1
Introduction to Electoral Systems
Michael Gallagher and Paul Mitchell
Electoral systems matter. They are a crucial link in the chain connecting the
preferences of citizens to the policy choices made by governments. They are chosen
by political actors and, once in existence, have political consequences for those
actors. They are an important object of study for anyone interested in the political
process, and in this book we subject them to systematic analysis.
In all but the smallest-scale societies, government is representative government,
in which the people do not govern themselves directly but rather delegate the task of
political decision-making to a smaller set of public officials. In democratic societies
these representatives are elected, and it is the question of how they are elected that is
the focus of this book. In particular, we are interested in exploring variations in these
methods of election, and in knowing whether, and in what ways, it makes a
difference how they are elected. The method of election is, quite obviously, a crucial
link in the chain of representative democracy.
First, we need to start with a definition. By an electoral system we mean the set of
rules that structure how votes are cast at elections for a representative assembly and
how these votes are then converted into seats in that assembly. Given a set of votes,
an electoral system determines the composition of the parliament (or assembly,
council, and so on as the case may be). The electoral system is narrower than what
we term electoral regulations, by which we mean the wider set of rules concerning
elections. Such rules—concerning, for example, ease of access to the ballot for
would-be candidates, the right to vote, the fairness of the administration of the
election, the transparency of the counting of the votes—are all very important in
determining the significance and legitimacy of an election. However, they should
not be confused with the more narrowly defined concept of the electoral system
itself.
Sceptical readers faced with a large book on electoral systems thus defined
might wonder whether it really matters so much which electoral system a country
adopts. Why should anyone care whether a country opts for the D’Hondt or the
Sainte-Lague¨ method of allocating seats? What difference does it make if the
weight of preference votes is increased or decreased? Would anyone other than
a few electoral system fanatics with nothing better to do with their time even notice
if a country moves from a parallel mixed system to a compensatory one or vice
versa?1
Anecdotal evidence suggests that many practising politicians do, indeed,
frequently react with bored indifference to what they see as trivial technicalities that
can be left to the anoraks in the back room to sort out while they decide the really
important questions. Ordinary citizens, too, might wonder whether the analysis in
this book is really something they need to know. The choices might seem obscure,
the terminology arcane, and the issues at stake unclear.
Needless to say, we believe these questions do matter—otherwise we and the
authors of the following chapters would not have taken the trouble to put this book
together. Moreover, even a little bit of reflection should be enough to convince
anyone that electoral systems can make a difference. Even those who do not feel
they need to understand the distinction between the highest averages and largest
remainders methods of seat allocation realize that there is a big difference between
single-member constituency systems (such as ‘first-past-the-post’) and proportional
representation (PR) systems. That is one choice that very few politicians would be
willing to leave to someone else to decide.
To illustrate this, consider the history of British government since the late 1970s.
Throughout the 1980s, the Conservative Party under Margaret Thatcher enjoyed
huge parliamentary majorities and implemented a series of radical right-wing
changes to economic and social policy. In 1997 and 2001, the Labour Party under
Tony Blair achieved equally large majorities in the House of Commons. Yet, each of
these majority governments was elected on 41–43 per cent of the votes. If Britain
had had a PR system then, even if there was no change in the way votes were cast,
the pattern of government formation would have been very different. In 2001, for
example, Labour, having won 41 per cent of the votes, would have had either to
negotiate a coalition with the third-placed Liberal Democrats or to try to form a
minority government on its own. Under either option, Tony Blair would not have
been nearly as free to commit British troops to the war in Iraq in 2003. Individuals
will have their own opinions as to whether this would have been a good thing or a
bad thing—what cannot be disputed is that a different electoral system would have
made a big difference to policy output.
Electoral systems matter in other ways too, as we shall see. They may make a big
difference to the shape of the party system, to the nature of government (coalition or
single-party), to the kind of choices facing voters at elections, to the ability of voters
to hold their representative(s) personally accountable, to the behaviour of parliamentarians,
to the degree to which a parliament contains people from all walks of
life and backgrounds, to the extent of democracy and cohesion within political
parties, and, of course, to the quality of government, and hence to the quality of
life of the citizens ruled by that government.
In this book, we are looking at two kinds of issues. First, we are interested in the
‘political science of electoral systems’—this book aims to join the canon of works
that have attempted to explore various relationships between electoral systems on
1
Or, as David Farrell (2001: 1) puts it, ‘How many wars were fought over whether the electoral
formula was ‘‘largest remainder’’ or ‘‘highest average’’?’
4 The Politics of Electoral Systems
the one hand and the kind of ‘outputs’ that we mentioned in the previous paragraph.
We do not, though, see electoral systems merely as causal agents—we will also be
examining the origins of those systems. Second, the book studies the ‘politics of
electoral systems’. It treats each country’s electoral system as, potentially at least,
constituting a political issue in its own right. We will be asking who supports an
electoral system and who opposes it, who benefits from it and who loses out, and we
will be focusing on the current debate in each country on the question of electoral
reform. This will highlight issues relevant to normative debates about which electoral
systems ‘work well’ and which ones do not, which ones operate uncontentiously
and which ones are a focus of division in the countries employing them.
Shortly, we will elaborate on these points by outlining the structure of this book.
First, we will present a brief overview of the various ‘families’ of electoral systems.
DIMENSIONS OF ELECTORAL SYSTEMS
‘It is the easiest thing in the world to get inextricably tangled among the complexities
of electoral systems’, wrote Eckstein (1963: 249) in the middle of the last
century. To avoid bogging the reader down in a morass of detail at this stage of the
book, we refer readers to Appendix A for a discussion of the mechanics of electoral
systems and an explanation of exactly how they work. Here, we outline some broad
categories into which electoral systems fall. For the purposes of this book, we have
assigned electoral systems to one of five categories, listed in Table 1.1, although in
some cases there is considerable variation within these.
Table 1.1 Categories of electoral system
Broad category Specific types Country examples
Single-member
constituency systems
Single-member plurality
(SMP)
Chapters 4–9
Australia, Canada,
Alternative vote (AV)
Two-round system (2RS)
France, India,
UK, USA
Mixed systems Mixed compensatory Chapters 10–15
Mixed parallel Germany, Hungary,
Italy, Japan, New
Zealand, Russia
Closed-list systems — Chapters 16–18
Israel, South Africa, Spain
Preferential list systems Open list Chapters 19–24
Flexible list Austria, Belgium, Chile,
Denmark, Finland,
Netherlands
PR-STV — Chapter 25
Ireland
Introduction to Electoral Systems 5
The first category consists of those systems under which all seats are allocated
within single-member constituencies (known in the USA as single-member districts
and hence often abbreviated, even outside the USA, to SMDs). There are many
different ways of allocating a single seat, and we will elaborate on these later in the
chapter and in Appendix A, but since such systems have a lot in common in terms of
their effects, it makes sense to treat them as a single broad category. As Table 1.1
shows, we will be looking in detail at six countries with such systems.
The second broad category is that of ‘mixed’ systems, in which some MPs are
elected by a plurality or majority formula (usually from SMDs) and others are elected
by PR. This type of system is growing in popularity, and six chapters examine the
operation of mixed systems. List systems are based on the idea of parties presenting
lists of candidates within each multimember constituency. They are conventionally
divided into two types: those using closed lists, in which the voter cannot express a
choice for individual candidates on the list, and those based on preferential lists,
where voters can do so. We will be looking in depth at three countries with closed list
systems and at six with preferential list systems. Finally, under PR-STV (proportional
representation by the single transferable vote) voters are able to rank-order all
candidates within each multimember constituency, and the final country chapter
examines the record of this system in Ireland. Before we move on to the country
studies in chapters 4–25, though, we need to outline more fully the main dimensions
on which electoral systems differ, and these are set out in Table 1.2.
District magnitude
The first dimension is district magnitude, the number of seats per constituency. As
we shall see throughout the book, this is not just a useful taxonomic aid but a factor
that makes a big difference to the effects of an electoral system and thus to a
country’s politics. Measuring average district magnitude is straightforward in countries
where all constituencies are of the same size: single-member constituency
systems such as Australia, Canada, France, India, the UK, and the USA, or those
few other countries where all the constituencies are multimember and of uniform
size such as Chile (2) and Malta (5). In a few countries there is only one (national)
constituency, so the number of seats is the district magnitude in the Netherlands
(150), Israel (120), and Slovakia (150).
In some other countries district magnitude varies, but we can easily work out an
average value. For example, in Spain 350 members of parliament (MPs) are returned
from 52 constituencies, so average district magnitude equals 6.7, while in Ireland
there are 42 constituencies and 166 MPs and average district magnitude is 4.0. We
might wonder, though, whether it matters how this mean is arrived at. In Ireland, as it
happens, all constituencies return either three, four, or five MPs—but suppose its
166 MPs were instead returned from 40 two-seat constituencies and 2 forty-threeseat
constituencies? Would this make any difference to the kind of outcomes we
could expect? Simulations conducted by Taagepera and Shugart (1989: 264–6)
suggest that in many ways it would not make a difference, but small parties can
6 The Politics of Electoral Systems
expect to fare better if there are at least a few really large constituencies. More
detailed study by Monroe and Rose (2002) of the consequences of this ‘magnitude
variation’ concludes that this factor is more important than generally recognized
and, because district magnitude in urban areas is usually larger than in rural areas,
the effect is to disadvantage large parties with a predominantly urban base.
We might also wonder whether the number of constituencies, as well as their
average size, makes a difference. The simple answer is that it does, and this question
is explored more fully in Appendix C.
Things become a bit trickier when there is more than one ‘tier’ of seat allocation,
but since we have not discussed that dimension yet, we will postpone the full
consideration of district magnitude until the end of this section.
Number of votes cast
Since ‘one person one vote’ is a hallmark of a democratic system, why would we
encounter any variation here? The reason is simple: giving people more than one
vote does not violate democratic principles provided everyone still has the same
number of votes. Having just one vote is very much the norm, but in most cases
within the family termed ‘mixed’ systems everyone has two votes. For example,
when voters in Germany or New Zealand go to the polling station on election day
they are confronted with a ballot paper that invites them to cast one vote for a
candidate to represent their local single-member constituency, and another vote for a
party in the contest for seats awarded at the national level (see Figure 10.1 or 14.1).
Ballot structure
Douglas Rae (1971: 17–18) was the first to make a distinction between ballot papers
under which voters must cast a vote for one and only one party, which he termed
‘categorical’ or ‘nominal’, and those under which the voter can rank-order the
parties or candidates, which he called ‘ordinal’. The significance of the distinction
is explained by Rae (1971: 18) in this way: ‘Categorical systems channel each parcel
of electoral strength into the grasp of a single party, while ordinal balloting may
disperse each parcel of electoral strength among a number of competing parties’.
Unfortunately, Rae seemingly did not realize that this ‘clarification’ goes beyond his
initial definition and leaves considerable confusion about how we should classify
ballot structures that allow the voter to ‘divide’ his or her vote between two or more
parties but not to do any rank-ordering.
The first category, at least, is clear enough. It covers ballot papers in most
countries. In these cases, the voter expresses support for the sole candidate of a
party (under single-member plurality), for a party list (Spain, Israel), or for one
candidate (Finland, the Netherlands, and others) or perhaps several candidates
(pre-1994 Italy) on one party’s list.
Rae’s ‘ordinal’ category, as we have said, is a little confused, and does not cover
all the systems in which the ballot structure is not categorical. Rae’s own treatment
Introduction to Electoral Systems 7
Table 1.2 Dimensions on which electoral systems vary
Dimension of
variation Value Examples
District magnitude
(number of seats
per constituency)
1 Single-member plurality (Canada,
India, UK, USA)
Alternative vote (Australia)
Two-round system (France)
More than 1 PR-list systems (Israel, Spain, South
Africa, Austria, Belgium, Chile,
Denmark, Finland, Netherlands)
Mixed systems (Germany, Hungary,
Italy, Japan, New Zealand, Russia)
PR-STV (Ireland)
How many votes
can a voter cast?
2 Mixed systems (Germany, Hungary,
Italy, Japan, New Zealand, Russia)
1 All other systems
Ballot structure Categorical (also
termed nominal
or integral)
Single-member plurality (Canada,
India, UK, USA)
Two-round system (France)
Virtually all PR-list systems
Dividual: can
‘divide’ vote
among different
parties
Mixed systems (Germany, Hungary,
Italy, Japan, New Zealand, Russia)
PR-list with panachage (Luxembourg,
Switzerland)
Ordinal: can rankorder
candidates
Alternative vote (Australia)
PR-STV (Ireland)
How much choice
does the voter
have regarding
individual
candidates?
No choice of
candidate within
party
Single-member constituency systems
(Australia, Canada, France, India,
UK, USA)
Mixed systems (Germany, Hungary,
Italy, Japan, New Zealand, Russia)
Closed-list PR systems (Israel, South
Africa, Spain)
Choice of candidate
within party
Preferential-list PR systems (Austria,
Belgium, Chile, Denmark, Finland,
Netherlands)
Choice of candidate
within party and
across party lines
PR-STV (Ireland)
(Continues)
8 The Politics of Electoral Systems
of such systems does not clear up the confusion, and Lijphart (1994: 119) has already
called attention to Rae’s ‘errors of classification’ here. Rae (1971: 42–4) describes
the German two-vote system as categorical (even though voters can cast their two
votes for different parties, thus ‘dividing’ their vote, in his terms). Logically, then, we
might expect him to deal similarly with those PR systems under which voters are
Table 1.2 (Continued)
Dimension of
variation Value Examples
How many levels of
seat allocation
does electoral
system have?
1 Single-member plurality (Canada,
India, UK, USA)
Alternative vote (Australia)
Two-round system (France)
Some PR-list systems (Belgium, Chile,
Finland, Israel, Netherlands, Spain)
PR-STV (Ireland)
2 (higher tier and
lower tier)
Compensatory mixed systems, also
termed corrective or MMP
(Germany, Italy—partially
compensatory, New Zealand)
Some PR-list systems (Denmark, South
Africa)
2 (both allocations
are at same level)
Parallel mixed systems, also termed
MMM (Japan, Russia)
3 (lowest, middle
and highest levels)
Some mixed systems (Hungary—
partially compensatory)
Some PR-list systems (Austria)
Measures to limit
the degree of
proportionality
Small district
magnitude (DM)
DM ¼ 1 (Australia, Canada, France,
India, UK, USA)
DM ¼ 2 (Chile), average 4 (Ireland)
DM is in effect small in mixed systems
when list seat allocation is separate
from single-member seat outcomes
(Japan, Russia)
Significant vote
thresholds that
parties need to
cross in order to
get any (or ‘fair’)
representation
Germany, Hungary, New Zealand,
Russia
Malapportionment USA (Senate), Chile, Spain, Canada,
France, India
Source: Chapters 4–25 of this book. The classification scheme draws in particular on the ideas and
discussions of Blais and Massicotte (2002); Cox (1997: 37–68); Farrell (2001: 4–10); Lijphart (1994:
10–56); Taagepera and Shugart (1989: 19–37).
Introduction to Electoral Systems 9
provided with the facility termed panachage, under which they have a number of
preference votes at their disposal and can distribute these among candidates on more
than one party’s list. This is used in Luxembourg and Switzerland (countries not
covered in this book). Inconsistently, though, Rae describes these as ordinal systems,
even though the voter cannot rank the options.
In reality, Rae’s classification would have been more useful with three categories,
allowing us to distinguish systems permitting rank-ordering from those permitting
simple vote-splitting. We term the latter ‘dividual’, since they enable votes to be
‘divided’ among more than one party.2
This category includes mixed systems in
which voters may, if they wish, cast their constituency vote for a candidate of one
party and their list vote for a different party, an option exercised by many voters in
New Zealand and by rather fewer in Germany. In a two-round system, voters may
switch from one party at the first round to a different one at the second—though
since voters cannot split their vote in any one round, and only one of their votes
can contribute towards the election of a candidate, this is probably better classified
as categorical. PR-list systems with the option of panachage belong in the
dividual category.
Ordinal voting, correctly defined, permits voters to rank-order the candidates on
the ballot paper. This is a central feature of both the alternative vote and PR-STV. In
each case, voters are faced with a list of all candidates in the constituency and may
rank all of them (or, at least, as many as they wish, depending on the specific
electoral laws) in order of their choice.
Choice of candidate within parties
The structure of the ballot will also make clear whether voters have any power to
choose among the candidates of their party. This facility is self-evidently unavailable
under single-member constituency systems, when parties do not offer more than
one candidate in the first place.3
PR-list systems differ on this dimension. Some, broadly termed preferential-list
systems, enable the voter to indicate a preference for one candidate (or sometimes
several candidates) on their party’s list, and these preference votes then play a role in
determining which candidates fill the seats that the party receives. Some preferential-list
systems are more open than others, and in Chapter 2, where this dimension is
explored fully (see pp. 41–4), a distinction is drawn between fully open lists, where
the voters alone determine which candidates receive the seats, and flexible lists,
where the party’s initial ordering of the candidates determines the outcome unless
sufficient numbers of voters combine to overturn this. How much of a role the
preference votes play therefore varies from case to case. In some countries, under
2
‘Dividual’ is defined by the Oxford English Dictionary as meaning ‘capable of being divided into
parts, divisible, divided into parts, fragmentary, divided or distributed among a number’.
3
As so often, an exception can be found even to this apparently solid generalization: in Japan the LDP
in safe seats sometimes allows two candidates to run and then admits the victor to its parliamentary party,
treating the election in effect as a primary (see Chapter 13, p. 283 below).
10 The Politics of Electoral Systems
fully open lists, they completely determine it (if the party wins three seats, for
example, the seats go to the three candidates with the highest numbers of preference
votes). In others, using flexible lists, the impact of preference votes is muffled by the
details of the rules. Chile and Finland epitomize the former approach, Belgium and
the Netherlands the latter. The sweeping generalization of Sartori (1997: 17–18),
based on Italian experience, according to whom party ‘machine bosses’ can manipulate
preference voting to ensure that they and their favoured candidates are elected
no matter how apparently ‘open’ the lists are, does not stand up to empirical scrutiny
as a broad proposition.
Other PR list systems, in contrast, employ ‘closed lists’, in which the voter can
choose among parties but not among candidates within parties, and the order of
candidates’ names that is decided by the party determines which of them receive its
seats. As it happens, in most of the mixed systems used to elect national parliaments
(and in all of those covered in this book) the list element employs closed lists, though
this is not an essential feature of mixed systems and in principle the lists could be
open, as they are in Lithuania. It is possible to see two different concepts of
representation underlying the choice to be made between preferential list and closed
list systems, a distinction that emerged when the question of which variant to adopt
was discussed in Sweden in the 1990s. According to one concept, the purpose of
elections is to enable the direct representation of the people, and consequently
preferential list systems, allowing the people to choose their own representatives,
are more appropriate. According to the other, representation takes place through the
political parties and the purpose of elections is to enable the parties to secure their
proper share of representation; consequently, closed lists are more appropriate than
open ones because the parties’ candidate selectors are better judges than the voters of
who is best able to realize the ideas and goals of the parties (Petersson et al. 1999:
117–23). In ‘principal–agent’ terms, MPs are the agents; closed list systems seem to
assume that parties are the sole principals, while open list systems assume that MPs
have two principals, parties and voters.
Finally, PR-STV gives voters a choice not only among their party’s candidates but
also across party lines; voters are not constrained by party lines when deciding how
to rank-order the names of all the candidates on the ballot paper.
Levels of seat allocation
Most of the dimensions that we have looked at so far are fairly straightforward, but,
all too often, it is when we get on to levels of seat allocation that those not
instinctively enthused by the subject of electoral systems find their eyes glazing
over. This is a pity because, even though the details of specific systems can be
complicated to master, the basic principles are easy enough to grasp.
In many countries there is only one level of seat allocation. In other words, each
voter casts a vote in a constituency; seats in that constituency are awarded, in
accordance with the rules, to parties (and candidates); and each party’s national
total of seats is simply the sum of the seats it won in each of the constituencies. There
Introduction to Electoral Systems 11
is, by definition, only one level of seat allocation in single-member constituency
systems such as Australia, Canada, France, India, the UK, and the USA. There is
also just one level in about half of the PR systems that we cover in detail in this book
(see Table 1.2).
Why, then, complicate matters by having more than one level or ‘tier’ of seat
allocation? There are various reasons for doing this, perhaps the most common of
which is that it gets round the problem caused by one of the most robust findings in
electoral systems research, namely that the smaller the average district magnitude,
the greater the disproportionality. This relationship is unfortunate because it points
to a trade-off between two desirable properties of electoral systems, namely ensuring
a close correspondence between the overall levels of electoral support and seats
in parliament for parties, and providing a local constituency representative for
voters. With just one tier, the two poles are a single-member constituency system,
which scores well on the local representation dimension but poorly on proportionality,
and a PR system with just one constituency covering the whole country (as in
Israel and the Netherlands), which gives excellent proportionality but no direct
representation for localities. With only one level of seat allocation, we are forced
to sacrifice a bit of one desirable property in order to get more of the other.
Having more than one level means that we might be able to have our cake and eat
it. Archetypal mixed systems, such as that in Germany, illustrate this point. Here,
half of the MPs are elected from single-member constituencies, while the other half
are elected from party lists. The list seats are awarded to parties in such a way as to
ensure that the total number of seats received by each party is proportional to its
share of the list votes.4
Hence, the system delivers a high degree of overall proportionality,
while at the same time each voter has a local constituency MP. Mixed
systems have thus been described as ‘the best of both worlds’ (Shugart and Wattenberg
2003c: 595). While the details differ greatly, the same kind of thinking, i.e.
supplying both proportionality and local representation, underlies the choice of a
two-tiered or even three-tiered seat allocation in some other countries too: those
using mixed systems, such as New Zealand, and single-vote systems such as Austria
and Denmark.
Of course, in the real world, there are also less noble reasons to have higher tiers.
Sometimes these tiers mainly have the effect of giving additional benefit to the
larger parties, as in the ‘reinforced PR’ used in Cyprus and Greece in the past,
because of the high threshold a party needed to pass in order to qualify for any of
these seats. In Hungary, the existence of three tiers is not, as those confronted by the
system might initially suppose, designed to confuse and to ensure that only a handful
of initiates really understand what is going on but, as explained in Chapter 11,
reflects the outcome of bargaining at the time of the transition to democracy in the
late 1980s coupled with a degree of inertia.
4
This is a somewhat simplified account of the German system, omitting details such as the threshold
and U¨berhangmandate, which are explained fully in Chapter 10.
12 The Politics of Electoral Systems
In the above cases (other than Cyprus and Greece) the higher tier is convention-
ally5
termed compensatory or corrective, because the seats awarded at the higher
tier(s) are used to compensate the parties that were underrepresented at the lower
level and to correct disproportionalities that arose there (Shugart 2000). In Germany,
for example, the smaller parties such as the Greens and the FDP win few, if any, of
the single-member seats and so they are brought up to their ‘fair’ overall share by
being given the appropriate number of list seats. In other cases, though, the two
‘tiers’ are parallel; really, each is on the same level and neither can be seen as higher
or lower. In Japan and Russia, for example, voters have two votes just as in
Germany, but the list seats are awarded in proportion to the list votes only, without
any regard for the seats that the parties won in the single-member section of the
election, so large parties retain the seat bonus that they usually achieve in the
SMD component. Hungary and Italy are somewhere between the two, having
elements of parallel allocation but also providing for a degree of compensation, so
they can be seen as partly compensatory. In the terms of Shugart and Wattenberg
(2003b: 14–15; see Chapters 11 and 12 for details), they provide for ‘vote linkage’
rather than ‘seat linkage’ between the PR and SMD components, in that parties’ list
vote totals are in effect reduced for each SMD seat that they win. In parallel mixed
systems, the over-representation of the large parties in the single-member seats is
only partially ‘corrected’ by the list seats and proportionality is not particularly high.
Limitations on proportionality
Proportionality is generally regarded as a ‘good thing’—in moderation. Few electoral
systems go for broke on the proportionality dimension; most have, in practice,
some way of limiting it.
The most explicit entry barrier is the use of thresholds. Virtually every PR system
employs some kind of threshold that prevents the smallest parties getting their ‘fair’
share of the seats. In Germany, for example, the only parties that qualify for any list
seats are those that either win 5 per cent of the list votes, or win three single-member
constituencies. In Russia, there is a threshold that has an initial value of 5 per cent (to
be increased in future to 7 per cent) but can be adjusted downwards if this figure
debars parties representing too many voters—a rare example of a floating threshold
(see Chapter 15). In a number of other postcommunist countries (Czech Republic,
Latvia, Poland, Slovakia) parties receive no seats at all unless they win 5 per cent of
the national votes (Rose and Munro 2003). This discrimination against small parties
and their supporters is usually justified in terms of preventing excessive fragmentation
and thereby making it easier to form stable governments, a particular concern in
postcommunist countries given their usually weakly structured party systems.
Non-PR systems generally do not have rules specifying a threshold, mainly
because they do not need to. As has often been pointed out in the electoral systems
5
This is something of an overstatement given the terminological profusion in the field.
Introduction to Electoral Systems 13
literature, in practice there is always an ‘effective threshold’ that makes it next to
impossible for parties below a certain size to win a seat. This effective threshold is
determined above all by the district magnitude, with the seat allocation formula also
playing a part. While we cannot specify a formula that will tell us the effective
threshold in all circumstances, Lijphart (1997: 74) and Taagepera (1998: 394)
concur that it can best be estimated by the formula (75/(mþ1)), where m refers to
the district magnitude. In other words, in a constituency with 10 seats, for example,
the effective threshold equals 75/(10þ1), i.e. 75/11 or 6.8—meaning that a party
with fewer than 6.8 per cent of the votes in such a constituency is unlikely to win a
seat.6
Hence, if there is a formal threshold that is fixed at a level lower than 6.8 per
cent then it is likely to prove superfluous, while if it is higher than 6.8 per cent it may
well prove meaningful. In a two-seat constituency the effective threshold is 75/3, i.e.
25 per cent, meaning that only parties above this level of strength have a realistic
chance of gaining representation. Thus the effective threshold imposed by small
district magnitude is usually even more deadly to small parties than a legal threshold
in a PR system. In single-member constituency systems, certainly, proportionality is
already low enough to satisfy even its harshest critics, so there is no need for formal
thresholds. Proportionality increases as district magnitude increases (when a PR
formula is being used, that is), but even when district magnitude is in the 2–4 range
we can expect a significant deviation from complete proportionality.
Another way of building in a limit to proportionality is through malapportionment:
awarding some areas of a country more seats in relation to population than
others (Katz 1998).7
This is not an important factor in most of the countries
mentioned in this book, but it is in some. Both Chile and Spain feature in the ‘top
twenty’ most malapportioned lower houses of parliaments, with Canada, France,
and India not very far behind, and malapportionment in the US Senate is over twice
as high as in Chile’s Chamber of Deputies (Samuels and Snyder 2001: 660–2).
Malapportionment might be effected by the party in power for blatantly partisan
reasons—obviously, it would then give more seats to the areas where it is
strongest—but that is not always why it occurs. Small, peripheral, predominantly
rural regions of a country where population density is lowest and contact between
voters and MPs may be relatively difficult to bring about are the areas most likely to
receive generous representation—although, of course, this usually has political
consequences, with parties of the left typically losing out since they are weak in
such regions. The constitution or laws in many countries place some constraints on
how far the ratio of representation in each constituency can deviate from the national
6
It should be emphasized that this relationship applies only within an individual constituency. It does
not purport to tell us the effective national threshold in a country whose parliament is elected from a large
number of ten-seat constituencies. It is also worth noting that just as the effective threshold can be
computed from a known district magnitude, so an effective magnitude can be computed from a known
threshold. See Appendix C for a fuller discussion.
7
A related concept—in that both result in some parties paying a higher ‘price’ in terms of votes per seat
than others—is gerrymandering (see Glossary).
14 The Politics of Electoral Systems
average figure but, even so, the range of variation within a country is often surprising
(see also Grofman and Lijphart 2002).
District magnitude revisited
As we noted earlier, it is easy to calculate average district magnitude in single-tier
systems but more complicated when there are two or more tiers. For example, of the
598 MPs in Germany, 299 are elected in single-member constituencies, while the
other 299 are returned from lists. The list seats are awarded in such a way as to
ensure that the total number of seats (not the list seats) received by each party is
proportional to the share of the list votes it received. So, should we regard district
magnitude in Germany as being 1.99 (598 divided by 300, i.e. the 299 singlemember
constituencies plus the one national constituency), or as being 598 (on the
ground that all 598 seats are shared out in a single allocation among the parties in
proportion to their votes)? Or should we settle on a plausible-looking value somewhere
in between?
Rae (1971: 20–1) adopts the first of these approaches, but, perhaps inevitably for a
pioneering study, his work contained flaws that subsequent researchers were able to
identify. Lijphart (1990: 486) observes that in many instances, his method produces
a result that is simply logically impossible, being even smaller than the lower-tier
district magnitude. The correct calculation of district magnitude in two-tiered
systems (and, by extension, systems with more than two tiers) depends on which
tier is decisive in determining seat allocations, and this depends on the specific rules
in each case. A key factor is the relative number of seats awarded at the two levels.
In a compensatory or corrective two-tiered system, the question is whether the
number of higher-tier seats is sufficient to ‘correct’ the disproportionalities arising
at the lower level. As Taagepera and Shugart (1989: 129) put it:
The magnitude of the basic district becomes irrelevant to the final votes-to-seats conversion,
if sufficient numbers of remainder seats or compensatory seats are allocated at a second stage,
so that they compensate for district-level deviation from PR.
In Germany, the 50 per cent of seats returned from lists have proved enough to
correct these deviations, so if there were no legal thresholds restricting access to the
share-out of these seats, we should treat Germany as having a district magnitude of
598. If, on the other hand, Germany had 588 single-member constituencies and just
ten higher-tier seats, it is obvious that the district magnitude would in effect be very
little different from 1.
How many higher-tier seats, then, do there need to be to overcome the disproportionalities
arising at the lower level? Clearly, this depends on how much disproportionality
was generated at the lower level, and that in turn depends heavily on
average district magnitude (Taagepera and Shugart 1989: 131; Shugart and Wattenberg
2003b: 19–22). Whether it is possible to frame a precise relationship between
the two is a question for future research. The aim would be to find the function of M
(district magnitude at the lower tier) that generates an equation telling us what
Introduction to Electoral Systems 15
proportion of seats need to be reserved for the higher tier if we are to reduce
disproportionality to the bare minimum—an equation that would have the form:
HTS
TS
¼
1
f(M)
where HTS is the number of higher-tier seats and TS the total number of seats. For
example, the equation
HTS
TS
¼
1
M þ 1
would mean that when single-member constituencies are employed at the lower tier,
half the total number of seats need to be allocated at the higher tier, while if the
average district magnitude at the lower tier is 9, then only 10 per cent of seats need to
be reserved for the higher tier. A refined version could start with an agreed
‘acceptable level’ of disproportionality and a predetermined average district magnitude
at the lower tier, to establish how many higher-tier seats need to be provided
to ensure that disproportionality is unlikely to exceed the set limit.
Preliminary investigation suggests that the number of higher-tier seats needed is
probably lower than would be produced by the formula above. The biggest component
in the total amount of disproportionality is usually generated by the overrepresentation
of the largest party, so in practice the seats-to-votes ratio of the largest
party is a key variable.8
Even under SMP systems, this is rarely significantly in
excess of 3:2 (the approximate ratio seen in the example that we analyse in
Appendix C, where in the SMD component of the 1998 German election the
SPD won 65 per cent of the seats for 44 per cent of the votes). Hence, highertier
seats would need to amount only to a third of the total number in order to
ensure something close to full proportionality even when the lower-tier seats
are filled in SMDs, since the largest party’s SMD seats would now amount to
something very close to its ‘fair’ share of the total number of seats. This suggests
that the equation
HTS
TS
¼
1
2M þ 1
8
To be precise, the important variable in achieving full proportionality is technically the highest seatsto-votes
ratio achieved by any party. Of course, this might not be the largest party; a party with 0.6 per cent
of the votes might win 1.2 per cent of the seats and thus achieve a ratio of 2, which would require there to
be as many higher-tier seats as lower-tier seats, with this party receiving no higher-tier seats, to bring its
lower-tier seats down to 0.6 per cent of the total seats. However, a small party can be left with a high seatsto-votes
ratio without doing much damage to overall proportionality (because it has only a seat or two
more than its entitlement) whereas a large party, even if its seats-to-votes ratio is ‘only’ 3:2, is likely to
have tens or hundreds of seats more than its ‘fair’ share. Hence, in practical terms, the seats-to-votes ratio
of the largest party is usually what matters.
16 The Politics of Electoral Systems
might produce a reasonable estimate of the number of higher-tier seats needed to
achieve near-complete proportionality in a compensatory mixed system.
Even in the absence (for the time being) of a more precise formula, it seems safe
to say that in nearly all the countries covered in this book, district magnitude is
determined by the higher tier. In New Zealand, as in Germany, there are enough
higher-tier seats to ensure that (again leaving aside thresholds) the district magnitude
is in effect equivalent to the number of seats in parliament. In Denmark, although the
number of higher-tier seats is smaller (40 out of a total of 175), the lower tier itself
does not generate much disproportionality (135 MPs elected in 17 constituencies,
each with an average district magnitude of 7.9), so the 40 higher-tier seats are quite
sufficient to ensure that the overall results are highly proportional. The exception is
Italy, where only a quarter of the 630 seats are available at the higher tier, the rest
being awarded by plurality in single-member constituencies—moreover, the highertier
seats are only partially compensatory rather than fully compensatory, as we
noted earlier.
We should mention two further aspects of two-tier seat allocations. The first is
that, as Lijphart (1994: 32) points out, higher-tier seats may be either adjustment
seats or remainder-transfer systems. Those discussed above (Germany, New Zealand,
Denmark) are adjustment seat cases in that the number of higher-tier seats is
fixed and preset. In remainder-transfer systems, in contrast, all seats are in theory
available to be awarded at the lowest tier, but in practice this never happens.
Usually, in the lower-tier constituencies, each party receives a seat for each
‘quota’ of votes it wins, and any remaining votes the parties win over and above
their full quotas, along with any seats not awarded, are transferred to the higher tier.
What happens at the higher tier depends on the precise rules in a particular country.
In Austria, for example, seats are awarded in such a way as to make the outcome
proportional in terms of the total number of votes (not just the higher tier, or
remainder, votes) won by each party, and so district magnitude, again leaving
aside the thresholds in operation, is in effect the number of seats in parliament: 183.9
The second aspect concerns parallel mixed systems where, as we have said, the
two components of the election—the single-member constituency section and the
list section—are on the same level rather than constituting different tiers. In Japan,
for example, 300 MPs are elected from single-member constituencies and the other
180 from 11 multimember constituencies. In analytic terms it makes perfect sense to
treat this as if the country were divided into two, with single-member constituencies
used in one part and a PR-list system in the other. Here, then, it is valid for once to
employ Rae’s approach and to calculate district magnitude simply by dividing the
total number of seats (480) by the total number of constituencies (311), giving a
district magnitude of 1.5. Likewise, in Russia, the average district magnitude in the
2003 election equalled the number of seats (450) divided by the number of constituencies
(226), i.e. 2.0.
9
For a detailed account see Chapter 19 on Austria. Another example is South Africa, for which see
Chapter 17.
Introduction to Electoral Systems 17
THE STRUCTURE OF THE BOOK
In order systematically to explore the questions outlined in the first section of this
chapter, we have gathered together a large team of collaborators (thirty-one in all)
with expertise in the field of electoral systems, in one country or in many. The plan
of this book is straightforward. The core of the book is devoted to twenty-two
country studies in Chapters 4–25. Table 1.3 indicates where the electoral system
of each of these countries can be placed on the four most important of the dimensions
that we have just discussed (Table 26.1 presents a more detailed summary of
each country’s electoral system). The country chapters are grouped according to the
broad category into which their electoral systems can be placed.
In Chapters 4–9, contributors explore the dynamics of electoral systems in six
countries employing single-member constituencies to elect all their MPs. Four of
these use the simplest method of all of electing MPs, single-member plurality
(commonly, if misleadingly, termed ‘first-past-the-post’): Canada, India, the UK,
and the USA. Australia uses the alternative vote, while in France, deputies are
elected by the two-round system.
Chapters 10–15 focus on what are usually termed ‘mixed’ systems, under which
some MPs are elected in single-member constituencies while others are returned
from party lists. Of the six countries in this section, only Germany had such a system
in 1989, indicating that systems in this mould hold attraction for those setting the
rules in democratizing countries such as Hungary and Russia and for reformers in
established democratic regimes such as Italy, Japan, and New Zealand. As the
chapters make clear, even though these systems all look pretty similar at a superficial
glance, some of the differences in the rules can make a really big difference to the
outcomes.
The next nine chapters deal with countries employing some kind of list system to
elect all their MPs. In the first three (Israel, South Africa, and Spain, covered in
Chapters 16–18), voters merely cast their vote for a party list and have absolutely no
say in which individual candidates get elected; the votes determine how many seats
each party has, but which individuals get to fill those seats is a matter that is decided
entirely by the political parties themselves. In the other six list system countries
(Chapters 19–24), voters have some kind of choice as to which individual candidate
they wish to see elected, because they can cast a vote for a specific candidate as well
as (or instead of) just indicating which party they are voting for. The impact of these
preference votes for individual candidates varies dramatically. Preference votes
count for a lot in Chile, Denmark, and Finland, for somewhat less in Belgium, and
for relatively little in Austria and the Netherlands.
The last of the country studies (Chapter 25) concerns Ireland, whose electoral
system, PR-STV, cannot readily be placed in any of the above categories, although it
might be seen as sharing more of the characteristics of open list systems than of any
other type of system.
18 The Politics of Electoral Systems
Table 1.3 Main features of electoral systems in 22 countries
Country
Average
district
magnitude
Ballot
structure
Levels
of seat
allocation
Choice of
candidates
within party
Single-member constituency systems
Australia 1 Ordinal 1 None
Canada 1 Categorical 1 None
France 1 Categorical 1 None
India 1 Categorical 1 None
UK 1 Categorical 1 None
USA 1 Categorical 1 None at election stage; choice
provided by primaries
Mixed systems
Germany 598 Dividual 2 None
Hungary 2.2 Dividual 3 None
Italy 1.3 Dividual 2 None
Japan 1.5 Dividual 2 None
New Zealand 120 Dividual 2 None
Russia 2.0 Dividual 2 None
Closed-list systems
Israel 120 Categorical 1 None
South Africa 400 Categorical 2 None
Spain 6.7 Categorical 1 None
Preferential list systems
Austria 183 Categorical 3 Within party
Belgium 13.6 Categorical 1 Within party
Chile 2 Categorical 1 Within party
Denmark 175 Categorical 2 Within party
Finland 13.3 Categorical 1 Within party
Netherlands 150 Categorical 1 Within party
PR-STV
Ireland 4.0 Ordinal 1 Within and across parties
Note: The figures for average district magnitude here do not take any account of the legal thresholds that
might be imposed, and are not necessarily the same as the ‘effective magnitude’, for which see discussion
in Chapter 26 and Appendix C.
In Hungary and Italy the complex (partially compensatory) linkage between the two tiers makes it
difficult to establish a precise average district magnitude. The figures given in the table are based on the
simplifying assumption that both systems are parallel, i.e. have no linkages between the tiers.
Introduction to Electoral Systems 19