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Predicting Party SizesThe Logic of Simple Electoral Systems$

Rein Taagepera

Print publication date: 2007

Print ISBN-13: 9780199287741

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199287741.001.0001

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(p.287) APPENDIX Detecting Factors Other than the Seat Product

(p.287) APPENDIX Detecting Factors Other than the Seat Product

Source:
Predicting Party Sizes
Publisher:
Oxford University Press

(p.287) APPENDIX

Detecting Factors Other than the Seat Product

Predicting Party Sizes Detecting Other Factors

This appendix offers data in a form where the effect of the seat product MS has been removed (‘controlled for’) so that detection of other factors may become easier. The predictive models based on seat product account for a fair part of the observed variation in the number of seat‐winning parties, the largest seat share, the effective number of parties, and mean duration of cabinets. The pattern is the following.

The part of variation accounted for is 51 percent both for the largest seat share (Figure 8.4) and for the effective number (Figure 9.3). This means that all factors not correlated with the seat product account together for less than the seat product does alone. Hence, seat product clearly is the most important single factor. Other factors include features of electoral systems apart from M and S, such as the ones mentioned in Chapter 7, other institutions, cultural features, and path‐dependent historical developments.

For mean cabinet duration, the seat product accounts for only 24 percent of the variation (Figure 10.2). It may thus look as if some other factor may account for more than does the seat product. However, the input of other factors must largely come through the effective number of parties, which single‐handedly accounts for 77 percent of the variation in mean cabinet duration (Figure 10.1). Thus only 23 percent of the total variation is left for all other factors independent of N.

While assembly size is heavily determined by country population, the determinants of district magnitude are wide open. It is conceivable that some as yet undetected factors largely determine M and, quite separately, also determine the mean duration of cabinets. Even more broadly, all too many variables are interdependent rather than one‐directionally dependent. Sophisticated statistical procedures can point out all sorts of colinearities and covariations among variables—but causal linkages are another matter.

So I have followed a different path, a more naive one, if you will, but one that has served well in the advances of physics—advances that eventually enabled us to construct computers, so that even people with little mathematical sophistication (p.288)

Table A.1. Residuals of the number of seat‐winning parties (N 0)

Country, period and no. of elections

Seat product (MS)

(MS

Actual N 0

Residual, R 0 = N 0/(MS

M = 1

Germany 1871–1912, 13

396

4.5

13.6

3.02

Netherlands 1888–1913, 8

100

3.2

6.5

2.03

Norway 1906–18, 5

124

3.3

5.7

1.73

France 1958–81, 7

470

4.7

6.7

1.43

Denmark 1901–18, 7

118

3.3

4.7

1.42

UK 1922–87, 19

628

5.0

6.4

1.28

Australia 1901–17, 7

75

2.9

3.4

1.17

New Zealand 1890–1987, 32

81

3.0

3.5

1.17

Australia 1919–87, 28

106

3.2

3.7

1.16

Canada 1878–1988, 31

247

4.0

4.4

1.10

Italy 1895–1913, 6

508

4.8

5.1

1.06

Norway 1882–1903, 8

114

3.3

2.9

0.88

USA 1828–82, 28

240

3.9

3.0

0.77

USA 1884–1936, 27

396

4.5

3.3

0.73

Sweden 1887–1905, 8

226

3.9

2.8

0.72

USA 1938–88, 26

435

4.6

2.5

0.54

M > 1

Spain 1977–86, 4

2,345

7.0

12.8

1.83

Ireland 1922–89, 24

525

4.8

8.2

1.71

Switzerland 1919–87, 19

1,521

6.3

10.5

1.67

Japan 1928–86, 22

1,920

6.6

10.0

1.52

Norway 1921–49, 8

1,125

5.8

6.5

1.12

Luxembourg/2 1922–51, 7

359

4.3

4.7

1.09

Norway 1953–85, 9

2,707

5.9

6.3

1.07

Luxembourg 1919–89, 11

751

5.2

5.5

1.06

Portugal 1975–87, 7

2,814

7.3

6.9

0.95

Malta 1921–45, 6

99

3.2

3.0

0.94

Finland 1907–87, 30

2,800

7.2

6.8

0.94

Sweden 1952–68, 6

2,059

6.7

5.7

0.85

Malta 1947–87, 11

250

4.0

3.2

0.80

Sweden 1908–48, 14

1,886

6.6

5.2

0.79

Note: Calculated from data in Taagepera (2002b), as graphed in Figure 8.1. ‘Luxembourg/2’ indicates elections carried out in one‐half of the country.

on their own part can instigate sophisticated statistical analyses. Once this machinery is available, should we abandon the simpler approaches? I do write this book on a computer, but when conceptual thinking becomes tense, I grab for a pencil. It makes sense to use the most appropriate technology for the given purpose, not the most advanced one in a technological sense.This approach has led to predictive models that connect the seat product, the number of parties, and the mean cabinet duration. Are these connections really causal, so that a change in district magnitude truly would lead to a change in cabinet duration? We are reminded that maybe the best measure of overall technical development of a country is the per capita number of telephones, but it would be risky to put all national resources into buying telephone sets and hope (p.289) that the rest would follow. I think predictions based on seat product are on safer causal grounds, but one has to maintain a healthy dose of skepticism. This dose is between blind acceptance and blind rejection.

Some of my colleagues may wish to follow up on this simple but time‐honored approach of addressing only one or a few variables at a time, while carefully thinking through how (i.e. in what functional form) these variables might logically impinge on the number and size distribution of parties and other features that may derive from it. They may discover connections to which I may be blind. For this purpose, the following Tables A.1–A.3 are offered. They show the residuals, that means what is left to be accounted for when the expected impact of the seat product has been removed (‘controlled for’).

Table A.1 shows such residuals for the number of seat‐winning parties. The countries are listed in the order of decreasing residuals, which range from 3.0 to 0.54 for single‐seat systems and from 1.83 to 0.79 for multi‐seat systems. A residual value 1.00 means that the prediction by MS fits exactly. A residual of 2 means that the actual number of seat‐winning parties is twice the expected number, while a residual of 0.5 means that the actual number is one‐half of the expected. Only two countries fall outside this range. This limited range makes detection of causal (or at least correlated) factors so much more difficult. As mentioned in Chapter 8, operational measurement of number of seat‐winning parties presents difficulties, and hence a large part of the residual may be measurement error—which makes discovering further causal factors even harder. I offer these data nonetheless, just in case.

Table A.2 shows analogous residuals for the largest seat share. The countries are listed in the order of decreasing residuals, which range from 1.7 to 0.58 for single‐seat systems and from 1.30 to 0.67 for multi‐seat systems. Here measurement error is much smaller, which makes it more promising grounds for detecting further causal factors. On the other hand, the range of the residuals is even narrower than in previous table.

Table A.3 shows the residuals for the largest seat share, the effective number of parties, and the mean cabinet duration, all for the same data‐set. (For the largest seat share, overlap with previous table is appreciable.) The countries are listed in the order of decreasing residuals for the effective numbers, which range from 2.7 to 0.72. The residuals for mean cabinet duration have a much wider range—from 3.1 down to 0.20—which should make detection of further factors easier. However, the high correlation with the effective number must be kept in mind.

Here in particular, please note that the residuals refer to the theoretically expected relationship, not the empirical best fit. In the case of C versus MS, R 2 is 0.30 for the empirical fit but only 0.24 for the predictive model. This 24 percent is the part of variation that is not only accounted for in a statistical sense but also explained in a more substantive sense. Hence, this is the part other factors are to complement.

(p.290)

Table A.2. Residuals of the largest seat shares (s 1)

Country, period and no. of elections

Seat product (MS)

1/(MS)⅛

Actual s i

Residual, R 1 = s 1(MS)⅛

M = 1

Italy 1895–1913, 6, TR

508

0.46

0.78

1.70

Botswana 1965–94, 7

33

0.65

0.83

1.29

Antigua 1980–89, 3

17

0.70

0.86

1.22

United States 1828–1994, 84

344

0.48

0.59

1.22

United Kingdom 1885–1992, 29

643

0.45

0.53

1.18

Bahamas 1972–87, 4

42

0.63

0.73

1.16

Canada 1878–1993, 32

247

0.50

0.58

1.14

Trinidad 1961–91, 7

35

0.64

0.73

1.14

St. Vincent 1974–89, 4

14

0.72

0.82

1.12

Jamaica 1944–89, 11

47

0.62

0.65

1.12

Mauritius 1976–95, 6

68

0.59

0.65

1.10

Norway 1882–1903, 8

114

0.55

0.59

1.07

Barbados 1966–91, 6

26

0.67

0.69

1.04

Dominica 1975–90, 4

21

0.68

0.69

1.01

Sweden 1887–1905, 8

226

0.51

0.51

1.01

New Zealand 1890–1993, 34

81

0.58

0.58

1.00

Belize 1979–89, 3

24

0.67

0.66

0.99

Grenada 1972–90, 4

15

0.71

0.69

0.97

France 1958–93, 10, TR

496

0.46

0.44

0.95

Norway 1906–18, 5, TR

124

0.55

0.50

0.91

Cook Islands 1965–99, 10

23

0.68

0.61

0.90

St. Lucia 1974–92, 6

17

0.70

0.63

0.90

Australia 1919–96, 31, AV

106

0.56

0.50

0.89

Samoa 1979–2001, 7

47

0.62

0.51

0.86

Denmark 1901–18, 7

117

0.55

0.46

0.84

Australia 1901–17, 7

75

0.58

0.48

0.83

Cuba 1901–54, 23

64

0.59

0.48

0.80

St. Kitts & Nevis 1980–89, 3

10

0.75

0.51

0.68

The Netherlands 1888–1913, 8, TR

100

0.56

0.34

0.61

Germany 1871–1912, 13, TR

396

0.47

0.27

0.58

M > 1

Spain 1977–96, 7

2,360

0.38

0.49

1.30

Japan 1928–93, 24, SNTV

1,930

0.39

0.50

1.28

Portugal 1975–95, 9

2,770

0.38

0.42

1.14

Sweden 1908–68, 20

1,600

0.40

0.45

1.13

Ireland 1922–92, 25, STV

567

0.45

0.47

1.04

Norway 1921–93, 19

1,200

0.41

0.42

1.03

Malta 1921–92, 18, STV

180

0.52

0.52

0.98

Luxembourg 1919–94, 19

504

0.46

0.43

0.94

Finland 1907–95, 32

2,860

0.37

0.33

0.89

Switzerland 1919–95, 21

1,540

0.40

0.27

0.67

Note: Calculated from data in Taagepera and Ensch (2006), as graphed in Figures 8.3 and 8.4. M = 1 systems are FPTP, unless otherwise indicated: TR = Two‐Rounds; AV = alternate vote. M > 1 systems are List PR, unless otherwise indicated: STV = single transferable vote; SNTV = single nontransferable vote. District magnitudes remained the same during the periods shown and variations in assembly size were relatively minor, except for USA (213–437), Malta (from 10 for Government Council, 1939 and 1945, to 65) and Luxembourg (from 25 in partial elections to 64).

(p.291)

Table A.3. Residuals of the largest seat shares (s 1), effective numbers of parties (N), and mean cabinet durations (C)—R 1 = s 1(MS)⅛, R N = N/(MS)⅙, R C = C(MS)⅓/42 yrs.

Country and period

Seat product (MS)

s 1

R 1

N

R N

C

R C (years)

M = 1

Papua‐NG 1977–97

108

0.40

0.71

5.98

2.74

1.65

0.19

India 1977–96

542

0.55

1.21

4.11

1.44

2.4

0.47

Mauritius 1976–97

68

0.62

1.06

2.71

1.34

2.1

0.20

France 1959–2002, TR

508

0.44

0.97

3.43

1.21

3.1

0.59

Barbados 1966–94

26

0.70

1.05

1.76

1.02

9.5

0.67

Trinidad 1961–2001

36

0.75

1.17

1.82

1.00

10.0

0.79

Australia 1946–96, AV

128

0.51

0.93

2.22

0.99

9.9

1.19

New Zealand 1946–96

85

0.57

0.99

1.96

0.93

6.3

0.66

Canada 1945–93

270

0.56

1.12

2.37

0.93

8.0

1.23

Bahamas 1972–2002

42

0.73

1.17

1.68

0.90

14.9

1.23

USA 1947–2000

435

0.62

1.32

2.40

0.87

7.7

1.39

Jamaica 1962–89

55

0.76

1.25

1.62

0.83

9.2

0.83

Botswana 1965–2004

37

0.75

1.18

1.35

0.74

39.6+

3.14+

UK 1945–97

635

0.53

1.20

2.11

0.72

8.6

1.76

M > 1

Finland 1945–2003

2,940

0.27

0.73

5.03

1.33

1.5

0.51

Luxembourg 1945–99

809

0.41

0.95

3.36

1.10

6.0

1.33

Japan 1946–96, SNTV

1,940

0.54

1.39

3.71

1.05

3.9

1.16

Norway 1945–97

1,190

0.47

1.13

3.35

1.03

4.3

1.08

Ireland 1948–97, STV

538

0.48

1.06

2.84

1.00

3.8

0.74

Israel 1949–96

14,400

0.38

1.25

4.55

0.92

1.75

1.01

The Netherlands 1946–2002

19,600

0.34

1.18

4.65

0.90

3.3

2.13

Portugal 1976–2002

2,810

0.43

1.16

3.33

0.89

3.2

1.08

Costa Rica 1953–98

426

0.52

1.12

2.41

0.88

4.9

0.88

Malta 1966–87, STV

294

0.53

1.08

1.99

0.77

10.6

1.68

Spain 1977–2004

2,330

0.50

1.32

2.76

0.76

9.0

2.84

Note: Calculated from data in Taagepera and Sikk (2007), as graphed in Figures 9.4 and 10.2. M = 1 systems are FPTP, unless otherwise indicated: TR = Two‐Rounds; AV = alternate vote. France had one PR election in 1986. M > 1 systems are List PR, unless otherwise indicated: STV = single transferable vote; SNTV = single non‐transferable vote. District magnitudes remained the same during the periods shown and variations in assembly size were relatively minor. Countries are listed in the order of decreasing residual for N (which corresponds to locations in Figure 9.4).

(p.292)