Erik Moberg ã:
A Theory of Democratic Politics


When stating his law Duverger wrote (1964, p 217, his italics) that "Only individual investigation of the circumstances in each country can determine the real origins of the two-party system. The influence of such national factors is certainly very considerable; but we must not in their favour underestimate the importance of one general factor of a technical kind, the electoral system. Its effect can be expressed in the following formula: the simple-majority single-ballot system favours the two-party system. Of all the hypotheses that have been defined in this book, this approaches the most nearly perhaps to a true sociological law."

Part of the controversies about Duverger's law are, I think, a consequence of his formulation that majoritarianism "favours" a two-party system. Since a law should be law this has been interpreted as a claim that majoritarianism leads to a two-party system. After that, since it is easy to find exceptions such as India and Canada, it is also easy to conclude that Duverger is just wrong. But that is hardly sensible. What can be claimed is that majoritarianism, in contrast to proportionalism, involves strong forces tending to reduce the number of political parties. From this, by thinking in terms of equilibrium processes and taking countervailing forces into account, it is perfectly reasonable to conclude that, on the whole, we should expect fewer parties in countries with majoritarian elections than in those with proportional elections. This is a strong and important statement, which is perfectly compatible with Duverger's text, and it is this statement which I here call Duverger's law.

Our main interest here concerns the mechanisms behind Duverger's law. Why, other things being equal, should we expect fewer parties in a majoritarian system than in a proportional one? Duverger himself answered this question by referring (p 224) to "a mechanical factor and a psychological factor". The first one consists in the pure mathematical effects of the application of the electoral rule - essentially the suppression of all parties but the biggest in each constituency. The second factor consists in the parties' and voters' reactions, and adaptations, to this suppression.

Duverger's idea about a mechanical and a psychological factor is of course perfectly reasonable even if the mechanisms behind the law can be described in a more detailed manner. In particular it is important to distinguish between the constituency level, where the important mechanisms work, and the national level where the result we are interested in is manifested. Duverger himself was well aware of this and wrote (1964, p 223) that "the true effect of the simple-majority system is limited to local bipartism."

Starting at the constituency level we can assume, as an example, that we have a constituency with five candidates representing the parties P1-P5 (as in the table below). Let us furthermore assume that these parties, in an imagined first election, get 30, 25, 20, 15, and 10 % of the votes respectively. We shall also assume that these votes reflect the real preferences of the voters, and that these preferences remain constant over time.

P1 P2 P3 P4 P5
30 % 25 % 20 % 15 % 10 %

In the first election P1 thus gets a plurality and its candidate will consequently represent the constituency in the legislature. That result may make P1 and its voters happy, but the other parties, and their voters, are hardly likely to repeat their behavior exactly in the ensuing elections. Various adaptations are likely to take place. Thus at least some of the voters, who are not satisfied by merely expressing their opinion, but really want to affect things, may change their votes from the most preferred party to their second or even third preference, if that party is considered better than the incumbent P1 and is also judged to stand a better chance than their first preference to beat P1. As the years pass, and the number of effectuated elections increases, this means that some parties, perhaps the initially smallest ones, will become still smaller, while a few, perhaps just two, main combatants will increase their vote support. In the long run the voters themselves, by departing from their initial first preferences, are thus likely to concentrate their votes on a few main combatants having real chances to win.

As for the parties and their candidates, assuming that they really want to take part in decision-making and thus are not content with just manifesting their existence, a corresponding behavior is likely. The parties, which remain small, and perhaps even decrease, as the years pass, are thus likely to withdraw from the competition altogether.

The combined behavior of the voters, and the parties, is thus likely to bring about a long term equilibrium with just a few parties, say two or three. If, at some time, there are considerably more parties than that, some of them are consequently likely to be eliminated in the long run.

After this the consequences at the national level may be considered. Let us assume that we have a country in which, initially, there are 10 parties. We shall also assume that all constituencies in important respects have the same properties. They thus have the same size, and the same patterns of political opinions. Initially all ten parties are thus represented in each constituency. After this we should thus expect, over the years and in each constituency, an equilibrium process of the kind described above. Since the constituencies have the same properties the process will be the same everywhere. Therefore, if it ends with for instance two parties in one constituency, it will end with the same two parties in each constituency, and thus also nationwide. In this case therefore, and due to the assumptions made, what happens in one constituency happens in the same way in the other ones, and consequently nationwide as well. Everywhere there is a reduction from 10 to two parties.

Things may however be different. Let us change the assumption that the constituencies have similar properties into its opposite, namely that all constituencies, due to important regional differences, are very different from each other. Let us also specify that there are five constituencies altogether. As for the rest everything is as before. From the beginning there are thus ten parties, which we may call p1-p10, all of which are represented in each constituency. Now, as in example above, and as the years pass, the number of parties will be reduced in each constituency. Since the constituencies are different in this example the reduction will however affect different parties in the different constituencies. We may for instance assume that, in the end, there will only be two parties in each constituency, and that these remaining parties are p1 and p2 in the first constituency, p3 and p4 in the second, p5 and p6 in the third, p7 and p8 in the fourth, and p9 and p10 in the final and fifth constituency. In this example therefore, and although the number of parties in each constituency has again been reduced from 10 to two, there is no reduction at all on the national level.

These two examples are, of course, extremes. What they have in common is that the number reducing process in the individual constituencies is the same in both cases, and the same as in the description of the mechanisms at the constituency level above. The difference is that in the first example, where all constituencies have the same properties, the national number of parties is reduced as much as the number in each constituency, whereas in the other example, where the constituencies are utterly dissimilar, the national number of parties is not reduced at all. In real situations, where there are some differences between different constituencies, but also a lot of similarities, the result is likely to be something in between. When the mechanisms operating in the constituencies reduce the number of parties there, the national number of parties is also likely to be reduced, but not as much as in the individual constituencies.

The discussion about the effects on the national level has, so far, only considered the logical effects of similarities, or differences, between constituencies. No further mechanisms other than the ones operating at the constituency level have been introduced. Mechanisms operating at the national level are, however, also imaginable. Economies of scale may for instance be important. The formation of parties, and of party opinions and positions, are thus likely to be demanding tasks requiring considerable basic investments which are independent of the number of constituencies involved. Therefore, and in order to make these investments pay off, a certain minimum number of constituencies may be required. If so, we have a mechanism which is likely to reduce the number of parties nationally as well. This mechanism, however, is as relevant for proportional as for majoritarian elections, and therefore we need not consider it further here.

Summing up we may say that the numbers of parties is likely to be smaller in a majoritarian system than in a proportional one, other things being equal. The basic mechanisms leading to this result operate at the constituency level. The result will however, even if attenuated, remain at the national level, provided that differences between the constituencies are not too many and too great.