Are Voters Equal under Proportional Representation?
Orit Kedar The Hebrew University of Jerusalem
Liran Harsgor The Hebrew University of Jerusalem
Raz A. Sheinerman Yifat Media Analysis
Abstract: We develop and apply a new conceptual framework and measure for evaluating electoral systems, focusing on
(in)equality in parliamentary representation. Our main arena of interest is proportional representation with districts,
an electoral system employed by more than half of democratic states, and we draw on an almost entirely overlooked
fact: Electoral regimes vary substantially within countries, with some voters casting their ballot in semi-majoritarian
districts of few representatives and others in large and proportional ones. This within-country institutional variation, we
contend, affects representational (in)equality. Evaluating equality in parliamentary representation, we demonstrate that
districted proportional representation often leads to overrepresentation of voters supporting right-leaning parties. Utilizing
district-level data from 20 Western parliamentary democracies and complementing our within-country approach with a
cross-country analysis, we further show that where parliaments are elected by large and small districts, representational
inequality among voters is greater compared with countries in which parliament is elected by even-magnitude districts.
Replication Materials: The data, code, and any additional materials required to replicate all analyses in this article are available on the American Journal of Political Science Dataverse within the Harvard Dataverse Network, at:
http://dx.doi.org/10.7910/DVN/OJCQ5O. Replication materials are also available at http://politics.huji.ac.il/kedar.
A
re voters under proportional representation (PR)
equally represented in parliament? If not, is
there a systematic ideological bias in representation under PR? And finally, what districting principles
enhance representational equality among voters? Surprisingly, in spite of voluminous literature on electoral
systems and representation, a systematic analysis of representational equality of voters under PR is almost entirely
wanting.
From Spain to Finland, by far the most common
electoral system in Europe (and beyond) is proportional
representation with districts.1 Interestingly, in almost all
PR systems, some districts have only a few representatives and others many, with the largest district having as
many as 20 times more representatives than the smallest
one. Districts of the Portuguese Assembly of the Republic
(2009), for example, range in their magnitude from 2 to 47
seats. The Norwegian Storting (2009) has nine different
district magnitudes, ranging from 4 to 17. Compensatory
seats (an issue we address below) notwithstanding, this
creates variation of electoral regimes within states: Some
voters have their vote counted by majoritarian-like rules,
and others by proportional ones.
This basic and often overlooked institutional
variation within states brings up an issue with crucial
normative implications relevant for all democracies,
but particularly potent where the rules of the game
vary across voters: What if “one person, one vote” only
nominally holds as votes unequally translate to seats in
legislature in a fashion generating ideological bias?
Orit Kedar is Associate Professor, Department of Political Science, The Hebrew University of Jerusalem, Mt. Scopus, Jerusalem 91905, Israel
([email protected]). Liran Harsgor is PhD Candidate, Department of Political Science, The Hebrew University of Jerusalem, Mt.
Scopus, Jerusalem 91905, Israel ([email protected]). Raz A. Sheinerman is Media Analyst, Yifat Media Analysis, 98 Menachem
Begin Rd., Tel-Aviv 67138, Israel ([email protected]).
For assistance with Figure A3, we thank Omer Yair. For helpful comments and suggestions, the authors thank Dave Armstrong, Pablo
Beramendi, André Blais, Adi Brender, Momi Dahan, David Farrell, John Huber, Simon Hug, Georgia Kernell, Yotam Margalit, Maayan
Mor, Sigal Rabon, Nasos Roussias, Kenneth Scheve, Joel Selway, Michael Shalev, Moses Shayo, Mattan Sharkansky, Matthew Shugart, Randy
Stevenson, Rein Taagepera, and Omer Yair; seminar participants at Ben Gurion University, LSE, and University of Geneva; participants of
CSES Plenary Meeting–Berlin; as well as participants of conferences at the University of Mannheim (2011), Bank of Israel (2012), EPSA
(2013), Juan March Institute (2013), and APSA (2013). Orit Kedar acknowledges financial support by the ERC (Starting Grant 263630)
and the Israel Science Foundation (Grant No. 150/10).
1
In a survey we conducted, over 50% of democratic states in the world had districted PR as their electoral system.
American Journal of Political Science, Vol. 60, No. 3, July 2016, Pp. 676–691
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2015, Midwest Political Science Association
676
DOI: 10.1111/ajps.12225
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UNEQUAL REPRESENTATION
In answering these questions, we offer two contributions. First, we demonstrate that there is a systematic
ideological pattern to representational inequality under
PR. Borrowing analytic tools from the study of income
inequality, we find that substantial variation in district
magnitude often leads to bias of the parliamentary pie
in favor of right-wing voters (see discussion of Monroe
and Rose’s 2002 findings below). Simply, the smaller the
district, the more majoritarian is the electoral regime and
thus the more advantaged are the leading parties. Since
in Western democracies small districts tend to be conservative whereas large ones, usually cities, tend to be
both more liberal and more proportionate in comparison, voter support for right-wing parties is overconverted
to parliamentary seats and that for left-leaning ones is
underconverted.
Our second contribution identifies how different
districting schemes affect the level of representational
inequality across countries. While the vast literature on
electoral systems focuses on the average (or median)
district, we call attention to the distribution of districts:
It makes a difference if some are small and others are
large or all are of similar magnitude. We show that across
countries, irrespective of the average district, the share
of parliament elected via small districts affects voter
inequality. This finding has important implications for
institutional design.
Unequal Voters? A New Look at
Parliamentary Representation
It is well established that democracies with proportional
representation are characterized by better representation
compared with majoritarian democracies. PR allows diverse voices and interests to be heard and considered in
parliament, government, and the policymaking process
(e.g., Amorim Neto and Cox 1997; Clark and Golder
2006; Cox 1997; Duverger 1954; Lijphart 1999; Norris
2004; Rae 1967; Taagepera and Shugart 1989). It also enables better representation of minority groups (Shugart
1994), as well as women (Darcy, Hadley, and Kirksey 1993;
Norris 1985), and better ideological congruence between
the government and voters in comparison to majoritarian systems (Huber and Powell 1994; Powell 2000; Powell
and Vanberg 2000).2 Perhaps best established of all is
that parliamentary seats under PR are allocated (more or
less) proportionately to the votes obtained by the different
parties (Gallagher 1991), and indeed, students of electoral
politics offer different ways of accounting for disproportionality between votes and seats (Grofman 1983; Rose
1984; Taagepera and Shugart 1989, 105).3
Measures of representation such as congruence or
disproportionality at the national level compare median
ideology of the electorate to that of the median legislator,
national vote shares to seat shares, or some other attribute
of the electorate as a whole to the analogous one in parliament.4 While providing an excellent summary under
national-district PR, this approach to studying representation is in tension with ample evidence demonstrating
that where the electoral system is districted, both voters’
positions and representative behavior are colored by
districted interests. Studies of legislative behavior provide
evidence of geographically geared representation under
PR. In both the German Bundestag (Stratmann and Baur
2002) and the European Parliament (Bowler and Farrell
1993), variation in legislators’ behavior is explained
by whether they were elected in district or nationally.
District-specific efforts by legislators (Heitshusen et al.
2005) and the effectiveness of personal-vote attributes in
getting elected (Shugart, Valdini, and Suominen 2005)
were shown under multimember districts as well.5 It
is not the case, these studies show, that representatives
from one district serve their party supporters residing in
another district as much as they serve their own voters.
Informed by these studies, our analysis of representation
below identifies votes by both the party cast for and the
district in which they are cast.
A related line of research studies representational
bias (sometimes referred to as partisan bias; e.g., Besley
and Preston 2007; Browning and King 1987; Calvo 2009;
Linzer 2012). A recent study by Rodden (2010) is particularly relevant for our analysis. Analyzing bias under First
Past The Post (FPTP), Rodden shows that due to the legacy
of the Industrial Revolution, left-leaning voters tend to be
geographically concentrated, and hence left-leaning parties win their districts by a wide margin compared with
right-leaning parties. Thus, votes for left parties are less
efficiently turned into seats than votes for the right. At the
3
Grofman (1983) systematically examines measures of bias and
proportionality. Rose’s (1984) Index of Proportionality uses absolute gaps, Taagepera and Shugart (1989, 105) propose a measure of
deviation from PR, and Gallagher’s (1991) Index of Disproprtionality mentioned above uses squared gaps.
4
Of course, when district-level representation is examined, the
district-level figures are fed into the equation. Our point, however, that evaluation of national-level representation skips districts rather than building up representation from the district level,
stands.
5
2
Although see Golder and Stramski (2010).
Though see Gschwend, Shugart, and Zittel (2009) for results different from those of Heitshusen et al. (2005).
678
ORIT KEDAR, LIRAN HARSGOR, AND RAZ A. SHEINERMAN
core of Rodden’s argument, therefore, is the high skewness
of the distribution of votes in left-majority districts versus that in right-majority districts, both under the same
institution of single-member district.
We analyze representational inequality—and hence
representational bias—under proportional representation, an unlikely suspect. Unlike other studies, our
analysis draws attention to institutional variation within
countries as a potential source of the bias: Different voters
have their vote channeled by different rules of the game.
Our Analytic Framework of
Representational Inequality
We conceptualize the voter as embedded in two contexts:
the district she resides in and the party she votes
for. Figure 1 lays out our conceptual setup. Take two
neighbors, Anne and Bob, who reside in the same district
but cast their ballot for different parties first (see Panel
1A). We wish to know whether their votes are equally
converted to seats or whether the voice of one of them
is amplified at the expense of the other. Although our
framework is constructed for the individual voter, we can
group voters and more easily analyze representational
inequality across them. We group the electorate to groups
of voters categorized by the party they support and the
district in which they reside, as is described in Panel A.
There is thus a group of voters such as Anne who reside
in D1 and support P1 , a group such as Bob who reside in
D1 and support P2 , and so on.
This setup allows us to take an explicit account of the
fact that votes are cast and counted in and seats are allotted to districts. Just as in any given district some votes may
be overconverted to seats and others underconverted, it is
also the case that for a given party, electoral support originating from some districts may be overconverted and
that from others underconverted. A party, say P1 , which
Anne and Cindy both support, may form policy that inevitably prioritizes interests in society. These interests,
even if not regional per se, often correlate strongly with
geography. A tax code that benefits farmers over industry
will promote the interests of rural areas at the expense of
industrial ones; a developmental plan that invests in infrastructure in the north indirectly transfers wealth from
south to north; pork provision to Cindy’s district rather
than Anne’s will have clear consequences; and so on. In
other words, forming policy, a party may de facto allocate
resources across districts.
We borrow and adapt tools of analysis from the study
of income inequality. In particular, we adapt the Lorenz
curve of income inequality and Gini inequality index
score to the study of representation. To the best of our
knowledge, this is the first time this approach has been
taken in the study of representation.6
Assume a democracy with a PR electoral system of N
districts (i = 1, . . . , N) in which voters cast V votes in total,
electing representatives for an S seat in parliament. Assume further that K parties (j = 1, . . . , K) compete in the
elections.7 Let (vi j , s i j ) denote the number of votes and
seats in district i and of party j. For each group of voters in
the table (Figure 1B), we calculate its vote share and seat
share out of all votes cast and seats allocated (vi j /V and
s i j /S, respectively). We then calculate for the group (and,
in fact, for every member of the group) the conversion ras /S
tio of votes to seats: CRi j = viijj /V . Voters who contribute
a share of votes greater than the share of seats they receive
(CR < 1) have their voice diminished, whereas those
whose seat share is greater than their vote share have their
voice amplified (CR > 1). We line up voters by ascending
order of that ratio whereby every data point is a group
of voters residing in district i and supporting party j and
draw the representational inequality curve of the election.
The vote (seat) share of one group serves as a baseline for
the next, such that on the horizontal axis is the cumulative vote share and on the vertical axis the cumulative seat
share. For example, if of all NK groups of voters the two
smallest conversion ratios are for supporters of P1 in D3
(the party won 15% of the votes and 10 out of 100 seats
in parliament) and for P2 in D1 (the party won 8% of
the votes and no seats), the coordinates of the two lowest
points on the curve are D1 P2 = (0.08, 0.00) and D3 P1 =
(0.23, 0.10) with conversion ratios of CR12 = 0 and
CR31 = 0.67, respectively. The slope of the curve leading
to each data point thus stands for the conversion ratio of
the relevant group of votes.
Panel C presents a hypothetical curve of representational inequality among voters. We marked our four
voters from Figure 1A (initialed) on the curve. The
45-degree line denotes perfect equality in the conversion
of votes to seats. The figure reveals several interesting
quantities. First, as the figure in this example indicates,
5% of the votes were not converted to seats. Also, note
that voters such as Anne and Bob with a slope smaller
than 1 are underrepresented, whereas Cindy and David
are overrepresented. Third, the shape of the curve is
indicative of the type of misrepresentation in the country.
With the curve reaching a maximum vertical distance
from the 45-degree line at about 0.53, 53% of the votes
in the country are underrepresented, and the remaining
6
Jones and Mainwaring (2003) use Gini coefficient as a measure of
nationalization of party support.
7
National-district PR is a specific case where N = 1.
679
UNEQUAL REPRESENTATION
FIGURE 1 Voter (In)equality in Two Contexts
A
C
p1
p2
d1
Anne
Bob
d2
Cindy
David
…
pK
Total
:
sij /S
dN
V ,S
Total
B
p1
p2
d1
v11,s11
v12,s12
d2
v21,s21
v22,s22
vij /V
… pK Total
:
dN
Total
V ,S
Note: The setup (Panels A and B): Voters cast V votes in total, electing representatives for an
S seats parliament. K parties (j = 1, . . . , K) compete in N districts (i = 1, . . . , N). In Panel
C, the axes denote cumulative vote share against cumulative seat share. The downward arrow
notes the position (cumulative vote share) where the inequality curve dips the most and CR =
1 (hence, votes of voters to the left of it are underconverted to seats and those to its right are
overconverted).
47% are overrepresented in parliament. The more
rightward the curve reaches its maximum dip (“high
belly”), the greater the proportion of voters whose voice
is diminished in parliament. Fourth, an examination
of the actual parties/districts at different places along
the curve can reveal which votes (characterized by both
district and party) are systematically underleveraged to
seats and which voices get overleveraged.
Lastly, constructing a summary figure for the election, we calculate the Representational Inequality Index
(RI), which equals the area between the 45-degree line of
perfect equality and the curve divided by 0.5. Graphically,
other things equal, a curve denoting greater inequality
will be closer to the bottom right corner compared with a
curve of little inequality that will be closer to the 45-degree
line. Varying in size between 0 and 1, the more unequal
is the transformation of votes to seats across groups of
voters, the greater the RI index of the country as a whole.
Notice that the analysis we propose is informed by
both partisan and geographic components of votes-seats
discrepancy. The following illustration might shed light
on the relationship between our approach, disproportionality, and malapportionment. Assume a state with 20
single-member districts and no malapportionment. Assume further a two-party competition such that Party A
wins districts 1–10 with 51% of the vote and Party B wins
districts 11–20 with 51% of the vote. Each of the two
parties ends up with 10 seats in the legislature. At the national level, therefore, each of the two parties has 50% of
the votes and 50% of the seats. Both malapportionment
and measures of disproportionality would show no representational discrepancy. Our analysis, on the other hand,
would produce an inequality curve of a straight horizontal line at 0 up to 49% (20 of 40 groups of voters who
gained no representation in parliament and cast 49% of
the votes in their district each) and an RI index of 0.49. At
the same time, since our measure identifies votes (seats)
by party and district, other things equal, had the state
been malapportioned, representational inequality would
have been even greater.
Explaining Voter Inequality: Hypotheses
We are now able to derive hypotheses about the pattern
of representation both within and across countries. We
begin with the former.
680
Right-Wing Bias under PR. Our first question was as
follows: Are voters equal under proportional representation, and if not, who equals more? Some discrepancies
between the distribution of votes and that of representatives are inevitable. Below, however, we show substantial
inequality and turn to investigate its pattern.
We expect that large parties will enjoy a seat premium under districted systems, particularly under small
districts (Cox 1997). Ideologically mapping the majority
and minority parties in different magnitude districts, we
can substantively identify winners and losers. An electoral
district is often an institutional boundary of a community.
Communities in small towns, rural areas, and the periphery are usually small, whereas cities are often large districts. This is the case in the majority of Western European
countries (e.g., 47 and 39 seats in the two largest cities
while the median district magnitude equals 6 in Portugal;
42 and 28 while the median is 9 in Sweden). But there is an
additional important difference correlating with district
magnitude: In Western countries, cities tend to be more
liberal than rural areas and small towns. Thus, conservative parties tend to be a majority (or plurality) in those
districts where the rules of the game benefit the largest
competitor (relatively small districts), whereas liberal parties tend to be a majority (or plurality) in districts where
the rules of the game are relatively proportional (larger
districts in comparison). Our first hypothesis is thus:
H1a: In countries characterized by substantial variation in district magnitude, supporters of rightleaning parties are overrepresented compared
with their left-leaning counterparts.
H1b: Within countries, the effect declines with district
magnitude.
An exception to this pattern is small but geographically
concentrated parties. Calvo (2009) convincingly shows
that the geographic dispersion of voter support affects
the ability of small parties to compete and in particular
to withstand competition from new parties. Calvo as well
as Ziegfeld (2013) demonstrate that small and geographically concentrated parties are better able to secure seats
compared with their geographically dispersed counterparts.
Before we continue, a particularly insightful recent
work examines the relationship between geography and
the electoral success of particular interests and merits our
attention. Monroe and Rose (2002) offer an account of
representation of urban versus rural interests due to what
they term the variance effect—the fact that districted PR
often has large variation in the magnitude of districts.
They show that urban interests are better represented than
rural ones, that there is higher parliamentary fragmenta-
ORIT KEDAR, LIRAN HARSGOR, AND RAZ A. SHEINERMAN
tion of urban parties compared with rural ones, and that
the largest urban party is systematically disadvantaged.8
Our argument here, in combination with the rest of our
analysis of voter inequality, complements Monroe and
Rose’s in that we offer a general framework for examining
voter inequality. One can think of the right-wing bias we
identify as a specific case in which the magnitude of the
district and hence the rules of the game covary with voter
preferences and result in representational bias.
Representational Inequality across States. Does the districting structure in a country affect its representational
inequality? One of the most established stylized facts in
the study of electoral systems is that the greater the district
magnitude, the more proportional is the system (see, e.g.,
Lijphart 1984; Taagepera and Shugart 1989). Specifically,
the relationship established is between a central tendency
of district magnitude and the degree of proportionality
in the country, commonly specified in one of three ways:
average district magnitude in the country (e.g., Edwards
and Thames 2007; Taagepera and Ensch 2006), median
district magnitude (e.g., Carey and Hix 2011), and the
magnitude of the district electing the median legislator
(Amorim Neto and Cox 1997; Gabel and Scheve 2007).9
Our theorizing suggests that perhaps something else is
at work. If indeed supporters of right-leaning parties
are overrepresented in small districts more than in large
ones, as is the case in most Western countries, then the
share of parliament elected via small districts should
matter irrespective of the average (or median) district.10
This allows us to shift from winners and losers within a
country to cross-country analysis of the general level of
representational inequality. In particular:
H2: The greater is the share of parliament elected
via small districts, the greater is voter inequality
in the country, controlling for central tendency
district magnitude.
If supported empirically, this conjecture has key
implications not only for our understanding of
8
The potential effect of uneven district magnitude is also mentioned
by Taagepera (2007, 37–38). He writes that it is “considered a minor
deviation from simple electoral systems. Yet it can significantly alter
the survival chances of small parties. It can also alter the seat balance
for major parties” (38).
9
The median legislator is defined by the magnitude of the district in
which she is elected: This is the legislator who half of her colleagues
are elected in smaller districts.
10
While the limiting effect on permissibility depends on the distribution of votes and we do not call to identify a single point where
districts behave like “small” ones, districts of six seats or fewer often
hamper permissibility to a substantial degree.
681
UNEQUAL REPRESENTATION
parliamentary representation of different groups but also
for the design of electoral systems.
These hypotheses allow us to examine inequality
among supporters of different parties as well as differences in representational inequality across countries. We
turn now to empirically evaluate them.
Empirical Analysis
Cases and Data
We utilize district-level data of recent elections in 20
Western parliamentary democracies. These include a
wide range of electoral systems: 14 cases of districted proportional representation complemented by three cases of
FPTP and four cases of national-district PR in our crosscountry analysis. Geographically, 17 of our cases are Western European, and to those, Canada and New Zealand
1993 are additions on the majoritarian end, and Israel and
New Zealand 1996 are additions on the national-district
PR end.11 The two New Zealand cases, immediately
before and after the reform, give us additional empirical
traction. Excluded from our data is Austria. The Austrian
system allocates a large fraction of parliamentary
seats above the district level (e.g., in 2008, only 71 of
183 seats were allocated at the district stage). This
makes any attempt to empirically analyze representation
based on allocation of seats at the district level futile.
(Greece, too, has a fraction of parliamentary seats that
are allocated above the district level, but in the relevant
elections, 96% of the seats were allocated in the districts
themselves; hence, we include it in our analysis.) Table A1
in the supporting information presents a full list of our
cases and information about their districting structure.12
Our 14 districted PR systems vary both in their average and median districts and in the variation of their
district magnitudes. With the exception of Italy (22.5),
average district magnitude varies from 3.9 (Ireland) to
15 (Luxembourg) and is 9.4 on average. Within-country
range is as small as two in Ireland and as large as 45 in
Portugal. The distribution in most countries tends to be
right-tailed, with many districts of small magnitude and
a few districts of large magnitude.
Before we move on, an important issue needs to
be addressed. Some of our districted PR cases have
11
Given the focus of this study on the transition of party votes to
seats, we code both New Zealand 1996 and Germany as a nationaldistrict PR.
12
Given the electoral system that allows multiple votes per voters,
we normalize the district-level vote totals by district magnitude in
Luxembourg and Switzerland.
compensatory seats designed to mitigate district-level
distortions. Iceland, Norway, and Sweden have “at large”
seats tagged onto each district, consisting of 0.14, 0.11,
and 0.11 seats in their parliaments, respectively. These
seats are allotted to parties by national vote shares and
are added to every geographically defined district after
district-level gaps between votes and seats are calculated.
Put differently, districts have a few (or one) seats that are
allotted by a calculation different from that of the rest
of the seats in the district. Our data include these seats as
part of the district, and hence such mechanisms aimed
to mitigate distortion in representation are accounted
for by our data. Unlike these three cases, in Denmark,
a compensatory district of 40 seats exists separately
from the geographically defined districts. Similar to the
other cases, however, this district does not result from a
separate set of votes but rather from the regular votes cast
in the districts. In this case, our analysis does not include
that additional district (in fact, we cannot include them,
as they do not result from separate votes) and potentially
somewhat overestimates distortion in representation.
Overall, our data consist of 236 parties (153 of which
attained seats in parliaments) in 1,391 districts (330 in
districted PR systems). We included in our database all
competing parties but grouped voters of extremely small
parties and individual candidates if they failed to reach
0.2% of the national vote. Our data sources are official
online records of election results usually published by the
committee of national elections or the Ministry of the
Interior in the relevant country.
Voter Inequality: A General Picture
Figure 2 presents a general picture of representational
inequality in 20 democracies. These are the empirical realizations of the hypothetical graph in Figure 1C, with
every point on each curve representing voters who support a particular party and reside in a particular district
(NK points per country). The countries are organized by
ascending order of average district magnitude, beginning
with FPTP (the first three cases), moving onto districted
PR in the following 14 cases, and ending with nationaldistrict PR in the last four cases.
The first three cases display particularly high inequality, with an RI index of close to 0.6 and over 50% of
the votes that are not converted to seats in parliament (the
horizontal part of the curve at zero). For comparison, in
the United Kingdom, 53% of the votes cast in constituencies are not represented, whereas the parallel figure
ignoring constituencies and aggregating votes and seats
nationwide instead is no more than 7%. The smallest
682
ORIT KEDAR, LIRAN HARSGOR, AND RAZ A. SHEINERMAN
FIGURE 2 Representational Inequality in 20 Democracies
.6
.8
Cum. vote-share
1
1
1
1
1
1
.6 .8
.4
.2
Cum. seat-share
.2 .4
.6
.8
Cum. vote-share
1
0
.2 .4
.6
.8
1
.8
1
Cum. vote-share
.6
Cum. seat-share
RI .06
.8
1
Israel
RI .17
.8
1
.8
.8
RI .19
Italy
0
Cum. seat-share
.6
Cum. vote-share
.6
Cum. vote-share
0
0
0
.2 .4
.2 .4
Sweden
.4
1
RI .18
0
.8
0
.2 .4
.8
.6
Cum. seat-share
0
1
.6 .8
1
.6
Cum. vote-share
.2 .4
1
.8
.6
Cum. seat-share
0
.8
.2
Cum. seat-share
.2 .4
.8
1
.8
.6
RI .21
Luxembourg
Cum. seat-share
.6
Cum. vote-share
.4
Cum. vote-share
0
0
0
.2 .4
.2 .4
1
.8
.6
Cum. seat-share
0
1
.6 .8
.4
1
.2
Iceland
.2
Cum. seat-share
.8
.8
1
0
0
.2 .4
.6
.8
Cum. vote-share
1
0
.2 .4
.6
Cum. vote-share
Germany
1
1
Cum. seat-share
.8
.4 .6
RI .08
0
Cum. seat-share
.2 .4
.6
Cum. vote-share
RI .19
0
RI .02
0
0
.2 .4
.6
Cum. seat-share
1
1
0
0
0
.8
.8
Portugal
.2 .4
1
.8
.6
Cum. vote-share
.6
Cum. vote-share
RI .18
Belgium
.2
.8
.4 .6
.2
0
.2 .4
.2 .4
.6
1
the Netherlands
RI .08
0
.2 .4
.8
RI .15
0
New Zealand 96
1
.6 .8
1
.6
Cum. vote-share
.6
Cum. seat-share
1
.8
.4
Cum. seat-share
.2 .4
0
.8
.6
0
0
.2 .4
.6
.6
Cum. vote-share
.4
Cum. vote-share
RI .25
Finland
.2 .4
.2 .4
.2
.2
1
.6 .8
1
.2 .4
1
0
Norway
.4
Cum. seat-share
.8
RI .17
0
.8
1
0
.6
Cum. vote-share
.8
1
.8
.2
.6 .8
.4
.2
.2 .4
0
Cum. seat-share
.6
Cum. vote-share
RI .22
Denmark
1
.2 .4
Switzerlza
nd
0
Cum. seat-share
1
Spain
RI .23
0
.6
Cum. seat-share
0
0
.6
1
.2 .4
.8
RI .27
.8
.6
Greece
RI .09
.4 .6
.4
Cum. vote-share
Malta
RI .37
.2
.2
Ireland
RI .58
.2 .4
.6
Cum. seat-share
0
.2 .4
.8
.6
.2 .4
0
Cum. seat-share
Canada
RI .59
.8
1
New Zealand 93
0
Cum. seat-share
1
UK
RI .59
0
.2 .4
.6
.8
Cum. vote-share
1
0
.2 .4
.6
.8
1
Cum. vote-share
Note: The figure presents representational inequality curves for the 21 election years in our analysis. At the top left
corner is the Representational Inequality index (RI) for each election. Countries are organized in ascending order of
average district magnitude (see Table A1 in the supporting information for details).
inequality is observed in the four national-district PR
cases at the bottom row. There, only a relatively small
fraction of the vote is not converted to seats and the RI
index ranges from 0.02 to 0.08. Notice in particular the
dramatic difference between New Zealand 1993 and 1996.
The 14 districted PR systems are characterized by
greater voter inequality than one might expect. In fact,
they are as much as halfway between the PR in a single national district and the FPTP systems. Importantly,
voter inequality is not only about the votes that are not
converted to seats in the district. Recall that the shape
of the curvature is informative. In some countries, the
curve dips the most on the left while in others it dips on
the right—not only does the overall degree of misrepresentation vary by country, but so does the proportion of
underrepresented.
A bird’s-eye view, then, indicates that there is substantial variation in voter inequality within countries as
well as variation in the general level of inequality across
countries. The latter, it seems, is not only about the magnitude of the average district. We next turn to withincountry analysis, followed by cross-country comparison
in the subsequent section.
Who Equals More?
Whose voice is amplified and whose is diminished? As
mentioned above, large districts are often an electoral reflection of urban communities, whereas small districts
are those of rural and peripheral areas and small towns.
Given that in Western democracies the former are often more liberal than the latter and given the greater
UNEQUAL REPRESENTATION
inequality in small districts (a point we establish below), we hypothesized that supporters of right-leaning
parties are overrepresented compared with those supporting left-leaning parties and more so the smaller the
district.
To test the hypothesis, we utilize Benoit and Laver’s
(2006) expert survey of party placements conducted during the period of 2002–4. The survey includes data on
party placements on various policy dimensions, with the
general left-right dimension being most relevant for our
purposes. The placements are coded on a 20-point scale
such that high values denote a right-wing position. Since
the elections we analyze are not within that time window but rather one or two cycles later depending on
the country (in fact, not all countries held elections during the relevant time frame), we assume that there is no
major leapfrogging that changes the order of parties on
the left-right continuum in the relevant period. In terms
of coverage, in six of the cases all parliamentary parties
are coded in the expert survey, and in an additional five
cases almost all are coded.13 Italy has key parties missing a placement coding and is thus removed from this
analysis.
We estimated an interacted regression model of conversion ratio at the district/party level. On the right-hand
side, we have a party’s left-right placement, district magnitude, and their interaction such that at time t:
CRi j = b0 + b1 ln(dmi ) + b2 par tyLR j
+ b3 ln(dmi ) ∗ par tyLR j .
We ran the model for each of the 12 districted PR cases14
separately as well as pooled. Our key quantity of interest is the association between the ideological placement of a party and the conversion ratio of its votes
to seats and how this association is modified by district
magnitude (the estimates themselves are reported in the
Table A2 in the supporting information.
Figure 3 presents substantive effects based on this
analysis in each of the 12 countries that vary in their
district magnitude. On the vertical axis is the effect of
ideological placement on the party’s conversion rate in
the district, and on the horizontal axis is the (logged)
district magnitude (see the discussion in Brambor, Clark,
and Golder 2006 as well as Berry, Golder, and Milton
2012). An effect line above zero implies that right-leaning
683
parties better convert votes to seats than left-leaning parties do. A positive yet decreasing effect line that approaches zero from above implies that as the district
magnitude increases, right-wing voters lose their relative advantage of having their voice amplified compared
to their left-wing counterparts.
By and large, the findings support our predictions.
The mere correlation between the size of electoral communities and thus the degree to which their rules of the
game are proportional and the prevalent preference in
those communities tilts the playing ground.15 Let us carefully consider the results.
In those countries with substantial heterogeneity in
electoral regimes, supporters of right-leaning parties are
advantaged, and this advantage dissipates as district magnitude gets larger. This is the case in Greece, with district
magnitude spanning from 1 to 42, Spain (1 to 35), Sweden
(2 to 42), and Portugal (2 to 47, although in the latter the
interaction effect is significant only at 0.09). This is also
the case in Denmark, where heterogeneity is somewhat
smaller. In these cases, right-wing parties better convert
voter support to seats compared with left-wing parties
in small districts. With the exception of the two largest
districts in Sweden, this advantage becomes no different from zero once the district is large enough. In Spain,
for instance, it takes place for district magnitude larger
than 11.16
In two countries, Luxembourg and Ireland, the effect is positive, indicating an advantage to right-leaning
parties, but not necessarily declining with magnitude. In
Luxembourg, the small number of districts (four) may
contribute to the large standard errors. The Irish case is
an interesting one from several aspects. The combination of small districts and small variation in magnitude
(three to five representatives per district) as well as the
fact that left-right categorization might carry less information there compared with other countries might make
the estimation noisier. Additionally, Rodden’s (2010) argument about single-member districts can be extended
to this case: If indeed the left wins the district by a large
margin and the right by a small margin, right-leaning
parties better convert votes to seats compared with their
left counterparts in small districts, as in Ireland. Lastly,
in the remaining countries—Belgium, Finland, Norway,
and Switzerland—the effect is in the expected direction,
albeit not statistically significant.
13
The rate of missingness in terms of parliamentary seats is smaller
than 4% in Belgium, Greece, and Spain; 5.6% (one party) in Iceland;
and 11.5% (mostly independents) in Ireland.
15
We treat our data as random realization from an imaginary superpopulation of election results that could have been formed under
the same institutions (Berk 2004, 39–80).
14
Malta, with no variation on district magnitude, is omitted from
this analysis.
16
These assertions are based on the point in Figure 3 where the
lower-bound confidence interval intersects zero.
684
ORIT KEDAR, LIRAN HARSGOR, AND RAZ A. SHEINERMAN
FIGURE 3 Conversion of Votes to Seats: The Effect of Party Ideology
3
1
2
3
Effect of partyLR on CR
0
4
1
2
3
-.1 -.05 0 .05 .1 .15
Effect of partyLR on CR
0
4
-.1 -.05 0 .05 .1
.3
.2
.1
0
-.1
Effect of partyLR on CR
.3
.2
.1
0
.15
.05
.1
Effect of partyLR on CR
-.1
2
1.5
4
2
2.5
Denmark
(2-21)
Sweden
(2-42)
Finland
(6-34)
1
2
3
2.1 2.15 2.2 2.25 2.3
.5
1 1.5 2 2.5 3
Luxembourg
(7-23)
Pooled
Effect of partyLR on CR
.05
0
2
2.5
ln(DM)
3
3.5
2
2.5
3
Effect of partyLR on CR
Belgium
(4-24)
Effect of partyLR on CR
.05
0
0
1
2
3
4
ln(DM)
1.5
2
2.5
3
3.5
ln(DM)
-.1 -.05 0 .05 .1 .15
ln(DM)
-.02 0 .02 .04 .06
ln(DM)
-.05
Effect of partyLR on CR
0
Effect of partyLR on CR
0
-.06 -.04 -.02
4
ln(DM)
3
-.06-.04-.020 .02.04
Iceland
(8-10)
.1
Portugal
(2-47)
.02 .04 .06 .08
ln(DM)
.02
ln(DM)
Effect of partyLR on CR
ln(DM)
-.05
1.5
1
ln(DM)
.1
0
Effect of partyLR on CR
0
ln(DM)
-.05 0 .05 .1 .15
Effect of partyLR on CR
1.1 1.2 1.3 1.4 1.5 1.6
Norway
(4-17)
Switzerland
(1-34)
Spain
(1-35)
Greece
(1-42)
0
Effect of partyLR on CR
Ireland
(3-5)
0
ln(DM)
1
2
3
4
ln(DM)
Note: Countries are organized in ascending order of average district magnitude. Minimum and maximum district magnitudes are reported under country names. The line represents the marginal effect of party ideological
placement on CR modified by district magnitude. 95% confidence intervals are marked. Standard errors are clustered by districts. The pooled model includes country fixed effects and clustered standard errors by districts. Estimation results are reported in Table A2 in the supporting information. See the robustness checks for additional
estimations.
How Districting Schemes Affect Inequality:
A Comparison across States
Our insights from the within-country comparisons call
for cross-country analysis of the effect of districting
schemes on the overall level of representational inequality. As we show in Figure 2 above, the fact that systems of
single-member districts are characterized by particularly
high representational inequality and those of very large
districts (in fact, a national district) by a high level of
equality is only part of the story. There is a substantial degree of variation in inequality among districted PR cases,
and importantly, inequality does not simply decline with
average district magnitude.
To analyze variation in the overall level of representational inequality across countries, we first examine the
districting structure in our districted PR cases.17 Figure 4
presents histograms of district magnitudes in 13 countries. Given our findings about the high level of inequality
across voters found in small districts, we pay special
attention to the proportion of voters casting their ballot
in small districts. The dashed line marks the proportion
of parliament elected in districts smaller than five.
Most distributions are right-tailed with the average
being greater than the median (not reported here), and
some have a considerable number of small districts. Spain
17
Malta is ommited from this analysis as well.
685
UNEQUAL REPRESENTATION
FIGURE 4 Distributions of District Magnitudes under Districted PR
Ireland
Greece
Spain
40
50
10
0
0
10
20
30
40
Switzerland
20
30
40
20
30
40
50
0
District magnitude
6
Frequency
10
20
30
40
50
0
40
50
1
(0%)
1
0
Frequency
Frequency
50
30
Luxembourg
0
40
20
(3%)
2
1
0
30
10
District magnitude
Belgium
(0%)
20
50
0
1
Frequency
0
District magnitude
District magnitude
40
(1%)
0
50
Finland
10
30
Sweden
2
4
3
2
1
40
20
District magnitude
(1%)
District magnitude
0
10
Denmark
0
30
2
3
10
(0%)
20
50
0
0
Iceland
10
40
(10%)
Frequency
2
1
50
District magnitude
0
30
Portugal
3
10
20
District magnitude
0
0
10
(2%)
Frequency
0 1 2 3 4 5
Frequency
0
Norway
(8%)
Frequency
50
District magnitude
1
30
4
20
District magnitude
2
10
5
Frequency
10
5
0
0
Frequency
(18%)
15
(31%)
Frequency
0 5 10 15 20
Frequency
(67%)
0
10
20
30
40
District magnitude
50
0
10
20
30
40
District magnitude
50
Italy
1
0
Frequency
2
(0%)
0
10
20
30
40
50
District magnitude
Note: The figure presents histograms of district magnitudes in 13 Western European districted
PR systems. The black line marks district magnitude of five. In the upper right corner is the
percentage of seats in parliament elected in districts smaller than five. Countries are organized
in ascending order of average district magnitude.
686
is such an example. With an average district magnitude of
6.73 and a median of five, Spain has districts of magnitude
35 (Madrid) and 31 (Barcelona). At the same time, as
many as 18% of representatives in the 350-seat Congress
of Deputies are elected via districts whose magnitude
is smaller than five. Portugal, Sweden, and Greece are
similarly distributed. Yet not all distributions are righttailed, as one can see in Ireland or Denmark, among
other cases. The districting structure, then, varies across
states.
To evaluate the effect of the districting structure on
inequality, we shift to analyzing our summary RI index.
In particular, Table 1 presents the degree of country-level
inequality captured by the RI index as a function of
the proportion of parliament elected via districts with
magnitude smaller than three, five, or seven members
(see gray column). As above, the analysis in this table
includes all 20 states.18 We expect a positive coefficient
on the fraction of parliament elected via small districts
(leading to a greater level of inequality). Importantly, the
analysis controls for the magnitude of the central district.
We use three different measures of central tendency commonly found in the literature (see the discussion leading
to Hypothesis 2 above): the magnitude of the average
district, the median district, and the district electing
the median legislator.19 We also control for ordinal
ranking of the proportionality of the electoral formula, as
specified in Lijphart (1990; 1 = Hare or Sainte Laguë; 2 =
Hagenbach-Bischoff/Droop, modified Sainte Laguë, or
single transferable vote [STV]; 3 = d’Hondt; 4 = singlemember plurality). Lastly, we control for whether a state
has STV (Ireland and Malta in this case). The robustness
section below reports alternative specifications.
The results support our hypothesis. The greater is
the share of parliament elected via small districts, the
greater is inequality across voters. These results hold for
the three alternative magnitudes and for the three alternative central tendency measures.20 Notice further that
the coefficient on central tendency (Models 1, 5, and 9)
is reduced once the fraction elected via small districts is
added to the analysis. These results draw attention to an
aspect of districting design and its effect on the quality of
18
Recall that New Zealand appears twice, before and after the electoral reform; thus, we have 21 cases altogether.
19
We use both median(ln(DM)) and ln(median DM) and the same
for the average district. We report here the former, but the two
alternatives yield the same results.
20
In addition to the magnitudes reported here, Figure A2 in the
supporting information presents the coefficients for district magnitudes between 2 and 12. Results are consistent with the ones
reported here. We thank an anonymous reviewer for making this
suggestion.
ORIT KEDAR, LIRAN HARSGOR, AND RAZ A. SHEINERMAN
representation overlooked by the voluminous literature
of electoral systems. How representationally unequal a
democracy is is determined not only by how majoritarian
is the voting environment of the median or average voter,
but also to a large degree by the lower tail: how many legislators are elected in majoritarian or almost majoritarian
settings.
Confirmatory and Robustness Analyses
In addition to our hypotheses, we empirically evaluated
the behavior of our concept of representational inequality,
conducting two analyses. First, we analyzed the level of
representational inequality by district magnitude. To this
end, we ran a model at the party/district level within
each of the districted PR cases in which we estimated
the effect of (logged) district magnitude on the degree
to which the conversion ratio is different from one.21
In all cases, we find the relationship as expected—small
districts are characterized by greater inequality compared
with large districts—and in all but one, this relationship
is statistically significant.
Second, we analyzed parliamentary representation
of supporters of small and large parties. In particular, we
expected that voters of electorally large parties have their
voice amplified in parliament compared with that of
supporters of small parties, and that the effect is stronger
where district magnitude is small. We ran an interacted
regression model at the district/party level in which we
estimated the effect of party vote share in the district on
conversion ratio and let that effect be modified by district
magnitude. The results support our expectation (see Table A4 and Figure A1 in the supporting materials). In all
countries, voters who support large parties are overrepresented in parliament compared with their vote share at the
expense of those who support small parties, and in most
countries this effect declines with district magnitude.22
We estimated our models in various ways. The results
reported for Hypothesis 1 above are both country-bycountry and pooled, where the former includes standard
errors clustered by districts and the latter standard errors clustered by districts and country fixed effects.23 We
also estimated the models with party-clustered standard
21
The dependent variable is abs(1–CR). See the results in Table A3
in the supporting information.
22
The pooled analysis (with country fixed effects and clustered
standard errors) is consistent with our expectation as well. We ran
the analysis on 12 of the 13 districted PR cases (excluding Malta).
23
Given that analyses for Hypothesis 1 include district magnitude
on the right-hand side, a district fixed effect cannot be included.
687
UNEQUAL REPRESENTATION
TABLE 1 Representational Inequality: The Effect of Districting Structure
Model
Proportion of
Parliament Elected
in Districts < 7, 5, 3
1
2
%<7
3
%<5
4
%<3
0.38
(0.08)
0.39
(0.03)
0.35
(0.05)
Electoral
District
Formula
Magnitude
STV
(Lijphart)
Average District Magnitude
–0.07
(0.02)
–0.03
(0.01)
–0.03
(0.01)
–0.04
(0.01)
–0.06
(0.08)
–0.33
(0.08)
–0.10
(0.02)
–0.00
(0.04)
Constant
N
R2
0.04
(0.03)
–0.02
(0.02)
–0.03
(0.01)
–0.02
(0.02)
0.32
(0.09)
0.26
(0.06)
0.30
(0.02)
0.34
(0.05)
21
0.71
21
0.88
21
0.98
21
0.92
0.03
(0.03)
–0.02
(0.02)
–0.03
(0.01)
–0.03
(0.02)
0.34
(0.09)
0.26
(0.06)
0.31
(0.02)
0.35
(0.06)
21
0.71
21
0.88
21
0.98
21
0.92
21
0.77
21
0.89
21
0.98
21
0.92
Median District Magnitude
5
6
%<7
7
%<5
8
%<3
0.38
(0.08)
0.39
(0.03)
0.35
(0.05)
–0.07
(0.02)
–0.03
(0.01)
–0.04
(0.01)
–0.04
(0.01)
–0.07
(0.08)
–0.33
(0.08)
–0.10
(0.02)
0.00
(0.04)
District Magnitude of Median Legislator
9
10
%<7
11
%<5
12
%<3
0.34
(0.08)
0.37
(0.03)
0.31
(0.06)
–0.08
(0.01)
–0.04
(0.01)
–0.04
(0.01)
–0.05
(0.01)
–0.10
(0.07)
–0.32
(0.07)
–0.11
(0.02)
–0.02
(0.04)
0.03
(0.02)
–0.02
(0.02)
–0.03
(0.01)
–0.02
(0.02)
0.39
(0.09)
0.30
(0.07)
0.33
(0.02)
0.37
(0.05)
Note: Dependent variable: RI. Data are at the national level. For figures in boldface, p-value < .05. Standard errors are in parentheses.
STV is a control for electoral systems with single transferable vote (Ireland and Malta). Electoral formula is an ordinal index of electoral
formulas based on Lijphart (1990). Robustness checks are reported in the robustness subsection.
errors.24 The results are similar, although the standard
errors are larger. Additionally, we estimated hierarchical
models with partially crossed random effects. The results
are remarkably similar to the original ones reported in
Table A2 in the supporting information. The one exception is Denmark, where under the hierarchical model the
uncertainty of the interaction term exceeds standard levels of statistical significance. These results are reported in
Table A5 in the supporting materials.25 Lastly, in cases for
which the Chapel Hill Expert Survey data on party ideological placement are collected in years temporally closer
to the election years analyzed than Benoit and Laver’s data,
we reconducted the analysis using these party placements
(Bakker et al. 2015; Hooghe et al. 2010). The two data sets
correlate at 0.96, and the results are almost identical to
the original ones.
24
Given that the analysis for Hypothesis 1 includes party ideology
on the right-hand side, a party fixed effect cannot be included.
25
We are grateful to Dave Armstrong for his engagement, suggestions, and assistance on this part.
688
We also estimated various versions of our model testing Hypothesis 2 with the third central tendency measure,
the magnitude of the median legislator. In particular, we
varied inclusion of control variables, inclusion and specifications of the electoral formula ranking, and the cases
included in the analysis. In a nutshell: Results hold for
districts smaller than five in almost all specifications, and
depending on specification for districts smaller than three
or seven. What follows is a detailed account.
There is no one agreed-upon scale of proportionality
of electoral formulae, and in fact, nor is there a single
criterion by which to evaluate formulae (see Gallagher
1992, 494). Thus, we ran the analysis using three
additional alternative rankings: Rae’s (1967; consistent
with Farrell’s 2011 framework), Gallagher’s (1992), and
Benoit’s (2000).26
Results with control of electoral formula alone hold
for districts smaller than three and five given all rankings
and for districts smaller than seven depending on the
ranking. Results with control for single-member district
hold for districts smaller than five under Lijphart and
Gallagher’s rankings of formulae. Results with no control
variables hold for districts smaller than three and five.
When running the analysis controlling for Malta rather
than STV, results hold for all three district magnitudes
(both with and without formulae). Results with control
for single-member district and STV hold for districts
smaller than five depending on the formula coding.
When only the 13 districted PR states are included in
the analysis, results hold for districts smaller than five,
controlling for electoral formula (the four alternative
rankings) or STV. This is also the case when both formula
and STV are included in the model, although there, they
hold only under Lijphart’s and Gallagher’s formula rankings. Lastly, we ran the analysis on the districted PR cases,
omitting Malta. Results hold for districts smaller than
five and seven, and once the electoral formula is added,
they hold under Lijphart’s and Gallagher’s rankings.
Lastly, we included malapportionment, a key suspect
for causing representational disproportionality (Samuels
and Snyder 2001). Our inequality analysis is related to
malapportionment but is by no means identical to it. Results including malapportionment hold for magnitudes
smaller than three and five for almost all specifications
and hold in direction but are not statistically significant
Rae’s coding: 1= Hare or Hagenbach-Bischoff/Droop, 2 = Sainte
Laguë or modified Sainte Laguë, or d’Hondt, 3 = single-member
plurality. Gallagher’s coding: 1 = Hare or Sainte Laguë, 2 = modified Sainte Laguë, 3 = Hagenbach-Bischoff/Droop, 4 = STV, 5 =
d’Hondt, 6 = single-member plurality. Benoit’s coding: 1 = Sainte
Laguë, 2 = Hare, 3 = Hagenbach-Bischoff/Droop, 4 = modified
Sainte Laguë, 5 = d’Hondt, 6 = single-member plurality.
ORIT KEDAR, LIRAN HARSGOR, AND RAZ A. SHEINERMAN
for magnitudes smaller than seven. Malapportionment
itself is not statistically significant.
Issue Positions of Copartisans
Residing in Different Regions
Above, we contend that copartisans residing in different regions often differ in their interests. In the United
States, variation in ideological positions corresponding
with districts is established both among legislators (e.g.,
McCarty, Poole, and Rosenthal 2009) and among voters
(Gerber and Lewis 2004).
In an analysis conducted on a rich set of policy questions, we show that this is also the case under districted
PR. In particular, utilizing data from the 2009 Norwegian
Election Surveys, which include multiple policy questions
on various dimensions, we compared the positions of supporters of both Labour and the Conservatives residing in
the Oslo Metropolitan area with those of their respective
copartisans residing in the West, the two most populated regions of the country. We drew on two batteries of
questions: the first regarding economic policies, and the
second regarding social policies. Answers to these items
are on agreement scales.
We find that among Labour supporters, there is no
systematic variation in economic policy preferences between those living in the West and their counterparts
in the Oslo area. On social issues, however, positions of
residents of the Oslo area are more liberal than those of
the West, and on most issues substantially so. Among supporters of the Conservatives, we found differences on both
dimensions: Those residing in the Oslo area are more liberal compared with their counterparts living in the West
on questions of keeping tax revenues, economic inequality, and private schooling. They also hold more liberal
positions on social issues. Figure A3 in the supporting
information presents the results of this analysis.
This simple analysis suggests that differences correlating with districts among copartisans exist, that some
parties are characterized by greater such heterogeneity
than others, and that on some issues, party supporters in
different parts of the country think alike while on others
they do not.
26
Predictable Implications
Unequal representation has empirical implications. We
briefly reflect on two. Besley and Preston (2007) show that
689
UNEQUAL REPRESENTATION
under majoritarian democracy, representational bias has
policy implications: Policy pursued by the party enjoying
the bias tends to be assertive when the bias is large and
tamed when the bias is smaller. In our study, those on the
flatter part of the representational inequality curve have a
smaller share of parliamentary seats compared with their
share in the national vote. Given evidence on districted
efforts by parliamentarians discussed above, one might
expect that voters whose ratio of seats to votes is low are
likely to enjoy fewer services and weaker policy to their
benefit compared to their counterparts.
Given our finding of representational bias, it is likely
that a within-party bias exists as well. In particular, one
might expect that liberal parties in parliament underrepresent their supporters residing in small, conservative
districts who constitute a minority there and that conservative parties, on the other hand, overrepresent their
supporters residing in small, conservative districts. These
two groups are not representative samples of party supporters. The former (underrepresented by their party) are
likely closer on average to the center than other supporters
of liberal parties, and the latter (overrepresented by their
party) are likely further away from the center compared to
other supporters of the conservative party. This is likely to
create discrepancy between voters and parties’ positions,
consistent with the well-documented regularity in comparative politics whereby parties are more extreme than
their voters (e.g., see Adams, Merrill, and Grofman 2005;
Iversen 1994).
Conclusion
This article offers a new approach to the study of parliamentary representation. We take a bottom-up strategy whereby we focus on the representation of a single
vote and ask how equal it is to that of others under proportional representation. We find a systematic pattern
to voter inequality under districted PR—division of the
parliamentary pie is often biased in favor of supporters
of right-wing parties in comparison to the electorate. We
further demonstrate that districted PR is colored by majoritarianism more than common wisdom suggests, and
more so in those countries where the districting structure
relies on a few large districts and many small ones. Irrespective of the institutional environment of the average
(or median) voter, how many legislators are elected in
semi-majoritarian districts affects the bias in parliament.
The questions we ask about equality in representation
and the answers we provide suggest that districted PR, the
most prevalent electoral system in the democratic world,
does not deliver as well as perceived. Even if representational discrepancies across districts were to cancel out
entirely such that no systematic bias for some interests
over others would have existed, our analysis challenges
the common assumption that representation can be accomplished on average. Few voters would be comforted
by the fact that although their own voice is muted, an
anonymous supporter at the other end of the country has
her own voice amplified.
Our analysis opens the door to new avenues of research on electoral politics. First, our analysis points to
the importance of districting under PR. What is often
considered to be of key consequence in the Anglo American world of FPTP turns out to be no less central under
districted PR. Changing magnitudes of districts even if
keeping the median district unchanged is often politically
consequential for the representation of various interests.
The drawing of district boundaries may also affect minority representation as well as turnout.
On the voters’ side, it extends the definition of strategic voting. Commonly, strategic voting explains why voters shun parties whose viability in obtaining a seat is
in question. Our analysis suggests a potentially broader
consideration. Voters may desert parties whose ability to
convert their votes to parliamentary representation is just
hindered (Gunther 1989) and prefer those who amplify
their voice. In other words, strategic voting may be not
only about getting a seat but also about getting a smaller
or larger fraction of a seat for one’s vote.
Electoral districts are considered an effective democratic instrument that channels local interests into legislative politics. We show that this very same instrument,
even under a proportional framework, also compromises
a cornerstone of democracy: the equality of votes. It is the
association between district magnitude and interests of a
district community that biases the playing field: Within
one state, different interests are being channeled by different rules of the game. This puts both a normative question
and a professional challenge at the doorstep of institutional designers.
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Supporting Information
Additional Supporting Information may be found in the
online version of this article at the publisher’s website:
Table A1: Districting Structure in Twenty Western
Democracies
Table A2: Conversion of Votes to Seats: The Effect of Party
Ideology
Table A3: Voter Inequality and District Magnitude
Table A4: Conversion of Votes to Seats: The Effect of Party
Size
Table A5: Conversion of Votes to Seats: The Effect of Party
Ideology (HLM)
Figure A1: Conversion of Votes to Seats: The Effect of
Party Size
Figure A2: Representational Inequality and Small Districts: Eleven Cutoff Points
Figure A3: Issue Positions of Co-partisans: Norway 2009