016 0.018 0.018 0.017
Middle East
0.026 0.026 0.026 0.029 0.029 0.028
Americas
0.116 0.116 0.115 0.117 0.118 0.114
Source: Calculations by the authors
Table 5a: Voting Power Indices for Top Ten Countries withHighest Votes for Simple, 2/3rd, and 3/4th Majority RuleHypothesis 1Model 1aCountry
voteshare
SSISM
2/3
Inclusiveness3/4
SM
2/3
3/4
EU28
0.287 0.363 0.372 0.367 0.917 1.000 1.000
USA
0.167 0.153 0.163 0.195 0.584 0.959 1.000
Japan
0.075 0.071 0.061 0.064 0.579 0.610 0.862
China
0.062 0.057 0.051 0.052 0.570 0.600 0.774
India
0.040 0.036 0.035 0.033 0.541 0.565 0.666
Canada
0.023 0.020 0.020 0.018 0.522 0.537 0.594
Mexico
0.017 0.015 0.015 0.014 0.517 0.529 0.573
Hong Kong
0.016 0.014 0.014 0.013 0.516 0.526 0.567
Brazil
0.016 0.014 0.014 0.013 0.516 0.526 0.567
Korea
0.015 0.013 0.013 0.012 0.515 0.524 0.561Model 1bCountry
voteshare
SSISM
2/3
Inclusiveness3/4
SM
2/3
3/4
EU28
27.444 0.351 0.355 0.356 0.941 1.000 1.000
USA
14.408 0.134 0.138 0.162 0.560 0.967 1.000
Japan
6.575 0.061 0.057 0.058 0.557 0.634 0.920
China
5.432 0.049 0.047 0.048 0.553 0.615 0.848
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215
Hypothesis 1Model 1bIndia
3.545 0.032 0.031 0.030 0.535 0.571 0.702
Canada
2.001 0.018 0.017 0.017 0.519 0.542 0.618
Mexico
1.544 0.013 0.013 0.012 0.515 0.533 0.591
Hong Kong
1.487 0.013 0.013 0.012 0.514 0.531 0.588
Brazil
1.487 0.013 0.013 0.012 0.514 0.531 0.588
Korea
1.372 0.012 0.012 0.011 0.513 0.529 0.581Model 1cCountry
voteshare
SSISM
2/3
Inclusiveness3/4
SM
2/3
3/4
EU28
30.240 0.394 0.413 0.372 0.501 1.000 1.000
USA
15.888 0.137 0.153 0.190 0.501 0.986 1.000
Japan
7.276 0.069 0.056 0.062 0.502 0.556 0.958
China
2.336 0.020 0.019 0.019 0.501 0.534 0.609
Canada
2.270 0.020 0.018 0.019 0.502 0.532 0.604
Hong Kong
1.669 0.014 0.014 0.014 0.501 0.524 0.576
Mexico
1.535 0.013 0.013 0.013 0.502 0.521 0.571
Korea
1.469 0,013 0.012 0.012 0.502 0.521 0.569
Singapore
1.268 0.011 0.010 0.010 0.507 0.518 0.559
Taiwan
1.268 0.011 0.010 0.010 0.507 0.518 0.559
Table 5b: Voting Power Indices for Top Ten Countries withHighest Votes for Simple, 2/3rd, and 3/4th Majority RuleHypothesis 2Model 2aCountry
voteshare
SSISM
2/3
Inclusiveness3/4
SM
2/3
3/4
USA
