Abstract
We combine consideration of Duverger’s Law (Political parties: Their organization and activity in the modern state. London: Methuen, 1954) with Demsetz’s (J Law Econ 11:55–65, 1968) theory of natural monopoly to provide a novel perspective on the meaning and measurement of electoral competitiveness in a single member district, plurality rule electoral system. In the Duverger-Demsetz view we develop, the degree of competition is determined by the contestability of elections. Contestability declines with party fragmentation, and so an increase in the effective number of parties above the long run level of 2 predicted by Duverger’s ‘Law’ for plurality based single seat elections signals a decline in competitiveness. This argument runs contrary to the view, sometimes expressed in empirical studies of elections and public policy, that more candidates or parties, each with a smaller vote share reflects a more competitive environment. Using the history of the Canadian parliamentary system, we provide qualified support for the Duverger-Demsetz perspective by studying the relationship between the concentration of vote shares and a new index of electoral contestability. Extension of the argument to proportional electoral systems is also considered.
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Notes
- 1.
Empirical work that uses the effective number of parties (ENP) to measure competitiveness or a closely related index of party or vote fragmentation, such as 1 − 1/ENP or one minus the winner’s vote share v1, includes: Ashworth et al. (2014); Alfano and Baraldi (2015)—who use a normalized Hirschman-Herfindahl (HH) index; Gerring et al. (2015)—who use 1 − v1 which is practically similar to the HH index of party fragmentation [for Canada from 1867 to 2011, the correlation of 1 − v1 with ENP is about 0.89 and with Rae’s (1968) measure of fragmentation 1 − HH it is about 0.95]. See also Ghosh (2010) for India, among others. We also note other work that associates party fragmentation with ‘weak government’ and increased public expenditure, a view that is complementary with, but distinct from the Duverger-Demsetz view that we shall develop in what follows. Examples of this literature include Roubini and Sachs (1989), Ricciuti (2004), Chhibber and Nooruddin (2004), Borge (2005) and Geominne et al. (2008).
- 2.
- 3.
Many early Canadian elections featured acclamations, particularly in elections 1 (1867: 46/181), 2(1872:51/200), 3(1874:54/206) and 13(1917:31/235). In these cases, we set v1 = 1 in a constituency with an acclamation in the case of ENP defined for constituencies. The presence of 2-seat constituencies (123 before the 28th election in 1968) makes little difference to the averages over all constituencies that form the basis for the measures discussed in this section. It is interesting to note in this respect, however, that for one-seat constituencies, the mean for all elections of the constituency level ENP = 2.4, while for the two-seat constituencies, mean ENP = 4.0. We also note that there are 10,247 regular individual constituency elections in elections 1 through 41. The maximum number of candidates in any one constituency election from 1867 to 2011 (general elections 1–41) is 13. The maximum number of parties in any one election (taking self-named parties as a party without judgement of its success), independent candidates and candidates of unknown affiliation is 27, in the 19th election in 1940. On the party system in Canada up to 1908, see recently Godbout and Hoyland (2013). ON ENP in Canada, see Johnston and Cutler (2009).
- 4.
- 5.
The Law is not a point prediction, but a statement that there cannot typically be more than 2 candidates (Cox 1997, p. 271). So in the long run there could be less than 2.
- 6.
- 7.
There is perhaps some danger that we are setting up a ‘straw person’ in the rest of this section. However even if generalizing from the particular overstates our case, this exercise leads in interesting directions.
- 8.
The downward trend in Closeness(3) after about the 30th election is not picked up by the fragmentation indexes.
- 9.
The idea of adjusting vote margins for volatility is analogous to standardizing scores by dividing the differences by a standard deviation. In the usual difference of means test, whether a difference is large or small is defined in terms of the normalized value of that difference in standard error units, with the standard error of the mean simply a specialized version of a standard deviation. In this way, any conclusion about the existence of a “meaningful” difference will reflect the level of uncertainty as to whether any observed difference might be due to chance alone.
- 10.
After 1945, the issue of how to define a party is not problematical if one sticks to analyzing the major parties in Parliament plus a residual. Earlier decades are a different matter.
- 11.
The adjusted vote weight attributes an average vote to constituencies where there was an acclamation, and then adjusts vote share weights of all constituencies accordingly.
- 12.
If concurrent consumers cannot be excluded from consuming, competition among consumers for the lowest (zero) price will result in insufficient revenue being generated to support the efficient level of production. On the other hand, if concurrent consumers can be excluded, efficiency could be achieved by a producer setting the Lindahl (individual) prices needed to realize a level of output at which the sum of the individual marginal values equals marginal social cost. However in the absence of competing alternatives, the sole producer will exploit its market power, raise the set of Lindahl prices and under produce relative to the potentially efficient level.
- 13.
There is an additional, conceptually distinct source of inefficiency that may worsen with fragmentation. This stems from the possibility that as the number of parties increases, each party is forced by the division of the electorate to focus its electoral promises on a narrower segment of the electorate, thus moving the public sector towards special interest politics and away from concerns over the provision of general public services. See Lizzeri and Persico (2005) for an interesting exploration of this view. Chhibber and Nooruddin (2004) propose and positively test a similar hypothesis for Indian states. Bueno de Mesquita et al. (2001) present essentially the same view. See also the additional literature cited in the first footnote concerning the weak government hypothesis. A reasonable conjecture is that this source of inefficiency may be a problem in all SMP systems with weak national parties.
- 14.
We use the word ‘reliable’ here because we are aware that the matter is not straightforward. If the survival of the incumbent was always assured (i.e., absolutely certain), there is no political competition. Even if the incumbent is superior, preservation of competition as a principle of governance may require throwing out such an incumbent from time to time, thus introducing uncertainty into the process.
- 15.
It does this by adding leads and lags of all three variables into the equation, so that, in principle, the calculated residuals are orthogonal to the entire process despite the mutual interdependence of the three variables.
- 16.
In Canada from 1867 to about the start of the first world war, the number of parties as reflected by ENP12party declined steadily to about 2 at the outbreak of the war. Thereafter, both ENP12party and ENP defined as an average over the constituencies began to rise, with ENP12party being uniformly higher than ENP. Since Duverger’s Law is a long run result, it is not clear whether or not either enp index is systematically greater than 2 in the long run. Investigation of that issue requires a dynamic empirical model of enp, which to our knowledge has not yet been constructed for Canada or elsewhere.
- 17.
Again, see the Appendix for the definition of party used here.
- 18.
There is an additional, conceptually distinct source of inefficiency that may worsen with fragmentation under PR. This stems from the possibility that each party in a PR system focuses its electoral promises on a narrower segment of the electorate than does a party under SMP. If so, the public sector under PR will be driven more by the demands of special interests and pay less attention to the provision of public services, compared to an SMP system which effectively blocks some interests that are not regionally concentrated. (For example, the Greens in Canada may have 5 % of the vote in every constituency, but they elect only one member of parliament from a place known for voters who have a strong taste for the environment). On the other hand, some argue that candidates who must appeal to voters within a small geographic area and who can differentiate themselves from their competitors by making promises for narrowly targeted pork barrel items are more likely to arise in a SMP system than in a PR system (Carey and Shugart 1995; Persson and Tabellini 2000). We cannot resolve this debate over the role of electoral systems in the link between fragmentation, special interests and inefficiency here.
- 19.
Note that the use of one past period to construct our volatility measure means that the index can begin only in the second election. This also implies the unavoidable loss of some information when new provinces are added to the country, such as Newfoundland’s entry into Canada in 1949.
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Acknowledgements
This work is partly supported by a Social Sciences and Humanities Research Council of Canada grant to Winer and Ferris and by the Canada Research Chairs program. Grofman’s participation is partly funded by the Jack W. Peltason Chair of Democracy Studies at the University of California, Irvine. We gratefully acknowledge the research assistance of Haizhen Mou, Alexandre Couture-Gagnon, Derek Olmstead, Sarah Mohan, Beatriz Peraza and Samira Hasanzadeh on related projects. Part of the material in this paper stems from a more general unpublished discussion of the measurement of electoral competition that has benefited from presentation at the Public Economic Theory Conference in Seattle, July 2014, at the University of Montreal in October 2015, at U.C. Irvine in February 2015, at The Political Economy of Social Choices, BIRS Workshop, Oaxaca, México, July 2015 and the IIPF Congress in Dublin, August 2015. We thank André Blais, Bill Cross, Momy Dahan, Marc Duhamel, Richard Johnston, Rein Taagepera, Carole Uhlaner, Marcel Voia and seminar participants for helpful remarks. Errors and omissions remain the responsibility of the authors. The paper is a part of a larger project on the meaning, measurement and consequences for public policy of electoral competitiveness in mature democracies including Ferris et al. (2008) and Winer et al. (2014).
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A.1 Appendix: The Data, Definition of Variables, and Measuring Vote Volatility Using Superconstituencies
A.1 Appendix: The Data, Definition of Variables, and Measuring Vote Volatility Using Superconstituencies
1.1 A.1.1 Data
Data on votes by constituency, by candidate and by party for regular parliamentary general elections 1–41 were collected for each election from series supplied by Elections Canada. This data is available online through the Parliament of Canada website at: http://www.parl.gc.ca/About/Parliament/FederalRidingsHistory/HFER.asp.
The 12 party classification employed throughout the paper is based on three criteria: A party exists as such if it gained at least 4 % of the popular vote in at least one election and contested at least 1 % of the seats in at least one election—there are 23 parties satisfying these two criteria—plus it must have won at least 1 seat in at least two elections. There are 11 parties satisfying all these criteria over the history of the modern state: Liberal, Conservative, Labour, the National Party, the Bloc Quebecois, Social Credit, Reform-Alliance, the CCF_NDP, Raillement Creditiste, the Progressives, and the United Farmers of Alberta, with a residual category denoted as ‘Other’. Liberal and Conservative include small groups that voted with the major party at various times as is the usual custom.
1.2 A.1.2 Variables
ENP = ENP calculated over candidates at the constituency level using candidate vote shares (max. 13 candidates in any one constituency).
ENP12party = ENP calculated over 12 parties (11 plus Other) at the national level using party vote shares.
ENP Ratio, ENP12party Ratio = 2 divided by the corresponding ENP number.
Fragmentation = 1 − HH = 1 − 1/ENP, where HH is the Hirschman-Herfindahl index defined using vote shares.
v i = vote share of the candidate in the ith place.
Closeness(3) = an index of the closeness of candidates’ vote shares vi, assuming ENP = 3, as in Endersby et al. (2002).
(v 1 − v 2 ) / volatility = the winner’s vote margin v A.1.2 1 − v 2 at the constituency level relative to historical volatility for that constituency.
PS vol-adj. margins = the Przeworski-Sprague (1971) volatility adjusted vote margins by constituency by party.
AMS_1std = an asymmetry adjusted measure of marginal seats, using an historical volatility and a 1 standard deviation test to define when an incumbent’s seat is safe.
ww1 = 1 for election number 13 (1917); 0 otherwise.
ww2 = 1 for election numbers 19 and 20 (1940 and 1945); otherwise 0.
party_formation = 1 for elections between 1 and 9 (1867 until 1900); 0 otherwise.
1.3 A.1.3 Volatility
Adjusting vote margins for volatility is not easy to do over long periods of time because of redistricting. For a country like Canada that has had consistent growth in the number and frequent changes in the size of individual constituencies, new ridings appear in many elections. Without a past, a constituency can have no history of vote variability and cannot be included in the construction of a volatility adjusted vote margin. To circumvent the loss of information on winning margins through growth and redistricting, we construct a large number of regional super-constituencies—80 in total—based on geographic regions that persist throughout Canada’s election history and that can be used to establish small area vote volatility in the period when a new constituency is created or an old one is reshaped. The number and name of individual constituencies in a superconstituency may change over time, but its geographical boundaries remain fixed. To give one example, the area around Ottawa was used as the base for one of Ontario’s 29 superconstituencies. Electorally it consisted of 1 riding in 1867 and rose to include 7 ridings by 2011. Footnote 19
Aggregate volatility is then computed as follows: Average vote shares by party over constituencies within a superconstituency for each election are computed. For each superconstituency in each election, the absolute value of the changes in these (party-specific) average vote shares across adjacent elections is computed, summed and divided by 2. Each of these superconstituency specific differences in vote shares is then weighted by the relative number of constituencies inside each superconstituency, and summed to derive an aggregate volatility number for each election.
Volatility so computed is shown in Fig. 5 for the 2nd to 41st election (1869–2011) in Canada. The peaks in the 14th and 35th elections are noticeable. Whether there is a trend in volatility or not is difficult to determine.
Historical volatility of party vote shares using superconstituencies Canadian General Elections 2–41
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Ferris, J.S., Winer, S.L., Grofman, B. (2016). The Duverger-Demsetz Perspective on Electoral Competitiveness and Fragmentation: With Application to the Canadian Parliamentary System, 1867–2011. In: Gallego, M., Schofield, N. (eds) The Political Economy of Social Choices. Studies in Political Economy. Springer, Cham. https://doi.org/10.1007/978-3-319-40118-8_5
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