Voting by Count and Account:

 

Reconciling Power and Equality in International Organizations

 

 

Barry O'Neill

Center for International Security and Cooperation

Stanford University

 

and

 

Bezalel Peleg

Center for Rationality and Interactive Decision Theory

Hebrew University

 

August 2000

 

Abstract:  Organizations whose members are national governments face a recurring problem in choosing a voting mechanism: they need one that recognizes the greater power and contribution of the larger members while preserving some influence for the smaller ones.  Voting by count and account is suggested here as a good compromise between power and equality.  Passing a motion requires both a majority by numbers and a majority by some weight of importance, like financial contribution.  It avoids certain surprising counterintuitive results produced by other systems now used to give some power to small states, such as weighted voting.  For international organizations it is the natural analogue of a two-house system. 

 

Changing the voting methods of an existing body is difficult, but we propose the method for newly-formed ones.  At the organization's founding it is easy to negotiate.  It symbolizes the accepted relationships of legitimate power in an international body better than current methods do, thus giving a decision more legitimacy.

 

 

The authors would like to thank Bruce Russett, Hana Shemesh and Benjamin Weiss for their help and suggestions, and Gideon Schwartz for naming the method.  We are grateful to William Thomson of the University of Rochester, and Robert Aumann of the Hebrew University, who passed the method on to us as one of interest and relevance.  Barry O'Neill would like to thank the Center for Rationality at the Hebrew University for its support and inspiring atmosphere.


 

Since the end of the Cold War, nations have set up more intergovernmental organizations and entrusted them with more tasks.  There are hundreds of institutions whose members are national governments, that monitor trade regimes and treaties, establish standards of measurement, conduct military actions, and perform other activities.  However, their increased importance has led to disputes over their voting rules.  The arguments have shown a recurring pattern, with rich states demanding more power because of their greater financial support, and poor states arguing for sovereign equality.  Intergovernmental organizations have used special voting methods to accommodate the rights of large and small; typically these are weighted voting schemes where the share of votes given to a small nation is out of proportion to its size but less than a large state's share.

            This paper advocates a different method, drawn from the responsa of the leader of a 17th century Moravian community.  We call it voting by count and account.   As will be discussed, the situation that prompted its use there is similar to that nations face now.

Voting by count and account is defined as follows: when a vote is taken, two tallies are made.  The first is simply the number of supporters, and the second is the sum of their weights.  A country's "weight" is some pre‑agreed‑upon objective quantity, most likely its financial contribution or “account,” but possibly its population or its degree of use of the organization's resources.  A motion passes only if it attains a majority by both count and account.

The first section discusses the conflict between the rights of large and small states in intergovernmental organizations.  The next section discusses the rule of count-and-account and shows its advantages.  It is then compared with other current methods that are meant to set a compromise between the rights of the two groups.  A first advantage is that it is easy to negotiate; a second is that it avoids many of the unintended consequences of other methods, which, in spite of their purpose, sometimes may increase the inequity.  The third advantage is its appropriate symbolism.  Like other voting methods it makes a symbolic statement about the legitimate social order of the intergovernmental organization, but unlike other methods its symbolism is correct.  The proper symbolism makes a decision more legitimate in the minds of those who will carry it out.

 

1. Large versus small in international bodies

 

Egalitarianism and power come into conflict in all types of political interactions ‑‑ in setting up a municipal council or combining provinces into a federal system ‑‑ but international bodies face it most severely.  There are 50,000 citizens of India to one Palaun, but in the United Nations each country has one vote.  Japan contributes 20,000 times as much to the regular UN budget as Cambodia, but each has one vote.  This is unfair, but it would be unfair to deprive Cambodia of a significant voice because of its poverty.  Disparities of wealth and population across countries are so great that if the larger or richer countries had voting weights in proportion, the small countries would have miniscule influence.  The large countries could impose their way by vote, violating the principle of sovereignty.  Big powers will inevitably apply pressure behind the scenes, but a world body needs fairness in its formal procedures.  Realpolitik assertions that large states should simply take control of world affairs are in fact unrealistic.  The small countries may be seen as negligible individually but they are considerable as a group, and in any case their participation is necessary for the organization's legitimacy.

The conflict of equality and power should not be seen as one of principle versus coercion, since the claims of the rich nations can also be grounded in fairness.  They should expect more say in the activities that they are funding.  Also, those states with larger populations are more affected by a typical international decision, simply because they have more people experiencing the consequences.  There are also practical reasons for giving the larger states greater voting power, since otherwise they may reduce their participation or use their influence behind the scenes to try to undo the group's formal decisions.  An organization's official decisions cannot depart too far from the underlying power relationships.

Disputes of large versus small often occur at the founding of the organization, one case being the International Fund for Agricultural Development, which saw obstructive debates about weighted versus unweighted voting (Zamora, 1980).  Controversies also arise in functioning organizations.  Concerning the United Nations, in 1985 the US Congress passed the Kassebaum Amendment, by which the United States would lower its contribution by one fifth unless the UN adopted weighted voting for budgetary matters.[1]  Since then, the conflict over control of the UN budget has steadily expanded and harmed the organization's effectiveness, especially in regard to peacekeeping.  Voting issues also arise when new members are admitted to an international body: the small‑versus‑large tension has been central in the debate over expanding the European Union.

 

 

 

2. Voting by count and account

 

Voting by count and account takes into consideration both size and equality and does so in a simple way.  Votes are counted twice, first with each party weighted equally, and then with each weighted by its financial contribution or some other objective measure.  A proposal passes if it gets a majority in both ways.  The rule formalizes the idea that an organization should act only when it has the support of both the general membership and the important members.       

The method came to our attention through a legal decision rendered in a 17th Moravian community.  In 1635 Rabbi Menahem Mendel Krochmal moved from Krakow to Kremsier to take up his post, and the congregation brought a dispute to him for his judgement.  In an election for a shamash, a position much like a church sexton, forty of the forty‑five members had voted for one candidate, but the five in opposition comprised a rich man, his two sons and two sons‑in‑law, and together they contributed 60% of the tithes.  By a longstanding rule in the community, a candidate needed a majority of both people and money.  The supporters wanted Rabbi Krochmal to set this rule aside as unfair and unworkable.  Rabbi Krochmal upheld it, however, on the grounds that it was established custom, and also because it had a basis in justice, since those who would pay more for a post deserved a greater say.[2]

Rabbi Krochmal argued for the method on grounds of justice, that the majority deserved influence but so did those who will pay for the shamash.  He referred the method as deciding by a majority of minyan and a majority of binyan, of numbers and of structure.  His phrasing drew on a certain analogy: as used in the Talmud, the words relate to the issue of when incomplete human remains legally constitute a person's body.  Is it sufficient to have just a numerical majority of the bones, the minyan?  Or does it matter that the main parts of the structure, the skull, backbone and hips, etc., which form the binyan, be found?  In the community of Kremsier the general membership provided the numbers and the rich members provided the structure.

A number of double‑criterion rules are in use, but it is important to distinguish them from count-and-account.  Swiss referenda require a majority of population and a majority of cantons.[3]  Many countries use a system of two legislative houses ‑‑ a typical bill in the US Congress requires a majority of both the Senate, where states have equal representation, and the House of Representatives, where the delegation increases with the state's population.  Other voting rules add a quorum‑like requirement: to change property taxes in the state of Oregon, 50% of the voters must turn out and 50% of these must support the proposal.  These methods seem like the one advocated here, but they are not the same.  They do not have the feature that each member votes only once and that vote is counted twice, unweighted and weighted.  The Swiss referendum counts the choices of the voters, but then counts where the cantons stand on the issue, although the cantons do not literally vote.  The typical bicameral system is also different, since a US Senator and a member of the House from the same state can vote in opposite ways.  A bicameral system would make no sense internationally since the delegates would have the same instructions from their capitols and would vote identically in the two houses.   For the intergovernmental context, the reasonable analogue of two houses is count-and-account.

 

3. Advantages of international voting by count-and-account

 

The argument for using count-and-account internationally involves three considerations.

 

Ease of negotiation

 

Its first advantage is its ease of negotiation.  At an organization's founding parties must decide on the rules, and the 50% criterion is especially prominent.  It would be hard for some critic to come up with a counterproposal that is really persuasive, such as increasing or decreasing the majority.  Since the 50% rule is most natural, that proposal is less likely to lead to haggling.[4]

A few voting bodies have used systems that are like count-and-account, but, oddly, none seems to have set the quota at 50%.  In the OPEC Special Fund, which was founded in 1976 to finance development in non‑oil‑producing countries, support for a motion must include at least 2/3 of the members who represent at least 70% of the contributions to the Fund (Zamora, 1980).  The 1982 formula for amending the Canadian Constitution required "resolutions of the legislative assemblies of at least two‑thirds of the provinces that have, in the aggregate, according to the then latest general census, at least fifty percent of the population of all the provinces" (Kilgour and Lebesque, 1984).  The Montreal Protocol on Substances that Deplete the Ozone Layer set goals for decreased production and consumption of controlled substances.  The goals to be achieved by 1998 were amendable by a two‑thirds majority of the voting parties, representing two‑thirds of the total consumption.  In the Global Environmental Facility, an agency of the World Bank founded in 1993, a motion must be approved by at least 60% of the countries representing 60% of the contributions.[5]  In the Council of Ministers of the European Community, countries are assigned voting weights from 2 votes up till 10, roughly on the basis of their size, and certain motions, those that were not proposed by the Commission, require approval by 10 countries out of 15, with a combined voting weight of 62 out of the total 87 (Hosli, 1996).[6]

       These methods are like count‑and‑account except for their higher majority quotients.  The history and background of these groups suggest that the designers wished to build in inertia for certain kinds of motions that changed the status quo, so they included the double majority criterion and raised the majority quotient above 50% as well.  Our view, however, is that the double 50% rule has a much broader use – it is appropriate for the regular work of the organization, in place of the a simple majority by count.  One might worry that adding a second majority would make motions harder to pass and hamper the group, but our studies indicate that the rule is only slightly more conservative than the regular simple majority unless the organization is significantly polarized between large and small.  (This issue will be discussed shortly.) 

            The argument about negotiability of the 50% rules is somewhat circular, since it is based partly on its innate salience but also on precedent.  The more groups that are using it, the more acceptable it will become for further adoption.

 

 

Transparent simplicity

 

The purpose of count-and-account is to require assent both from the masses as well as those countries that supply the resources.  It is clear that it implements this goal and it is clear how it implements it.  Other rules that address the problem seem simple enough but they conceal unacceptable flaws; as will be shown below, some may actually diminish the power of the small countries they mean to help.  However, this phenomenon cannot arise in voting by count and account.  According to a reasonable measure of voting power, the rule always distributes power among the members more equitably than a voting rule based purely on weight (e.g., based on financial contribution.)[7]

The most common way that international organizations have tried to reconcile the claims of small and large states, is by assigning assign weights to countries and declaring a motion passed if its supporters have a majority of the total weight.  The weights increase with some quantity like size or financial contribution to give large members more power, but they are not in strict proportion to the quantity.  Small countries get more than their share.  In the European Community Council of Ministers, for example, 10 votes are given to the UK, Germany, France and Italy, 2 to Luxembourg, and the rest of the fifteen lie in between.  The votes increase roughly with population, but not in proportion or Luxembourg would get near zero.

In the Council of Ministers voting weights are assigned more or less by negotiation, case by case, but other bodies set the weights by rules.  The most common system internationally is that of basic votes.  The total weight is divided into two portions, part being divided equally among the members and the other assigned in proportion to size.  As a consequence the small members receive less than average weight, but more than a share based on size alone. 

The system of basic votes is especially common in two kinds of international organizations: those for commodity regulation, like the International Sugar Council and the International Jute Council, and international banks and development funds, like the International Monetary Fund, the World Bank and the Inter‑American Development Bank.  In the commodity organizations, the total votes are often divided equally between exporters and importers, for example, 1000 votes to each group with 100 votes distributed equally within a group, where passing a motion requires a simple or two‑thirds majority from both groups.

One difficulty with basic votes is the arbitrariness in deciding what proportion to set aside for equal division.  This issue must be negotiated at an organization's founding and can stall an agreement.  Large states will want few votes to be basic and small states want more.  Unless the group is willing to divide the votes 50/50, i.e., basic votes equal to proportional votes, there is no prominent split that makes for a natural agreement.   A basic vote proportion of 50% is more generous than the large states have been so far, and typically the share has been set so low that the small states get negligible benefit.  This consequence is most striking in organizations that give a fixed number of basic votes to each member and divide the rest by the nominal dollar values of the members' contributions (in contrast to rules that keep the basic votes at a fixed fraction of the total votes.)   If the total contributions to the organization go up, then the proportion of basic votes will fall.  In some groups the basic votes have drifted down to insignificance due to inflation, the growth of the organization or of the world economy.  In the IMF, for one, the basic vote proportion started at 11.15%, and increased early on as more countries joined.  However inflation and economic growth overwhelmed this trend, and the basic votes are now about 2% of the total and gives no more than a nod to equality.  The history of the Inter‑American Development Bank (IDB) is even more extreme, starting at 3%, and falling to .07%.  Some international banks have a significant proportion of basic votes, like the African Development Bank, at 45%, but these are typically ones with no predominant wealthy members.  They have tended to be less effective in promoting development, precisely because they lacked large and rich contributors.

A second difficulty of basic votes is a fundamental conceptual one ‑‑ they sometimes do not accomplish what they are supposed to.  They can give a small country more voting weight but less power.  In order to show this, it is first important to distinguish voting weight from power.  These concepts are often treated as synonymous but are not ‑‑ a member's real power can be different than its weight.  Consider a three‑member committee with weights 1, 3, and 3, where a motion needs a simple majority of 4 out of 7 to pass.  It is easy to see that each member has equal power since any two are necessary to win, so the larger two voters should not feel that their larger weights give them more power.  Suppose, however, that the majority quota is raised to 5 out of 7.  Then the power of the 1‑vote player disappears ‑‑ there is no configuration of support where it can make a difference.  The example shows that voting power depends on more than one's own weight, that it is also influenced by the weights of the other members and by the majority quota.

Because of the distinction between voting weight and voting power, introducing basic votes can sometimes decrease the power of the smaller players.  Consider an organization of five members where their accounts are in the proportions 3: 4: 4: 4: 10.  When 100 votes are divided by the accounts, the members receive the following weights:       

(1) 100 votes allocated proportional to account: 12, 16, 16, 16, 40.

Now introduce a system of basic votes, where 25 votes are divided equally and the remaining 75 are allocated in proportion to account.  Simple arithmetic gives the following weights:

(2) 25 votes shared equally and 75 by account: 14, 17, 17, 17, 35.

(For example, the largest member gets 5 of the basic votes plus 10/25 of the 75 proportional votes, or 35 votes in all.)[8]

            Here introducing basic votes wipes out the power of the small voter.  Assuming that 51 votes are needed to pass, in the original arrangement (1) the small voter had some power.  It could combine with the 40‑vote member, or with all three 16‑vote members to make a majority.  In (2), however, the small voter has no power.  Power means making a difference, and there is no group the small voter can join and change a loss into a win.  It can no longer put the large voter over the top, since the latter has become weaker, and the middle three voters now have more weight and can produce a majority without the small one.  Power here is different from weight since it depends on the details of possible alliances, and basic votes have removed those possibilities for the small state.

Of course, some members might abstain on a motion and this event would give the smallest state a role again.  Abstentions often occur on issues that are less significant, or sometimes they are devices to avoid committing oneself on an important issue.  However, the small states would probably not find it appealing that the method gives them power only in situations when others do not want to vote.

This example is constructed to show that basic votes may fail to achieve their goal.  This result is only a possibility, and such examples become quite unlikely when the group is large, since large groups allow so many configurations of support and opposition that there is usually some way a small player can make a difference. [9]  However, the example should be a warning that the relationship between voting power and weight is subtle.  Even if introducing basic votes does not rob a small player of all power, it may do less or more than was intended. 

This phenomenon cannot happen under voting by count and account.  According to a theorem of Peleg (1991), the method always distributes power at least as equally or more so than voting purely by account.  (Peleg also showed the “dual” result, that it is at least as favorable to the large states as voting purely by count.) 

A more general method of guaranteeing a voice to the smaller nations is to introduce a voting floor, where a country, however small, receives some minimum voting weight.  In the EC Council of Ministers, for example, Luxembourg receives two votes, although a proportional rule would put it at almost zero.

Voting floors can be accused of arbitrariness in setting the minimum level of votes.  Also, as with basic votes, adding a floor can have unexpected consequences for power -- in particular, it may sometimes help the largest member.  Although one can expect that a floor will help those who are raised to the floor, their added power can come from those just above their size, even though the latters' votes have not changed.  To illustrate this possibility, consider a body of four voters with weights 1, 2, 2, and 6, which as usual, we assume are determined by their size or account.  Assuming a majority quota of 2/3, a motion passes if it gets 8 votes.  Note that the smallest voter has no power.  If we now set a floor of 2 votes then the weights become 2, 2, 2, and 6, and the two‑thirds majority quota stays at 8.  The smallest member can now make a significant alliance, but with more 2‑vote members available, it is easier for the 6‑vote member to find an ally.  Equivalently, there is stiffer competition among the two original 2‑vote members to be the ally of the large voter, so they are less able to demand a lot for their support.[10]  Adding the floor increases the power of the 6‑vote member and reduces the power of the two existing 2‑vote members.  The original 1‑vote player does indeed acquire some power, but it comes from the middle states, with the large voter actually gaining power from them as well.  Here the floor system helps the poor and the rich by taxing the semi‑poor.  Examples like these cannot be generated for count-and-account.

 

Correct symbolism

 

A final grounds for using the method is less precise but probably more important: voting by count and account embodies the correct symbolism for the public decisions of an international organization.  Accordingly it gives a vote more legitimacy.

One type of symbolism is based on analogy (described as “focal symbolism,” O'Neill, 1999).  The symbol and the larger idea being symbolized have a similar structure, onlookers note the similarity, they know that others are noticing it, and they form mutual expectations about how they will act on the important matter being symbolized.  The Berlin Wall, for example, became a prominent symbol for the Western nations during the Cold War.  It was seen as dividing East and West Berlin, imprisoning those behind it, analogous to communism's division of Europe into free and oppressed peoples.  Recognition of this in the West increased expectations of an anti‑communist stance.  In another example, Handelman (1990) describes the symbolism of Israel's memorial day at the Western Wall.  The participants include the nation's president, the chief rabbi of the Israel Defense Forces, soldiers, members of bereaved families, and others.  Further symbolic elements involve the flame to represent the war dead, the flag standing for the modern state, and the Western Wall to recall the tradition of the Jewish people.  The ceremony has these elements interact in a way that that models the proper relationships among the represented groups and ideas.  It reaffirms those relationships, and makes the audience more aware of the basis of their social bond, and as a public event, more confident that the rest are aware of it.

When an important deliberative body takes a public vote, it has an opportunity to assert its structure and ideals, to reinforce the general order of the group.  The body also gives legitimacy to the particular decision being voted for, by reminding the group that the decision is being taken according to the accepted structure.  One example is the bicameral system of the United States where the vote in the Senate, in which states are represented equally, expresses the equality of their rights in the federal system.  At the founding of the International Monetary Fund, a motive for including a small number of basic votes rather than assigning voting weights strictly by financial contribution, was symbolism, according to Gold (1981), to avoid having the Fund look like a corporation with stockholders.

The voting rules of the United Nations Security Council show attention to this symbolism of analogy.  A motion requires a majority of 9 of 15 members that includes all the Big Five permanent members.  Several authors have noted that the system can be restated as based on voting weights and a supermajority.  If the Big Five had seven votes each and the other ten states had one vote each and if the majority were 39 out of the total 45 votes, then the same motions would pass and the same would fail.  These are two equivalent ways of describing what is, in the abstract, the same voting rule.  Symbolically, however, they are different.  The first way of putting it, the qualified majority, is the prevalent and officially accepted one.  It symbolically states that both the small and especially large states must concur in a Security Council action.  The alternative way of stating the rule seems to suggest that some nations are several times as important as others, and the key is to get a sufficient weight of support behind a proposal.  This formulation is politically unacceptable.  Nor is another popular way of putting the rule, that each of the Big Five has a "veto," since this suggests that there are two groups, the small states and the large states, and the latter are given the right to frustrate the former's wishes.  The difference may be semantics, but calling the Security Council a "veto" system is not a wording that would appear in the most official United Nations documents, since it makes an inappropriate suggestion about the power and dynamics of the UN system. 

Any weighted voting scheme is symbolically inappropriate for an international assembly.  It suggests that the nations have different importances according to their voting weights.  It fails to recognize the principle that all nations are equal in one important sense, sovereignty.  Voting by count and account, however, includes the latter principle, since one of the two tallies treats all nations alike.

Another aspect of symbolism is important for international voting rules ‑‑ the meaning of the rules within the body.  There are two broad classes of international organizations (Zamora, 1980).  Some make mostly declarations of principle and advisory pronouncements, usually to establish or reinforce international norms, while others make decisions that are directly implemented.  The former usually function by one country/one vote, while the latter tend to have voting rules that consider size.  In the latter, the voting system is often present but in the background, and decisions are made by the "sense of the group," sometimes called consensus.  However it is understood that this does not mean unanimity nor it does not mean equality of influence.  The group forms expectations of whose support is important for various decisions, and they do so largely on the formal voting rules.  The voting rules symbolize the power and expected role in decision-making of the different members, even though they are almost never used.

This argument, then, says that voting rules are symbolically important even when votes are rare.  In this case, voting by count and account gives more appropriate symbolism of the power relation in organizations.  It suggests that countries have two sources of importance ‑‑ their contribution and their sovereign equal status as states.  These two are incommensurable, so they should not be lumped together as a single weight.

 

4. Is count-and-account too conservative?

 

Voting by count and account is necessarily more conservative than using a straight majority or the account weights alone, since two criteria have to be satisfied rather than one and fewer resolutions get passed.  This can be seen either as a disadvantage of the method – it might block a useful action – or as appropriate – it might stop the assembly from trying to implement measures that crucial parties oppose.  The question is: How much would it reduce the proportion of motions passed?

 

         To estimate the decrease, one can look introduce count-and-account hypothetically in some international bodies.  The results will depend on what kinds of motions come before the body, and a plausible model is this: each motion that comes up has a certain "popularity" p, which is some number randomly and uniformly selected between zero and one; each member votes for the motion with a probability equal to its popularity, and given the popularity p, members’ votes are otherwise independent of each other.  A computer simulation repeatedly can bring forward imaginary motions and determine the proportion that would get through under a given voting system.15

         The Inter‑American Development Bank has forty-six members with votes weighted almost entirely by their contributions.  The weights range from a few thousand up to about 2.3 million votes for the United States.  Under a simple weighted majority, about half the motions pass; under count-and-account, about 42% pass.  The decrease is slight.  An example with even more inequality was COMECON, the Council for Mutual Economic Assistance of the former socialist bloc.  In 1969 the contribution of the Soviet Union dominated, at 64.3% of the fund, the next largest being Poland at 8.3%.  Formal voting was evidently by one nation/one vote (Szawlowski, 1976), however.  If one were to hypothetically add the majority-of-account requirement, the rate of motions passing would decrease from 45% to 36%.16  Thus, count-and-account tends to be more conservative when the weights have greater variance, but even in an extreme case it does not paralyze the organization.

In this model voting is determined by the motion’s popularity, and there is no systematic opposition between large and small voters.  To look at the latter case, one can use the votes recorded in the United Nations General Assembly from 1945 to 1996.  We divide the period into five approximate decades, and use the list of about 4300 roll calls from Gartzke, Jo and Tucker (1999) and the financial contributions of each member for each decade, to determine what proportion of the votes would get through under the actual system of majority rule and under count-and-account.

 

 

 

 

Period

 

 

Proportion of motions passed by majority

 

 

Proportion of motions passed

 by C&A

 

 

 

 

Difference

1945 - 1955

.775

.671

.104

1956 - 1965

.907

.777

.130

1966 - 1975

.853

.578

.275

1976 - 1985

.997

.672

.325

1986 - 1996

.962

.576

.386

 

Table 1. Proportion of motions passing the General Assembly in fact (simple majority) and using count-and-account.

 

The table shows a systematic trend, a uniformly growing difference from adding the criterion of a majority of account.  At the beginning changing the rule would have made little difference, only about 10% fewer would have passed, but by the 1986-1996 period the small and large nations were at odds and about 40% fewer would have passed.  The decrease would not necessarily have been bad, since if these resolutions are to be more than declarations, they need wide support.  Also, the United Nations might have avoided its financial crisis, if the United States had not felt spited by the General Assembly majority.

These numbers have to be taken with a qualification: if the voting system had been different, different resolutions would have been introduced.  Also we are not suggesting that the General Assembly switch to this method – whatever its merits, a change would be politically very difficult.  The emphasis should be on incorporating it in newly-formed bodies

In summary, the following general statements seem to hold.  For an unpolarized voting body, introducing count-and-account does not drastically reduce the rate of passing motions.  The reduction is greater when contributions across members are very unequal, and it is especially great when large members are set against the small.  However, if fewer motions pass in the latter case represents, the method is doing what it is supposed to do.

 

5. Conclusion

 

For decision‑making within a democratic state, a tried method is a two‑house system.  Voting by count and account is its analogue for intergovernmental organizations.  It tends to equalize power compared to straight voting by account, but still gives larger states appropriately greater power.  Compared to current systems of voting by assigned weights, it is less arbitrary, easier to agree on, and avoids certain perverse consequences where an attractive‑seeming set of voting weights leads to greater inequality.  Also it projects the correct symbolism, both within the voting body and to the world. 

It is curious that a voting scheme retrieved from the 17th century would have international uses today, but some aspects of Rabbi Krochmal's context suggest that this is more than coincidental.  In a modern urban community if someone feels that their city council is trampling on their rights they can appeal to the court system.  However, Rabbi Krochmal's community had to find a way to avoid this.  If a discontented party resorted to the higher authority, namely the state, it would cause a bitter division and threaten the community's autonomy.  A decision method was needed that would select a compromise between the elements and avoid higher appeals.[11]  The international system is like Rabbi Krochmal's community, since there is no higher authority.  One needs a method where the group acts only when there is wide agreement.

 


References

 

Salo Baron. Membership and Elections. Ch. 10 in The Jewish Community, Its History and Structure to the American Revolution. Philadelphia: Jewish Publication Society of America. 1942.

 

Erik Gartzke, Dong-Joon Jo, and Richard Tucker.  1999. “UN General Assembly Voting, 1946-1996.”  Version 2.0, at website http://www.vanderbilt.edu/~rtucker/data/affinity/un/assembly

 

Joseph Gold. The Origins of Weighted Voting in the Fund. Finance and Development. 18, 25‑28, 1981.

 

Donald Handelman. Models and Mirrors: Towards an Anthropology of Public Events. Cambridge: Cambridge University Press. 1990.

 

Madeleine Hosli. Coalitions and Power: Effects of Qualified Majority Voting in the Council of the European Union. Journal of Common Market Studies. 34, 255‑273, 1996.

 

Marc Kilgour and Terence Levesque. The Canadian Constitutional Amending Formula: Bargaining in the Past and the Future. Public Choice. 44, 457‑480, 1984.

 

Menahem Mendel Krochmal. Semeh Sedek. Amsterdam, 1675.

 

Barry O'Neill. Honor, Symbols and War. Ann Arbor: University of Michigan Press. 1999.

 

Bezalel Peleg. Voting by Count and Account. Pp. 45‑51 in Reinhard Selten, ed. Rational Interaction. Berlin: Springer‑Verlag. 1991.

 

William Riker and Lloyd Shapley. Weighted Voting: A Mathematical Analysis for Instrumental Judgements. Nomos. 9, 1966.

 

Richard Szawlowski. The System of the International Organizations of the Communist Countries. Leyden: Sijthoff. 1975

 

Stephen Zamora. Voting in International Economic Organizations. American Journal of International Law. 74, 566‑608, 1980.

 



[1] The amendment put the discontents of the Congress succinctly, reading in part (Foreign Relations Authorization Act, Fiscal Years 1986 and 1987, Section 143, p. 21):

 

(a)  Findings ‑ The Congress finds that the United Nations and its specialized agencies which are financed through assessed contributions of member states have not paid sufficient attention in the development of their budgets to the views of member governments who are major financial contributors to these budgets.

 

(b)  Voting Rights ‑‑ In order to foster greater financial responsibility in preparation of the budgets of the United Nations and its specialized agencies which are financed through assessed contributions, the Secretary of State shall seek the adoption by the United Nations and its specialized agencies of procedures which grant voting rights to each member state on matters of budgetary consequence.  Such voting rights shall be proportionate to the contribution of each such member state to the budget of the United Nations and its specialized agencies.

 

[2] Consistent with his reputation as a defender of the poor, Rabbi Krochmal found a way around the rule in the particular case.  The fund that paid the salary of the shamash came in part from a per‑person contribution, and the masses of the congregation had given a greater amount to the source of the salary than their usual proportion.  Based on his calculations, which he included in his written judgement, their candidate had the support of most of the people and most of the money, and could be installed.  A further responsa in the volume (#84) clarifies his thinking ‑‑ he supported a voice for the poor on the grounds that even though their contribution was small, they made a greater sacrifice in rendering it.

 

[3] A similar system has been in use in Australia since the last century where a proposal must get a majority of the whole population, plus win a majority in a majority of the states.  A version in which specified constituencies must give their support has been introduced in Canada to increase minority representation.

[4]  There is nothing unworkable about a rule that raises one or both majority quotas above 50%, or, if one quota is at 50% or more, that sets the other at a lower value.  However if both are below 50%, problems arise since two opposing factions might both be winning.

 

[5] This procedure adds a complication in that countries group together into constituencies to put members on the Council, and a Council member can then cast the total voting weight of its group.

 

[6] One proposal for voting by count and account is for the European Council of Ministers, a 1994 document from Germany’s Christian Democratic Party suggesting its use based on count of countries and by size of population.  France opposed the plan at the 1997 Intergovernmental Conference ‑‑ Germany and France have equal votes now and the change would advantage Germany, which is more populous.  The episode shows that it is easier to get a rule adopted in the founding discussion than to change the system in place.

 

[7]  Peleg's result extends to systems in which the majority quota may differ from 50%.  He used the Shapley‑Shubik index, which is regarded by many as the best measure of voting power due only by the constitutional rules of the body.

[8]  An equivalent definition of basic votes involves moving each voter one quarter of the way from its original set of weights towards equal weights, where here each of the five gets 20 votes.

[9] In most organizations with large memberships, power is more or less proportional to weight, with a slight relative advantage held by the larger players (Riker and Shapley, 1966), unless voting weights are carefully set up to avoid this result. 

 

[10] The Shapley‑Shubik index of voting power reflects this argument.  In the original game the players' respective values were 0, .167, .167, and .667; in the game with the floor, they are .083, .083, .083, and .75, indicating that the greater power of the big and small players comes at the expense of the middle ones.

     15 This model is not a good description of the surface behaviour of the Council or other body.  It suggests that half the motions will fail, but in recent years only about 15 - 20% have failed and in fact only about 20 - 25% have received any negative votes at all (Lane and Mattila, 1998).  One should not require a numerical matching, however, since the goal is to fit to the real power relationships, where a motion not be expected to pass would usually not be brought to a vote.  Conversely nations see no point in casting a formal negative vote against a motion that they know will pass.

     16 Another example of the consequences of adding a second majority comes from the Council of Ministers of the European Union   It is real, but not purely the method advocated here, since supermajorities are required for both count and by weight and the weights correspond to no real property.  The range of weights is relatively small: Luxembourg has two votes and the four large powers ten votes (Table 1).  A motion requires 62 out of 87 votes for passage.  Under the model, about 31% of the motions would pass.  For motions not arising as proposals from the European Commission, another requirement is necessary -- the support of 10 out of the 15 countries.  The system is in effect, count-and-weight with a supermajority.  The addition of the "10 of 15" requirement is almost superfluous, since it is very unlikely that a motion will get a total weight of 62 without that.  Again about 31% of motions pass -- the decline is negligible.

[11] On issues of setting taxes, conducting elections, or representation on deliberative bodies that perform assessments of wealth, a strong tradition in rabbinical judgements has been to follow whatever rule was in place in the particular community (Baron, 1942).  One should not raise arguments from the law to indicate the community has been doing it wrong, or insist on justice grounds that the community must adopt the method used elsewhere.  On matters of allocation of resources and power within the community, the prime precept is not to disturb whatever has been working.