Assessing the Mechanical and Psychological Effects of District Magnitude: Appendix
Romain Lachat, André Blais, and Ignacio Lago
Journal of Elections, Public Opinion & Parties
This appendix is divided in three sections. The first one presents a summary of electoral
system effects based on a different specification of the voting choice model in the 2005
analysis. Section 2 includes descriptive information on the distribution of votes and seats in
the 2009 election. Section 3, finally, summarizes the results of the model replication based
on the 2009 election.
1. Robustness test, 2005 election
Table A1 summarizes the electoral system effects obtained with a different specification of
the 2005 voting choice model. For that robustness test, party viability was measured not as
a dummy, but as a function of the number of votes needed to win the last allocated seat. For
parties that did win a seat in the previous election, viability is equal to 1. For parties that
did not, we computed the number of additional votes that party would have needed to win
the last allocated seat, expressed as a proportion of the total number of votes cast in that
electoral district. The viability variable is then computed as 1 minus that proportion of
votes. The lower the value, the less viable the party is. For instance, a value of 0.8 (1 - 0.2)
means that the non-viable party had to increase its results by 20 percent to win a seat in the
district.
1
Table A1. Summary of electoral system effects in the 2005 election, by district magnitude.
Results when viability is measured as a ratio variable.
All districts
17
<8
7
By district magnitude
8-21
8
21.13
3.25
15.11
2.53
16.38
2.88
7.14
2.04
21.24
3.27
12.37
2.41
23.31
3.39
22.09
2.91
Psychological effect
Δ % votes small parties
Δ ENEP
Δ % seats small parties
Δ ENPP
0.18
0.01
0.47
0.02
0.53
0.03
0.00
0.00
0.24
0.01
1.03
0.05
0.00
0.00
0.00
0.00
Mechanical effect
Δ % seats small parties
Δ ENPP
3.76
0.21
9.65
0.63
4.70
0.26
0.63
0.02
Total effect
Δ % seats small parties
Δ ENPP
4.23
0.24
9.65
0.63
5.73
0.31
0.63
0.02
Number of districts
Party system characteristics
% votes small parties
ENEP
% seats small parties
ENPP
>21
2
2
2. Results of the 2009 election
Table A2 presents the distribution of parties’ votes and seats in 2009, at the district level. (This is the equivalent of Table 1 in the main
text for the 2005 election.)
Table A2. 2009 Portuguese election (resident districts): Percentage of votes and number of seats received by the five main parties
PS
Lisbon
Porto
Braga
Setúbal
Aveiro
Coimbra
Leiria
Santarém
Viseu
Faro
Madeira
Viana do Castelo
Azores
Vila Real
Castelo Branco
Guarda
Beja
Bragança
Évora
Portalegre
Total seats
% votes
% seats
Districts with seats
Votes
36.4
41.8
41.7
34.0
33.8
38.0
30.1
33.7
34.7
31.9
19.4
36.3
39.7
36.1
41.0
36.0
34.9
33.0
35.0
38.3
Seats
19
18
9
7
6
4
4
4
4
3
1
3
3
2
2
2
2
1
1
1
96
36.6
42.2
20
PPD/PSD
Votes
Seats
25.1
13
29.2
12
30.8
6
16.4
3
34.6
7
30.6
4
34.9
4
27.0
3
37.5
4
26.2
3
48.1
4
31.3
2
35.7
2
41.1
3
29.8
2
35.6
2
14.6
0
40.6
2
19.0
1
23.8
1
78
29.1
35.2
19
PCP-PEV
Votes
Seats
9.9
5
5.7
2
4.6
1
20.1
4
3.8
0
5.7
0
5.1
0
9.2
1
2.9
0
7.8
0
4.2
0
4.2
0
2.2
0
2.9
0
5.1
0
3.3
0
29.1
1
2.4
0
22.3
1
12.9
0
15
7.9
6.5
7
CDS-PP
Votes
Seats
11.0
5
9.3
4
9.7
2
9.1
1
13.0
2
8.8
1
12.6
1
11.2
1
13.4
1
10.7
1
11.1
1
13.6
1
10.3
0
10.1
0
8.4
0
11.2
0
5.7
0
12.6
0
6.4
0
8.0
0
21
10.4
9.1
12
BE
Votes
10.8
9.2
7.8
14.0
9.0
10.8
9.5
11.8
6.5
15.3
6.2
8.6
7.3
5.5
9.1
7.6
10.0
6.2
11.1
10.8
Seats
5
3
1
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
16
9.8
7.0
9
Note: The districts are ordered by decreasing magnitude. The results of the smaller parties, which received a total of 6.2 per cent of the votes and 0 seats, are not included.
3
3. Replication of the analysis with data from the 2009 election
In 2009, the model of voting choice on the basis of which the electoral systems are
computed is similar to the one of 2005. The only difference regarding the model
specification, as explained in the main text, is the operationalization of leader evaluations.
More detailed information was available in 2009, in the form of like-dislike scales for the
leaders of each of the five main parties. Instead of a dummy variable identifying the leader
that best represents one’s views, the 2009 model includes an eleven-point scale of
sympathy for a party’s leader (coded from 0 to 10, with higher values indicating a higher
level of sympathy). Another difference is sample size and the number of available districts.
As the 2009 sample was much smaller than in 2005, we not only have fewer respondents,
but also fewer districts. The 2009 analysis includes respondents from 15 districts,
corresponding to a total of 200 seats.
The estimated coefficients for this model of voting choice are presented in Table A3. The
summary of electoral system effects, for all districts or by district size, can be found in
Table A4. Electoral system effects are also presented in the form of figures, showing how
the size of the electoral system effects varies with district magnitude. Figure A1 shows the
psychological effect in terms of votes (changes in the percentage of votes for small parties
and in the Effective Number of Electoral Parties), Figure A2 shows the psychological effect
in terms of seats (changes in the percentage of seats for small parties and in the Effective
Number of Parliamentary Parties), and Figure A3 shows the size of the mechanical effect.
4
Table A3. Model of vote choice, 2009 election (Conditional logit model)
Variable
Viability
Left-right distance
Left-right distance * Viability
Party sympathy
Party sympathy * Viability
Leader sympathy
Leader sympathy * Viability
Party identification
Party id. * Viability
BE
CDS-PP
PCP-PEV
PPD/PSD
N (observations)
N (respondents)
Log likelihood
McFadden R2
Coef.
1.26
-0.15
-0.13
0.47***
-0.09
0.30**
-0.04
0.83
0.73
-1.56***
-1.39***
-1.63***
0.02
Std. Err.
1.07
0.11
0.12
0.13
0.14
0.11
0.12
0.69
0.75
0.28
0.27
0.28
0.20
2937
599
-257.68
0.73
† p<0.10; * p<0.05; ** p < 0.01; *** p < 0.001
5
Table A4. Summary of electoral system effects in the 2009 election, by district magnitude.
All districts
15
<8
5
By district magnitude
8-21
8
>21
2
28.15
3.97
23.01
3.02
25.33
3.66
9.76
2.11
29.19
4.07
24.24
3.09
28.30
4.00
27.91
3.38
Psychological effect
Δ % votes small parties
Δ ENEP
Δ % seats small parties
Δ ENPP
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.00
0.00
0.00
Mechanical effect
Δ % seats small parties
Δ ENPP
2.47
0.12
12.20
0.52
2.99
0.17
0.17
-0.01
Total effect
Δ % seats small parties
Δ ENPP
2.26
0.14
12.20
0.64
2.56
0.19
0.17
-0.01
Number of districts
Party system characteristics
% votes small parties
ENEP
% seats small parties
ENPP
6
Figure A1. Psychological effect in the 2009 election: Change in vote shares of small parties
and in the ENEP when all parties are deemed to be viable, by district magnitude
7
Figure A2. Psychological effect in the 2009 election: Change in percentage of seats of
small parties and in the ENPP when all parties are deemed to be viable, by district
magnitude
8
Figure A3. Mechanical effect in the 2009 election: Change in percentage of seats of small
parties and in the ENPP when all districts are as proportional as the largest one, by district
magnitude
9