Why are there exceptions to Duverger's Law?

Question

Duverger's law states that in a first past the post electoral system, the system will end up with a two party system.

However, many countries with first past the post electoral systems (such as India, Canada, and the United Kingdom) do not have two party system.

Why?

Answer 1

Two of these examples were discussed in an American Political Science Review* article back in 1982. Canada and India are well-known counter-examples to Duverger's law.

In an examination of 121 elections of which 30 were conducted under plurality rules ("winner take all"), 7 had significant numbers of votes for a third party. All 7 of those were in Canada. The researcher (Rae's) conclusion was that Canada's decentralized government provides incentives for parties to also be decentralized (because provincial control is enough of a reward). In Canada, this led to regionalization of elections: a party might be one of the Big 2 in one province, but considered a third-party in another. In some sense, this preserves Duverger's law at the sub-national level. The rules of the election in each region lead to the expected conclusion, but at the national level don't appear to follow Duverger's Law at all.

India is harder to explain. At the time of the article, there were two explanations:

• First, many of the "parties" are a form of identity-politics. Rather than a serious strategic organization which is attempting to win elections, they provide a kind of emotional satisfaction to members. Since these parties aren't strategic they aren't expected to have any meaningful impact on the election, and the electoral rules are capable of supporting multiple parties.
• Second, there is a spatial voting explanation. At the time of writing Congress was the dominant party in India, and it was believed to occupy the policy-space which attracts the median voter (and thus, it is the optimal position to occupy). The rest of the parties were struggling to pick up marginal votes in smaller policy-spaces. Under this view, India is really a one-party system with a large number of minority parties. Duverger's law is violated by the existence of a single party which monolithically occupies the ideal policy-space.

The article proposes an alternative formulation of Duverger's law, which at least when I was in graduate school (early 2010's) was familiar:

Plurality election rules create and maintain a competitive two-party system except where (1) one party is almost always the Condorcet winner or (2) elections are contested regionally, rather than nationally (paraphrased)

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APSR is the most prestigious publication in political science, except in some specific niches which have their own publication.

Answer 2

Two of the countries you mentioned have two major parties which take turns forming the government:

• Every prime minister in the history of Canada was from either the Liberal party or the Conservative party
• Every prime minister of the United Kingdom in the past 100 years was from either the Labour party of the Conservative party.

Minor parties might get a few parliament seats in these countries because every parliament seat is the result of an individual FPTP-election in a single district. But there is usually an individual two-party systems in each individual district. The two major parties might just be different than in the rest of the country. The problem for the individual voter is the same in that case: You have to choose between the two major parties in your voting district, and if you vote for any other party you could just as well stay at home.

Also, one could argue that Duverger's Law also applies on the parliament level in such countries, because usually every minor party feels more aligned with one of the two major parties and will support them over the other.

The timeline of prime ministers in India is more colorful. But India is a country which is still a rather young democracy. And contrary to Canada, the Indian people do not have a democratic cultural background. So it might still take some time until two major party blocks form in India.