More explanation of Duverger-law graphical data

The picture (png) (jpg) is based on data covering the years 1981-1985 from table 8.1 in Rein Taagepera & Matthew S. Shugart: Seats and votes: the effects and determinants of electoral systems, Yale University Press, 1989. However, we have added 2002-2005 data from ElectionWorld.org, namely:

The original data were:

Plurality:
Bahamas 1982, Botswana 1984, Canada 1984, Dominica 1980, India 1984, Malaysia 1982, New Zealand 1984, St.Lucia 1982, St.Vincent+Grenadine 1984, S.Africa 1981, Sri Lanka 1977, United Kingdom 1983, United States 1984.
IRV & STV:
Australia 1984 (Nationals counted as "separate" party from the Liberals, otherwise ENPPseats would be reduced as indicated by red lines), Malta 1981, Ireland 1982. Australia's lower house uses IRV but Malta and Ireland house elections use multiwinner STV.
Proportional Representation:
Austria 1983, Belgium 1985, Brazil 1982, Costa Rica 1982, Denmark 1984, Ecuador 1984, Faeroe Islands 1984, Finland 1983, Greenland 1983, Guatemala 1984, Israel 1984, Italy 1983, Luxembourg 1984, Netherlands 1982, Norway 1985, Portugal 1983, S.Korea 1985, Spain 1982, Sweden 1985, Switzerland 1983.
Hybrids & other:
Japan 1983 (was hybrid of single-winner and multiwinner plurality [SNTV]; in the mid-1990s PR replaced multiwinner plurality), W.Germany 1983 (hybrid of PR and single-winner plurality), France 1981 (employs plurality with second runoff election if necessary to determine single winner).

All data lower houses only. The vertical line represents exactly two equal-seats parties and as you can see almost all the plurality (green) datapoints lie to its left, representing 2-party domination. If another vertical were to be drawn at ENPPseats=1, that would represent single-party domination, i.e. "tyranny." As you can see, several plurality countries are edging dangerously close to that imaginary line. The lower diagonal line is the line of perfect proportional representation. Most countries lie above that line indicating a departure from proportionality due to minorities being squeezed out of power. (Note: number of parties based on seats is what counts. The amount by which the ENPPs based on votes is larger, merely is a measure of voter futility.) The upper diagonal line is a better fit to reality and represents exactly "one party effectively vanishing."

The "effective number of political parties" (ENPP) is the reciprocal of the sum of the squares of the seat (or vote) fractions got by the parties.

(Want still more data? See Arend Lijphart: Democracies Yale Univ. Press 1984, tables 7.3 and 8.4.)

More detailed look – are there some exceptions?

There are a few interesting exceptions to the usual trends visible in this data. First of all, Canada and India seem to be plurality countries with more than two parties, i.e. "exceptions" to Duverger's law. Their 2004 datapoints are the two furthest-right green points. I believe in India that is because there is a lot of religious, geographic, and linguistic segregation, allowing many parties to exist – plus Indian democracy has only been operating for 60 years, temporarily interrupted by a massively undemocratic interval under Indira Gandhi – which may not have been enough time for 2-party control to set in. Also, although Canada may seem to have 3 parties from its 2004 ENPP datum, in fact it plainly seems historically to be dominated by the Liberal and Conservative parties, with only two occasions since 1867 (namely the Progressives in 1921 and the New Democrats in 2011) in which a third party got more seats than the minimum among the top two.

Second, South Africa seems in 2004 to be – remarkably for a PR country – under (<2)-party control – it is the left-bottom-most blue data point at (1.97, 1.97). In the 1980s, the S.Africa data point was the other most-left-bottom point. Both seem to be invading the green plurality country regime and far from their home blue PR regime. At least at present that is because S.Africa let the blacks have power in the early 1990s and their party the ANC then quickly dwarfed all the others. (Really there is the ANC and a lot of small white-dominated parties, a combination which the ENPP formula views as "1.97 effective" parties.) Ultimately I predict (or hope) that race will cease to be such a giant feature in South African politics, at which point the ANC probably will split up into many parties.

For a somewhat more sophisticated look at "exceptions" to Duverger's law, see W.H.Riker: Number of political parties, re-examination of Duverger's law, Comparative Politics 9,1 (1976) 93-106 where he argues that really, Duverger should be rephrased to say that once 2-party domination locks in it stays that way, but various random effects and transitions may need to happen before the lock-in occurs. (He explains and has a model.) With this revised wording/model, Riker doesn't know of any exceptions anymore.

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