Duverger's Law and the UK

Matt Merrell

Political Science 150

11/1/12

Blog 7: Duverger’s Law

                In the political game, political parties are often what have the most impact on policy-making within a nation. The commonality that political parties provide is what allows politicians to get elected, appealing to the nation’s citizens. But how many parties within a nation can truly be considered successful? How many parties truly make an impact on policy-making decisions? Duverger’s Law is a formula developed to help answer this question.

                According to Duverger’s Law, if a nation’s government is a single-member-district-plurality system (SMDP), it will produce two effective parties. The formula, Neff = 1/∑(p²), states that the number of effective parties is determined by one over the sum of the seats or votes for a party squared. To test this formula we will look at the results of the 2010 election in the United Kingdom.  This formula proves true in this case study. Duverger’s law can accurately determine the number of effective parties in legislature.  

The district magnitude of the UK, or the number of seats allotted to each district is only one, seeing how the UK is a SMDP system. It uses a “first-past-the-post” formula in allocating seats to the candidates with the most votes, and is considered a parliamentary system with no hybrid structure.  It has an open list structure, allowing voters to elect their candidates specifically. There is no threshold, or vote percentage requirement for parties, mainly because there is no need for one. The smaller parties must win districts to win votes, which rarely happens.

Below is a table with the number of seats won with its percentage of the total number of seats in Parliament in the 2010 election². It also includes its percentage squared, the number necessary for calculating Duverger’s Law:

Political Party	2010	Fraction of Total	p²
Conservative	306	.471	.22
Labour	258	.397	.16
Liberal-Democrat	57	.088	.008
SNP	6	.009	.00008
Sinn Fein	5	.008	.00006
Democratic Unionist	8	.012	.0001
Plaid  Cymru	3	.005	.00002
SDLP	3	.005	.00002
Green	1	.002	.000004
Alliance	1	.002	.000004
Speaker	1	.002	.000004
Independent	1	.002	.000004
Total	450	1.00	.3883
1/∑(p²)			2.6

Duverger’s Law proves to be fairly accurate in determining the number of effective parties. The results state that there are 2.6 effective parties in UK legislature. The two most dominant parties in the UK are the Conservative and Labour parties. The reason that Duverger’s formula doesn’t result in a perfect 2 is because another party, the Liberal Democrats did receive a substantial number of seats in Parliament. However, the number of seats they received pales in comparison with the percentage of seats held by both the Conservative and Labour parties. The ideology of SMDP systems producing only two effective parties is proven correct in this case study.

Works cited

¹ "IPU PARLINE Database: UNITED KINGDOM (House of Commons), Electoral System."IPU PARLINE Database: UNITED KINGDOM (House of Commons), Electoral System. N.p., n.d. Web. 02 Nov. 2012. <http://www.ipu.org/parline-e/reports/2335_B.htm>.

²"United Kingdom General Election, 2010." Wikipedia. Wikimedia Foundation, 30 Oct. 2012. Web. 02 Nov. 2012. <http://en.wikipedia.org/wiki/United_Kingdom_general_election,_2010>.