Maurice Duverger, in Party Politics and Pressure Groups
(New York: Thomas Y. Crowell, 1972), pp. 23-32.

The Technical Factor: The Electoral System

To these socio-economic and historical factors a technical factor must be added: the electoral system. I expressed its effects in 1946 in the formulation of three sociological laws: (1) a majority vote on one ballot is conducive to a two-party system; (2) proportional representation is conducive to a multiparty system; (3) a majority vote on two ballots is conducive to a multiparty system, inclined toward forming coalitions.

The brutal finality of a majority vote on a single ballot forces parties with similar tendencies to regroup their forces at the risk of being overwhelmingly defeated. Let us assume an election district in which 100,000 voters with moderate views are opposed by 80,000 communist voters. If the moderates are divided into two parties, the communist candidate may well win the election; should one of his opponents receive more than 20,000 votes, the other will be left with less than 80,000, thereby insuring the election of the communist. In the following election, the two parties with moderate views will naturally tend to unite. Should they fail to do so, the weaker party would gradually be eliminated as a dual consequence of “under-representation” and “polarization.” Under representation is a mechanical phenomenon. Elections determined by a majority vote on one ballot literally pulverize third parties (and would do worse to fourth or fifth parties, if there were any; but none exist for this very reason). Even when a single ballot system operates with only two parties, the one that wins is favored, and the other suffers. The first one is over-represented–its proportion of seats is greater than its percentage of the votes-while the party that finishes second is usually under-represented–its proportion of seats is smaller than its percentage of the votes. The English, with their two-party system, have expressed this phenomenon by the law of the cube: the relationship in the percentage of seats held by the two parties would be equal to the relationship of the cubes of the percentages of the votes received (if a and b are the percentages of the votes, and a’ and b’ the percentages of theseats, then we find that a’ / b’ = a3 / b3).

[Janda’s note: The cube law attempts to predict the percentage distribution of seats won in parliament from the percentage distribution of the electoral vote in a two-party system. If the parties divide the vote 50-50, each would win 50% of the seats. But as a party’s vote increases over 50%, the percentage of seats won is not linear, but curvilinear. That is, each percentage point advantage in vote won yields more than one percentage point increase in seats won. This curvilinear relationship can formulated mathematically. The ratio of seats won equals the ratio of the cubes of the votes won.]

When there is a third party, it is even more under-represented than the second. The gap is generally quite large, with the proportion of seats far below the proportion of the votes received. In 1964, the British Liberal party received 11.2 per cent of the votes cast, but only 1.4 per cent of the parliamentary seats. This under-representation tends to eliminate the effects of any votes cast for a third party. But voters are aware of this phenomenon. They also know that a division of votes between two parties holding similar views favors their common adversary. In the case mentioned before, the moderate voters would see clearly that a split between the moderate candidates guarantees a Communist victory: in a subsequent election they would drop the weaker of the two moderate candidates. Thus it is that voters tend to abandon the third party in order to concentrate their votes on the two strongest parties. This tendency toward polarization, a psychological phenomenon, strengthens the mechanical factors conducive to a two-party system.

In a system of proportional representation, the situation is quite different. The very principle of proportional representation explains the multiplicity of parties it produces. Since every minority, no matter how weak it may be, is assured of representation in the legislature, nothing prevents the formation of splinter parties, often separated only by mere shades of opinion. If the conservative party has 6 million votes in the country, corresponding to 300 seats in parliament, and if it splits into three groups about equal in numbers, proportional representation will give each of these about a hundred deputies, and the conservative family will have the same strength in parliament. In other respects, this electoral system does not encourage parties to unite. A coalition is useless from an electoral point of view since the entire system tends to permit everyone to take his chances at the polls.,Hence the reciprocal independence of the political parties.

In a system in which elections arc decided by a majority vote on the second of two ballots, political parties are numerous because the existence of a second ballot permits each party to test its chances on the first one without risking irrevocable defeat through the splintering of parties holding similar views; the regrouping occurs on the second ballot through the game of “withdrawals.” Let us again use the illustration of an election district in which the conservatives have 100,000 voters and the communists, 80,000. If the conservative electorate divides into two parties, with the first receiving 60,000 votes and the second, 40,000, while the communists vote as a bloc on the first ballot, there will still be a second ballot. For the second round, the weaker conservative candidate will withdraw. His supporters will switch their votes to the stronger candidate, who will normally be elected. New parties can thus multiply, but they are usually driven to form alliances with one another to check their opponents by means of “retreats” and “withdrawals.” The second ballot is essentially a voting by coalitions, as was seen in France during the Third Republic and in Imperial Germany, the two large countries that have practiced this system.

Although the preceding laws have been much discussed, often in heated debate, they have never been seriously challenged. The criticism directed against them has not questioned the reality of the phenomenon they express, which is fairly obvious, as much as the precise extent of its influence. It is clear that an electoral reform by itself will not create new parties: parties are a reflection of social forces; they are not born of a simple legislative decision. We can be sure that the relationship between electoral systems and party systems is not something mechanical and automatic. A given electoral regime does not necessarily produce a given party system; it simply exerts an influence in the direction of a particular type of system; it is a force, acting in the midst of other forces, some of which move in an opposite direction. It is also clear that the relationship between electoral and party systems is not a one-way phenomenon; if a one-ballot vote tends toward a two-party system, a two party system also favors the adoption of a single ballot voting system.

The exact role of the electoral system seems, in the last analysis, to be that of an accelerator or that of a brake. An election by a majority vote on a single ballot has a dual effect: first, it poses an obstacle to the appearance of a new party, although this obstacle is not insurmountable (the role of a brake); secondly, it tends to eliminate the weakest party (or parties) if there are more than two (the role of an accelerator). The braking effect was noticeable in Great Britain at the end of the nineteenth century, in the face of a socialist drive, and again after World War 1, in the face of communist and fascist movements. The accelerating effect was even more apparent in the case of the Liberal party, which was practically eliminated in fifteen years (1920-35), although it retains a certain number of supporters who are compelled by the electoral system to choose between Conservatives and Labourites. Deciding by a majority vote on one ballot accelerated in Great Britain the substitution of a two-party system for any other kind.

Proportional representation plays just the opposite role. It does not slow down the development of new parties. It passively registers their appearance, sometimes amplifying the vibrations they generate, like an echo chamber or a seismograph. (In order to check this tendency, proportional representation is rarely applied in toto; it is modified by such measures as permitting local districts to apportion residual votes and by establishing rules regarding the percentage of votes required to gain representation in the legislative assembly.) On the other hand, it retards the elimination of old parties which would otherwise tend to disappear as the social and political scene changes. The “salvaging” of the Belgian Liberal party through proportional representation, beginning in 1900, is a typical example of this phenomenon. Instead of giving way to a twentieth-century-style two-party system, the nineteenth-century system survived with the new system superimposed on it, producing an essentially three-party system (this was also the case in Germany and Austria), However, we must of course distinguish between old movements, deeply rooted among a portion of the population, and superficial movements reflecting temporary political moods or fashions. Proportional representation registers just as clearly the appearance as it does the disappearance of parties of this latter type. Typical examples were the case of “rexism” in Belgium, and, in France, the RPF [Rassemblement du Peuple Francais] in 1951, and Poujadism in 1956.

The results of the two-ballot majority system are similar to those of proportional representation, with a few differences. The two-ballot system seems to be more discouraging to the formation of new parties than proportional representation (but it is far less effective in this than the single-ballot majority vote). Perhaps it is also more helpful to older parties, but it is difficult to formulate any definite conclusions in this matter. Furthermore, it seems to present a certain barrier to brusque changes of political opinion, to movements reflecting momentary moods or impulses, to political groups that are “fashionable” but ephemeral (even though the example of the UNR [Union Nouvelle pour la Republique, the Gaullist party] in 1958 proved to be of a different kind: but the circumstances in this instance were very special). The sharpest difference with the system of proportional representation concerns electoral alliances, A coalition system par excellence, the two ballot regime can sometimes permit the formation of a dual system of alliances, introducing a sort of two-party system in the midst of a multi-party situation. This phenomenon was quite evident in France during the Third and the Fifth Republics, and in Germany from 1870 to 1914.

Having said all this, the fact remains that a change in the electoral system does not always have a decisive influence on the existing party system. However, it seems certain that if proportional representation were to replace the majority vote in Great Britain, a three-party system would appear before very long, making party splits within the ranks of the Labourites and the Conservatives much more likely. The influence of a one-ballot vote in maintaining an already established two-party system is beyond question. It is much less certain that the adoption of such an electoral system would destroy an already existing multiparty system and, for example, reduce to two the number of parties in France or Italy. In any event, a reform of this nature is inconceivable, because an election determined by a majority vote on a single ballot gives rise to unforeseen results when more than two parties are involved. Yet in the German Federal Republic and in Austria, such an electoral reform would very likely hasten the trend, already underway, toward a two-party system. Above all, it would prevent any move in the opposite direction by posing a serious obstacle to possible splits within the two major parties, and would also discourage the revival of small political parties.

Factors in a Two-Party and Multiparty System

Maurice Duverger, in Party Politics and Pressure Groups
(New York: Thomas Y. Crowell, 1972), pp. 23-32.

The Technical Factor: The Electoral System

To these socio-economic and historical factors a technical factor must be added: the electoral system. I expressed its effects in 1946 in the formulation of three sociological laws: (1) a majority vote on one ballot is conducive to a two-party system; (2) proportional representation is conducive to a multiparty system; (3) a majority vote on two ballots is conducive to a multiparty system, inclined toward forming coalitions.

The brutal finality of a majority vote on a single ballot forces parties with similar tendencies to regroup their forces at the risk of being overwhelmingly defeated. Let us assume an election district in which 100,000 voters with moderate views are opposed by 80,000 communist voters. If the moderates are divided into two parties, the communist candidate may well win the election; should one of his opponents receive more than 20,000 votes, the other will be left with less than 80,000, thereby insuring the election of the communist. In the following election, the two parties with moderate views will naturally tend to unite. Should they fail to do so, the weaker party would gradually be eliminated as a dual consequence of “under-representation” and “polarization.” Under representation is a mechanical phenomenon. Elections determined by a majority vote on one ballot literally pulverize third parties (and would do worse to fourth or fifth parties, if there were any; but none exist for this very reason). Even when a single ballot system operates with only two parties, the one that wins is favored, and the other suffers. The first one is over-represented–its proportion of seats is greater than its percentage of the votes-while the party that finishes second is usually under-represented–its proportion of seats is smaller than its percentage of the votes. The English, with their two-party system, have expressed this phenomenon by the law of the cube: the relationship in the percentage of seats held by the two parties would be equal to the relationship of the cubes of the percentages of the votes received (if a and b are the percentages of the votes, and a’ and b’ the percentages of theseats, then we find that a’ / b’ = a3 / b3).

[Janda’s note: The cube law attempts to predict the percentage distribution of seats won in parliament from the percentage distribution of the electoral vote in a two-party system. If the parties divide the vote 50-50, each would win 50% of the seats. But as a party’s vote increases over 50%, the percentage of seats won is not linear, but curvilinear. That is, each percentage point advantage in vote won yields more than one percentage point increase in seats won. This curvilinear relationship can formulated mathematically. The ratio of seats won equals the ratio of the cubes of the votes won.]

When there is a third party, it is even more under-represented than the second. The gap is generally quite large, with the proportion of seats far below the proportion of the votes received. In 1964, the British Liberal party received 11.2 per cent of the votes cast, but only 1.4 per cent of the parliamentary seats. This under-representation tends to eliminate the effects of any votes cast for a third party. But voters are aware of this phenomenon. They also know that a division of votes between two parties holding similar views favors their common adversary. In the case mentioned before, the moderate voters would see clearly that a split between the moderate candidates guarantees a Communist victory: in a subsequent election they would drop the weaker of the two moderate candidates. Thus it is that voters tend to abandon the third party in order to concentrate their votes on the two strongest parties. This tendency toward polarization, a psychological phenomenon, strengthens the mechanical factors conducive to a two-party system.

In a system of proportional representation, the situation is quite different. The very principle of proportional representation explains the multiplicity of parties it produces. Since every minority, no matter how weak it may be, is assured of representation in the legislature, nothing prevents the formation of splinter parties, often separated only by mere shades of opinion. If the conservative party has 6 million votes in the country, corresponding to 300 seats in parliament, and if it splits into three groups about equal in numbers, proportional representation will give each of these about a hundred deputies, and the conservative family will have the same strength in parliament. In other respects, this electoral system does not encourage parties to unite. A coalition is useless from an electoral point of view since the entire system tends to permit everyone to take his chances at the polls.,Hence the reciprocal independence of the political parties.

In a system in which elections arc decided by a majority vote on the second of two ballots, political parties are numerous because the existence of a second ballot permits each party to test its chances on the first one without risking irrevocable defeat through the splintering of parties holding similar views; the regrouping occurs on the second ballot through the game of “withdrawals.” Let us again use the illustration of an election district in which the conservatives have 100,000 voters and the communists, 80,000. If the conservative electorate divides into two parties, with the first receiving 60,000 votes and the second, 40,000, while the communists vote as a bloc on the first ballot, there will still be a second ballot. For the second round, the weaker conservative candidate will withdraw. His supporters will switch their votes to the stronger candidate, who will normally be elected. New parties can thus multiply, but they are usually driven to form alliances with one another to check their opponents by means of “retreats” and “withdrawals.” The second ballot is essentially a voting by coalitions, as was seen in France during the Third Republic and in Imperial Germany, the two large countries that have practiced this system.

Although the preceding laws have been much discussed, often in heated debate, they have never been seriously challenged. The criticism directed against them has not questioned the reality of the phenomenon they express, which is fairly obvious, as much as the precise extent of its influence. It is clear that an electoral reform by itself will not create new parties: parties are a reflection of social forces; they are not born of a simple legislative decision. We can be sure that the relationship between electoral systems and party systems is not something mechanical and automatic. A given electoral regime does not necessarily produce a given party system; it simply exerts an influence in the direction of a particular type of system; it is a force, acting in the midst of other forces, some of which move in an opposite direction. It is also clear that the relationship between electoral and party systems is not a one-way phenomenon; if a one-ballot vote tends toward a two-party system, a two party system also favors the adoption of a single ballot voting system.

The exact role of the electoral system seems, in the last analysis, to be that of an accelerator or that of a brake. An election by a majority vote on a single ballot has a dual effect: first, it poses an obstacle to the appearance of a new party, although this obstacle is not insurmountable (the role of a brake); secondly, it tends to eliminate the weakest party (or parties) if there are more than two (the role of an accelerator). The braking effect was noticeable in Great Britain at the end of the nineteenth century, in the face of a socialist drive, and again after World War 1, in the face of communist and fascist movements. The accelerating effect was even more apparent in the case of the Liberal party, which was practically eliminated in fifteen years (1920-35), although it retains a certain number of supporters who are compelled by the electoral system to choose between Conservatives and Labourites. Deciding by a majority vote on one ballot accelerated in Great Britain the substitution of a two-party system for any other kind.

Proportional representation plays just the opposite role. It does not slow down the development of new parties. It passively registers their appearance, sometimes amplifying the vibrations they generate, like an echo chamber or a seismograph. (In order to check this tendency, proportional representation is rarely applied in toto; it is modified by such measures as permitting local districts to apportion residual votes and by establishing rules regarding the percentage of votes required to gain representation in the legislative assembly.) On the other hand, it retards the elimination of old parties which would otherwise tend to disappear as the social and political scene changes. The “salvaging” of the Belgian Liberal party through proportional representation, beginning in 1900, is a typical example of this phenomenon. Instead of giving way to a twentieth-century-style two-party system, the nineteenth-century system survived with the new system superimposed on it, producing an essentially three-party system (this was also the case in Germany and Austria), However, we must of course distinguish between old movements, deeply rooted among a portion of the population, and superficial movements reflecting temporary political moods or fashions. Proportional representation registers just as clearly the appearance as it does the disappearance of parties of this latter type. Typical examples were the case of “rexism” in Belgium, and, in France, the RPF [Rassemblement du Peuple Francais] in 1951, and Poujadism in 1956.

The results of the two-ballot majority system are similar to those of proportional representation, with a few differences. The two-ballot system seems to be more discouraging to the formation of new parties than proportional representation (but it is far less effective in this than the single-ballot majority vote). Perhaps it is also more helpful to older parties, but it is difficult to formulate any definite conclusions in this matter. Furthermore, it seems to present a certain barrier to brusque changes of political opinion, to movements reflecting momentary moods or impulses, to political groups that are “fashionable” but ephemeral (even though the example of the UNR [Union Nouvelle pour la Republique, the Gaullist party] in 1958 proved to be of a different kind: but the circumstances in this instance were very special). The sharpest difference with the system of proportional representation concerns electoral alliances, A coalition system par excellence, the two ballot regime can sometimes permit the formation of a dual system of alliances, introducing a sort of two-party system in the midst of a multi-party situation. This phenomenon was quite evident in France during the Third and the Fifth Republics, and in Germany from 1870 to 1914.

Having said all this, the fact remains that a change in the electoral system does not always have a decisive influence on the existing party system. However, it seems certain that if proportional representation were to replace the majority vote in Great Britain, a three-party system would appear before very long, making party splits within the ranks of the Labourites and the Conservatives much more likely. The influence of a one-ballot vote in maintaining an already established two-party system is beyond question. It is much less certain that the adoption of such an electoral system would destroy an already existing multiparty system and, for example, reduce to two the number of parties in France or Italy. In any event, a reform of this nature is inconceivable, because an election determined by a majority vote on a single ballot gives rise to unforeseen results when more than two parties are involved. Yet in the German Federal Republic and in Austria, such an electoral reform would very likely hasten the trend, already underway, toward a two-party system. Above all, it would prevent any move in the opposite direction by posing a serious obstacle to possible splits within the two major parties, and would also discourage the revival of small political parties.