Duverger’s Law: A Twist

Duverger’s Law: A Twist

In the 1950’s and 60’s, Maurice Duverger began publishing his findings concerning the link between the party system and the electoral system. Titled as a “Law” by the vast majority of political scientists, Duverger found that the single-member district plurality (SMDP) rules produce two effective parties, while proportional representation rules allow for more political parties. In this blog I will put this theory to the test by computing the number of effective parties for a certain country, and describing that country’s electoral rules. The country that I have chosen is France.

            We will begin by computing the number of effective parties in France. According to Duverger’s Law, if France is a SMDP, the number will average out to two, however; if the country follows a proportional representation system, the end result will average to three or higher. The formula “N_eff = 1 / Σ(proportions)²” is applied to the following table in order to find the results[1].

Party	# of Seats	Proportions
Socialist Party	258	.45
Union for a Popular Movement	185	.32
Other left wing parties	21	.04
Europe-Ecology-The Greens	16	.03
Other parties of the right	14	.02
New Centre	11	.02
Left Radical	11	.02
Left Front	10	.02
Radical Party	6	.01

Any other parties were excluded from the forum because the size made them somewhat irrelevant. The applied formula looks like the flowing:

(.45 + .32 + .04 + .03 + 4(.02) + .01)² → .2 + .1 + .0016 + .0009 + 4(.0004) + .0001 = .3042

1/.3042 = N_eff = 3.28

Therefore, according to the formula alone, France has a proportional representation system. Before that result is set in stone, it should be double checked against the electoral rules of the country.

            France uses the “runoff election” system, a system which allows for two separate elections to ensure that there can be a majority rule even with multiple parties. They do not use a threshold to allow for a third of fourth election, but rather the two most popular candidates are presented on the ballot during the second election. The candidates come from the French legislature, which is comprised of 277 seats, representing 277 districts both in France, and abroad. Thus the district magnitude (or amount of seat allotted to each district) is 1[2]. All of this information supports that France follows the single-member district plurality system.

            Now, how does all of this information go together? One might be tempted to call this a hybrid, as it contains elements of both the SMDP and proportional representation (from the formula). When looking more closely we see that although there are three main effective parties, only two contest each other in the final election. In the end this drives France to be a SMDP country. Although it is not the perfect example of Duverger’s Law, it does conform well enough to support his theories.

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[1] http://www.ipu.org/parline-e/reports/2113_E.htm -  Inter-Parliamentary Union - France

[2] http://en.wikipedia.org/wiki/Constituency_(France) - Wikipedia