In Defense of Proportional Representation with a Limited ...In Defense of Proportional Representation with a Limited Majority Bonus case, parties start negotiations after the election

ARTICLE

In Defense of Proportional Representation with a Limited Majority Bonus

Seiki Okazaki ＊

Introduction

1 ．The False Dichotomy between PR and SMD

2 ．PR with a Majority Bonus

3 ．A Case for a Limited Majority Bonus

4 ．A Case for PR

Concluding Remarks

Abstract

The purpose of this article is to provide a normative basis for proportional

representation (PR) with a limited majority bonus. Some opponents of PR have

argued that voters cannot choose a government under PR. This is a strong

argument against it. Yet, as I have argued, PR with a majority bonus enables

voters to not only elect members of parliament but also choose a government.

In this article, I will strengthen the arguments for PR with a majority bonus

by refuting some possible arguments against it, which will likely be raised by

proponents of PR as well as proponents of single-member districts (SMD). In

addition, I will propose a slight revision to PR with a majority bonus.

＊　Seiki Okazaki （岡﨑晴輝） is a professor of political theory and comparative politics at Kyushu University, Japan. E-mail: [email protected] KENKYU, Vol. 85, No. 3-4, March 2019.

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85 Hosei Kenkyu（2018）

Introduction

The purpose of this article is to offer a normative basis for proportional

representation (PR) with a limited majority bonus. As is well known, general

elections have two functions in parliamentary democracies. One is to elect

members of parliament, who are expected to represent a variety of voters.

The other function is to choose a government through an elected ruling party

or parties. This duality is the source of theoretical and practical disagreement

between proponents of PR and those of single-member districts (SMD). Those

who attach weight to the former prefer PR, while those who attach weight to the

latter prefer SMD. The mixed-member majoritarian (MMM) or parallel system is

a compromise between them.（１）

I have argued that PR with a majority bonus dialectically overcomes the false

dichotomy between PR and SMD. Under the electoral system, voters can choose

both members of parliament and a government (Okazaki 2009:13-15, 2012: 213-215,

2016: 70) .（２）

However, PR with a majority bonus will be attacked by proponents

of PR, as well as those of SMD. The former argue against the majority bonus

because of its disproportionality. In contrast, SMD supporters argue against PR

because of its proportionality. Thus, PR with a majority bonus faces a pincer

attack. In this article, I will strengthen the arguments for PR with a majority

bonus by refuting some possible arguments made against it, which will likely be

raised by proponents of both PR and SMD. I will also propose a slight revision to

PR with a majority bonus.

1 ．The False Dichotomy between PR and SMD

As a political theorist, I have taken a position in favor of PR. However, I have

admitted that one of the arguments against PR is persuasive. According to this

argument, it is difficult for voters to choose a government under PR, because

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the government is often formed by post-electoral negotiations between parties.

Michael Pinto-Duschinsky expresses the argument explicitly in an influential

article, “Send the Rascals Packing.”（３）

According to him,

　 In short, democratic elections are not principally about membership of the

legislature. The key condition of people power is that the voters should have a

direct effect on the selection and ─ even more important ─ on the expulsion

of prime ministers and cabinets. (Pinto-Duschinsky 1999: 118)

Coalition governments, which are usually formed under PR, are the norm in

parliamentary democracies (see Hobolt and Karp 2010: 300-301). Yet, they have

faced difficulties in recent years. A remarkable event occurred in Belgium earlier

this decade: it took eighteen months to form a government after the election

in June 2010. In 2016, a re-election was held in Spain after negotiations failed.

Further, the centre-right government installed after the re-election was replaced

by the centre-left government with no election in 2018. In New Zealand, the

parties with the second- and third-largest number of seats formed a coalition

government after the election in 2017. Germany experienced intense negotiations

between major parties after the election in 2017. As these examples show, it is

getting harder and harder for voters in PR democracies to choose a government.

Thus, proponents of PR must take this problem seriously.

Before proceeding to the problem, we must clarify the concept of ‘choosing

a government’ for the discussions that follow. What do voters choose? Some

theorists think of the actors who have executive power, especially prime

ministers and the ruling party or parties. Others think of a set of policies adopted

by those actors as well (e.g. Takahashi 2006: 64-67). In this article, I will use the

concept of ‘government’ in a broader sense: ‘government’ refers to the prime

minister, ruling party or parties, and a set of policies. However, it is useful to

distinguish the three elements in specifying clearly what voters choose.

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The concept of ‘choice’ should be clarified as well. How do voters choose a

government? Some theorists think of a prospective choice, whereas others think

of a retrospective one. For those taking the prospective perspective, the focus is

on whether voters can identify a prime minister, ruling party or parties, and a

set of policies through elections. The adopters of the retrospective perspective

focus on whether voters can reject them. Following the conceptualization by G.

Bingham Powell, Jr., I will refer to the ability to make a prospective choice as

‘identifiability’ and the ability to make a retrospective one as ‘accountability’ (see

Powell 2000: 10-12, chapters 3-4) .（４）

Although the two choices can be distinguished

conceptually, voters can choose a government both prospectively and

retrospectively.（５）

Now it will become clear that the difficulty in choosing a government under

PR is one of the strongest arguments against it. Faced with this argument,

some proponents of PR contend that pre-electoral coalitions enable voters

to choose a government (e.g. Farrell 2011: 217-218, Ishikawa 1990: 54; Powell

2000: 71-72). However, the recent examples mentioned earlier show that pre-

electoral coalitions do not necessarily work. Parties tend to seek as free a hand

for themselves as possible. And they often seek a partner or a set of partners

to form a government after the election. As a result, voters face difficulty in

choosing a government. If this is the case, we must abandon the naive belief that

PR is more representative than SMD.（６）

In response to this, some proponents of PR object that voters are not

necessarily able to choose a government under SMD. First, the party forming

the government often polls only a plurality of the votes. This means that a

majority of the voters often cast in favor of the opposition parties (e.g. Ishikawa

1990: 50, 1993: 24-25; Lijphart 1999: 134-135).（７）

Second, there may be a case wherein

the party that polls the second-largest share of votes gains a plurality, or indeed

a majority of the seats (e.g. Ishikawa 1990: 50, 1993: 25-27). Finally, there can be

a ‘hung parliament,’ wherein no party gains a majority of the seats. In such a

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case, parties start negotiations after the election to form a coalition government.

A well-known example would be the 2010 parliamentary election in the United

Kingdom.

They have a point, but I cannot deny the fact that post-electoral negotiations

are far more frequent under PR than SMD. It is true, however, that pre-electoral

coalitions enable voters to choose a government under PR. According to Sona

Nadenichek Golder,

　 In fact, one could argue that pre-electoral coalitions provide a unique

opportunity to combine the best elements of the majoritarian vision of

democracy (increased accountability, government identifiability, strong

mandates) with the best elements of the proportional representation vision of

democracy (wide choice, more accurate reflection of voter preferences in the

legislature). (Golder 2006: 138)

No doubt, this is an important step to dialectically overcome the false

dichotomy between PR and SMD. However, there seems to be a difficulty in

her theory, because Golder demonstrates that the disproportionality of electoral

systems and the large number of parties encourage pre-electoral coalitions (Golder

2006: 8, 36, 99-102, 140)（８）

. If this is the case, it seems reasonable to conclude that it

is difficult, if not impossible, to form pre-electoral coalitions under PR. A crucial

question now arises: is there no PR system that promotes the formation of pre-

electoral coalitions and thus enables voters to choose a government? As I have

argued, there exists such a system: PR with a majority bonus (Okazaki 2009:13-15,

2012: 213-215, 2016: 70).

2 ．PR with a Majority Bonus

The Italian Parliament employed PR with a majority bonus in 2005. The

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electoral reform is said to have been based on the interests of the Berlusconi

government（９）

. However, what is important for a theory of electoral systems is

that the system can rectify one of the chief disadvantages of PR. With a majority

bonus, voters can choose not only members of parliament but also a government.

In this sense, PR with a majority bonus can reconcile the two ideals that are

often regarded as irreconcilable: the proportionality of PR and the identifiability/

accountability of SMD.

However, the system of PR with a majority bonus for the Italian Chamber

of Deputies was changed in 2015. Although both the 2005 system (the so-called

Porcellum) and the 2015 system (the so-called Italicum) are PR with a majority

bonus, there is a crucial difference between them.（10）

The former is coalitional and

gives bonus seats to the largest coalition or the single-largest independent party.（11）

In contrast, the latter is non-coalitional and gives bonus seats to the largest party.

Let us compare the two systems in brief.

Under the 2005 system, parties were allowed to form an electoral coalition.

Every coalition or independent party had to submit an electoral program, which

included a candidate for prime minister. Voters cast a vote not for a coalition,

but for a party.（12）

If the tentative number of seats that the largest coalition or the

largest independent party in terms of votes gained was equal to or more than

340 (about 55 percent of the total seats, excluding 12 seats for overseas constitu-

encies and 1 seat for Valle d’Aosta), the seats were distributed to each coalition

and each party proportionally. However, if the tentative number of seats of the

largest coalition or independent party was less than 340, bonus seats were given

to it to guarantee 340 seats. Except for the bonus seats, the distribution was pro-

portional. In both cases, coalitions and parties had to reach the electoral thresh-

old provided by the electoral law to be eligible for representation. Owing to the

majority bonus, parties had a strong incentive to form an electoral coalition: if a

party did not form an electoral coalition, the party was likely to lose the election

(see Ashida 2006: 132-137, see also Chiaramonte 2015: 15-16; Massetti 2006: 264-266;

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Newell 2006: 804-805; Pasquino 2007: 82-83; Passarelli 2018: 857-858; Wilson 2009: 217-

218).

The coalitional type of PR with a majority bonus brought about a bi-coalition-

al system, where the centre-right and centre-left coalitions struggled to form a

government. In fact, the centre-left coalition formed a government after the 2006

election and the centre-right coalition formed a government after the 2008 elec-

tion (see Newell 2006; Wilson 2009). However, the bi-coalitional competition did not

last for a long time. In 2011, Silvio Berlusconi resigned from his position as the

prime minister and Mario Monti formed a non-partisan government in the midst

of an economic crisis. In the 2103 election, ‘a ‘three-and-a-half poles’ format’ (Chiar-

amonte 2015: 18) emerged owing to the rise of other camps (M5S and the centrist

coalition). As a result, the number of bonus seats increased: the centre-left got

about 55 percent of the seats in the Chamber of Deputies despite polling about

30 percent of the votes. Further, the centre-left had to join hands with the cen-

tre-right and other parties, because it did not gain a majority of the seats in the

Senate (see Garzia 2013).

It should be emphasized that the multi-coalitional competition was not caused

by the electoral system but by a serious economic crisis in Italy. Therefore, it

should be seen as an exceptional and transitional phenomenon. If several elec-

tions had been held under the 2005 system, the Italian party system would have

been transformed into a new bi-coalitional one. The reason is simple: opposition

parties have a strong incentive to form an electoral coalition to win in the next

elections. And the new bi-coalitional competition would have made it possible for

voters to choose a government again.（13）

However, the Italian Constitutional Court ruled that the 2005 system was

unconstitutional. Thus, the electoral system for the Chamber of Deputies was

changed in 2015. Under the new electoral system, parties are not allowed to form

an electoral coalition with other parties. The single-largest party, which polls a

plurality of the votes, is guaranteed 340 seats, provided that the percentage of

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votes it has polled is equal to or more than 40 percent of the votes. If the vote

percentage is less than 40 percent, the largest and second-largest parties contest

a run-off election. The 340 seats are then allotted to the winner. The remaining

seats, except for the overseas seats, are distributed to the other parties that

crossed the threshold in proportion to the votes that they polled in the first

round (see Ashida 2015, see also Baldini and Renwick 2015: 169, 172-173; D’Alimonte

2015: 287-289; Pasquino 2015: 296-297; Passarelli 2018: 858-859).

No elections were held under the 2015 system because of yet another electoral

reform in 2017 (see Ashida 2018a). As a consequence, it is difficult to comprehend

the effects of the non-coalitional PR on the party system. However, the following

scenario will be most probable. In the first election, no party would poll 40 per-

cent of the votes and the top two parties would contest a run-off election. After

one or several elections, some parties would try to merge into a larger party to

poll more than 40 percent of the votes in the first round itself. If only one camp

succeeded in its attempt to merge, the non-coalitional type of PR with a majori-

ty bonus would bring about a predominant party system. However, the system

would not last in the long run, because there would be a strong incentive for op-

position parties to merge with another larger party to win in the next elections.

Thus, the non-coalitional type of PR with a majority bonus would ultimately re-

sult in a two-party system, although it would leave some seats for minor parties.

While voters can choose a government, they face difficulty in choosing a pre-

ferred party under this system. It is true that the non-coalitional type of PR gives

voters a broader choice than SMD: it can guarantee some seats even to minor

parties. Compared to the coalitional type of PR, however, the non-coalitional type

gives voters only a limited choice, since it virtually gives voters two large parties

to choose from. This is the reason why the coalitional type of PR with a majority

bonus is considered to be more desirable than the non-coalitional type. It can rec-

oncile the two seemingly incompatible ideals: proportionality and identifiability/

accountability.

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3 ．A Case for a Limited Majority Bonus

Having explained the basic system of PR with a majority bonus, we may now

proceed to a discussion on the argument raised by proponents of PR. They will

argue against PR with a majority bonus on the grounds that it distorts the pro-

portionality of PR. It should be noted that they oppose the majority bonus, rather

than PR.

I acknowledge the empirical fact that the majority bonus usually distorts the

proportionality of PR. However, I disagree with the normative judgment of PR

proponents that the majority bonus is not acceptable. A certain degree of dis-

proportionality is justifiable as long as it achieves some other ideal of democracy.

For example, while an electoral threshold may distort the proportionality of PR,

it has been accepted as a reasonable instrument for enhancing the stability of

governments. Likewise, the majority bonus has a good reason to be accepted as

an instrument that enables voters to choose a government.（14）

However, some proponents of PR will not accept the thesis that the ideal of

governmental choice justifies a majority bonus. Is there any instrument that

would make a majority bonus more acceptable even to them? The answer is yes,

if we consider the electoral system in some Italian regions.（15）

In Tuscany, for exam-

ple, PR with a majority bonus is accompanied by a minority bonus: the opposition

parties are guaranteed to gain at least 35 percent of the seats in total. While Arti-

cle 17 characterizes the minority bonus as a ‘guarantee for the minorities’ (garanzia

per le minoranze), I believe that the concept of ‘minority bonus’ （少数派プレミア

ム） (Ashida 2018b: 120) is better suited to connect the two kinds of disproportion-

ality.

Let us simplify the percentage of bonus seats for the majority and the

minority. Suppose that the electoral system gives 55 percent of the seats to the

largest coalition or independent party. At the same time, the system does not

give the coalition or independent party more than 55 percent of the seats, even if

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it polls more than 55 percent of the votes. This means that the other parties gain

45 percent of the seats, even if they poll less than 45 percent of the votes. This

would be PR with a limited majority bonus, which I will now explain further.

The majority bonus is limited in two respects. First, it is limited in its number.

An excessive number of bonus seats destroys PR itself. The majority bonus is, as

it were, a powerful medicine. If one takes too large a dose, one will suffer from its

side effects. PR with a majority bonus, as employed by Mussolini, is an example.

However, if taken appropriately, the medicine of the majority bonus helps to

reconcile the two ideals: proportionality and identifiability/accountability. How

many bonus seats are appropriate? It depends on the details of parliamentary

rules and the degree of party discipline in each country. However, it may be

unacceptable to guarantee the first coalition or independent party more than

approximately two-thirds of the seats. The appropriate number may be around

55 percent of the total seats.

Second, the majority bonus is also limited by the minority bonus. The

majority bonus is vulnerable to the charge of disproportionality. However, the

disproportionality of the majority bonus can be offset by the disproportionality of

the minority bonus. In this sense, the counterbalancing function of the minority

bonus has a passive character. However, more active functions may be added to

the minority bonus. This bonus makes it easy for parties to recruit the talented

and to groom them over the long term, because it decreases the risk of defeat for

individual candidates. In addition, the minority bonus maintains competitiveness

between ruling parties and those in the opposition, because opposition parties are

always given 45 percent of seats.

With such a limitation, one would expect PR with a majority bonus to be

more acceptable to proponents of PR. However, an objection may be raised from

another direction. Some proponents of SMD will argue that the limited majority

bonus fails when decisions must be taken by a special majority. It is true that

a 55 percent majority of the seats is sufficient for passing bills. However, it

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precludes achieving the special majority of two-thirds that is often required for a

constitutional amendment.

Although the objection seems to be persuasive at first glance, I disagree

with it. A limited majority bonus makes it impossible for the ruling coalition

or independent party to amend the constitution unilaterally when a two-thirds

majority is required. However, this does not prevent government and opposition

parties from proposing a constitutional amendment jointly. In fact, this joint

proposal is highly desirable because it promotes constitutionalism, the essence

of which is to restrict the abuse of power by ruling parties through appropriate

constitutional constraints.

4 ．A Case for PR

We will now discuss the arguments that will likely be raised by proponents of

SMD. According to them, PR with a (limited) majority bonus enables voters to

identify the coalition that forms a government, but the coalition government is

formed by parties with different ideals and policies. Owing to its heterogeneity,

efficient decision-making is difficult for a coalition government. If conflicts and

compromises between ruling parties occur repeatedly, the coalition government

will become unstable. Moreover, voters will be unable to identify which party

is mainly responsible for the government’s performance (see Lardeyret 2006: 87;

however, there are some differences between his description and mine).

It is true that these arguments hold more or less for many types of PR.

However, these do not necessarily hold for PR with a (limited) majority bonus,

which include some inherent mechanisms that help in overcoming these

difficulties, even though they may be not perfect. Let us discuss each of them in

turn.

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（ 1 ）　Efficiency

Coalition governments are often said to be less efficient than single-party

governments. According to this argument, single-party governments can make

decisions smoothly as long as they are free from factionalism. In contrast,

coalition governments must spend a lot of time and energy to reach decisions.

Even a small party holds bargaining power: it can persist in following its own

policies by threatening to exit from the coalition if it is not allowed to do so. The

aim of a party is not only to get the coalition to adopt its own policies, but also

to compete with its partners in the next elections. Lanny W. Martin and Georg

Vanberg point out that such a dilemma is inherent in coalition governments.（16）

According to them,

　 ... while they make policy jointly, parties that participate in coalition are held to

account separately. Each coalition party must compete for votes under its own

label. (Martin and Vanberg 2011: 3)

　 To govern successfully, coalition partners must be able to overcome the

inherent tension between their collective interest in mutual accommodation and

their individual incentives to pursue their particular policy objectives. (Martin

and Vanberg 2011: 4)

It is true that every party has such incentives. However, the dilemma will not

come to the fore in PR with a (limited) majority bonus. First, the cost of exit is

too high. If a ruling party exits from the coalition government, the party will

have to fight independently in the next elections. Of course, the party can join

the rival coalition, but the coalition will hesitate to accept the exiting party. Such

a risk will discourage the small party from exiting the coalition in power. Second,

parties are bound by pre-electoral agreements. If one of the ruling parties breaks

the agreements, the party will lose the trust of its supporters, as well as partners.

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Thus, the ruling parties must honor the agreements they have made. Therefore,

the necessity of maintaining the existing coalition and the constraint of pre-

electoral agreements are the two inherent mechanisms that enable coalition

governments to make decisions smoothly.

（２）　Stability

Coalition governments are also said to be less stable than single-party

governments. The argument is that single-party governments are free from

instability as long as the ruling party has few factional conflicts. In contrast,

coalition governments tend to be unstable because of the conflicts between ruling

parties.

Some proponents of PR reject the alleged instability of PR (e.g. Farrell 2011:

214-217). It is true that the data presented by David M. Farrell (2011: 216), which

is based on Arend Lijphart’s Patterns of Democracy (1999), shows that coalition

governments, which tend to be formed under PR, are not necessarily unstable.

However, the data shows that, except for a few cases, coalition governments are

generally less stable than single-party governments.

However, the instability associated with coalition governments does not

necessarily hold for PR with a (limited) majority bonus. To be sure, the Prodi

government in Italy collapsed owing to the conflicts between ruling parties

(see Wilson 2009).（17）

However, PR with a (limited) majority bonus has two

inherent mechanisms that make coalition governments stable. The first is the

necessity of maintaining the existing coalition to win in the next elections. The

other mechanism is the constraint of pre-electoral agreements. Svenja Krauss

demonstrates that the existence of coalition agreements, especially extensive

ones, decreases the ‘risk of early government termination’ (Krauss 2018).

Compared to post-electoral negotiations, there are two advantages in pre-electoral

negotiations. Parties can avoid hasty agreements, because they have a lot of time

to negotiate. They can also avoid entering into agreements against their will,

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because small parties do not have a pivotal position.

Moreover, there are some additional instruments that can reinforce the

stability of coalition governments. For example, electoral thresholds will reduce

the number of ruling parties. The so-called constructive distrust will discourage

collusion against the existing government. Further, the loss of bonus seats will

discourage a party from exiting the coalition government.（18）

These instruments will

all enhance the stability of coalition governments.

（ 3 ）　Accountability

Finally, coalition governments are said to be less accountable than single-

party governments. The argument is that it is self-evident which party has the

responsibility for the government’s performance in single-party governments.

In contrast, the location of responsibility is not clear in coalition governments,

because their policies are often the products of compromises between ruling

parties. To make things worse, the process of compromise usually takes place

behind the scenes.

Related to this argument, there is an important empirical study by Stephen

D. Fisher and Sara B. Hobolt that examines the relationship between coalition

government and electoral accountability. According to them, retrospective voting,

which is considered to be a mechanism for electoral accountability, is weaker in

coalitional governments than in single-party governments. Additionally, within

coalition governments, the retrospective voting for the party of the head-of-

government is stronger than that for the other parties (Fisher and Hobolt 2010).

Do these empirical findings also hold for PR with a (limited) majority bonus?

Coalition governments under this form of PR are more coherent than the

coalition governments under simple PR, because the ruling parties have fought

an election with a common candidate for prime minister and with a common

policy program. Of course, there can be conflicts and compromises over

particular policies. However, they will not occur frequently because of the two

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inherent mechanisms mentioned earlier: the necessity of maintaining the existing

coalition and the constraint of pre-electoral agreements. Under PR with a (limited)

majority bonus, coalition governments are relatively coherent, so voters can

identify which party is mainly responsible for the government’s performance and

‘send the rascals packing’ in the next election.

Concluding Remarks

So far, I have discussed the possible arguments against PR with a majority

bonus that will likely be made by proponents of PR (Section 3) and proponents of

SMD (Section 4). Throughout the discussion, I have strengthened the normative

basis of PR with a limited majority bonus. As a normative political theorist, I

have argued for it in a speculative manner. Needless to say, my arguments are

open to criticism from normative political theorists, as well as empirical political

scientists. I welcome any kind of criticism. My main objective is not to defend

the arguments presented in this article but to seek alternatives to PR and SMD,

and indeed alternatives to ‘consensus democracy’ and ‘Westminster democracy’

(Lijphart 2012).

Finally, I want to emphasize that PR with a limited majority bonus should

be regarded as the electoral system for the Lower House of parliament, which

is responsible for government formation. PR with a limited majority bonus will

make the House more representative as well as more identifiable and accountable.

However, every election has its own limitations: those elected are professional

politicians, whose thinking may diverge from that of ordinary citizens. To bridge

the gap, there is a need to employ another method of selecting members of the

Upper House.

Regarding Japanese politics, I have proposed the replacement of the House

of Councillors with the House of Citizens, the members of which are chosen not

by election but by sortition. The House of Citizens examines the deliberations

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and decisions of the House of Representatives and exercises veto power when

it regards them as unreasonable. The common sense of citizens is enough

to perform this task. The sorted House of Citizens will enrich democracy by

checking the House of Representatives (Okazaki 2018, see also Okazaki 2013: 201).（19）

I will leave the detailed design of the sorted House of Citizens to another article.

Acknowledgments

I read the first draft entitled ‘In Defense of Majority Bonus,’ in Japanese, at a

conference held at Kyushu University on June 16th, 2018. I thank the participants

for their insightful comments. I also thank Dr. Jun Ashida （芦田淳） for his pio-

neering works on the Italian electoral systems and his generosity toward me. I

will also give a special thanks to Professor Nobuo Okawara （大河原伸夫）, who

gave me a chance to study electoral systems at Kyushu University and led me

to think over the identifiability/accountability problem of PR. Finally, I thank Ed-

itage for their editing service.

Notes

（１）　Matthew Soberg Shugart and Martin P. Watternberg point out that mixed-member systems, especially mixed-member majoritarian (MMM) systems, encourage two-bloc party systems (Shugart and Watternberg 2001: 583-584). MMM systems may indeed promote two-bloc party systems and thus enable voters to choose their governments, but they are not proportional. In contrast, mixed-member proportional (MMP) systems are proportional, but they are weak in promoting two-bloc party systems.

（２）　I took a hint from a sentence in Ashida 2007: 100. Based on their empirical studies on regional elections in France and Italy, Camille Bedock and Nicolas Sauger argue that the electoral systems with a majority bonus, which should be regarded as mixed systems, lead to a bipolar and fragmented competition (Bedock and Sauger 2014: 99, 109). I will emphasize here that this type of competition has a potential to dialectically overcome the false dichotomy of PR and SMD.

（３）　The article was reprinted in Representation, Vol. 36, No. 2 (1999). The issue also contains four critical essays by G. Bingham Powell, Jr., Arend Lijphart, Jack Vowles and Matthew Soberg Shugart, as well as a reply by Michael Pinto-Duschinsky.

（４）　Mark Bovens distinguishes between ‘accountability as a virtue’ and ‘accountability as a mechanism,’ though he acknowledges that the two concepts are related (Bovens 2010: 946-954). The concept of ‘accountability’ in this article is used in the latter sense.

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（５）　Karl Popper also takes the two choices into consideration when he writes that PR has difficulties both in ‘government formation’ (Regierungsbildung) and in ‘dismissing a government’ (eine Regierung zu entlassen) (Popper 1987: 54).

（６）　Some proponents of SMD advance another reason to deny that PR is more representative than SMD. According to them, perfect representation is impossible, because it requires a countless number of parties. The preferences of voters must be integrated into an adequate number of parties. How many parties, then, are adequate? There is no reason to suppose that a multi-party system based on PR is more representative than a two-party system based on SMD (e.g. Machidori 2018: 94-95). Although this is a plausible argument, I cannot agree for two reasons. First, two-party systems cannot adequately represent the preferences of voters. Thus, they lead to the emergence of many voters who are disappointed with the existing parties and support new ones. Second, PR is an electoral system that gives voters the power to choose the legislative number of parties. It is true that PR systems have brought about multi-party systems in most countries. However, it should be noted that PR does not force a multi-party system on the voters: voters may choose a two-party system if they wish. There is no doubt that it is desirable for voters to choose a party system freely.

（７）　Philip Norton points out that ‘[i]f 40% of electors vote for party A and 20% for party B, a post-election coalition of the two parties does not enjoy the support of 60% of electors. It enjoys the definitive support of zero per cent’ (Norton 1997: 86).

（８）　The disproportionality is measured quantitatively by the effective electoral threshold (Golder 2006: 90).

（９）　Alan Renwick shows that there were differences in interests between the ruling parties (Renwick 2010: 125-127).

（10）　Gianfranco Pasquino states that the difference between the 2005 system and the 2015 system is so minor that we should call it ‘Porcellinum (small pig)’ (Pasquino 2015: 297).

（11）　Given the fact that the 2005 system gave parties a strong incentive to form an electoral coalition, there is little likelihood that an independent party would win the election. This is the reason why I regard the 2005 system as a coalitional one.

（12）　The term ‘party’ is not exact, because parties could make a common list under the 2005 system, as well as the 2015 system. However, I will use the term for the sake of convenience.

（13）　The strength of the incentive for opposition parties to form an electoral coalition depends not only on institutional factors (e.g. the degree of the majority bonus) but also on non-institutional factors (e.g. ideological distance between opposition parties). The greater the ideological distance, the weaker the incentive.

（14）　Jun Ashida acknowledges that the majority bonus can be reasonable more or less for the purpose of government stability (Ashida 2008: 372-373).

（15）　I thank Jun Ashida for helping me formulate this point. Further, Jiro Hasumi gave me useful information on a similar system in Kyrgyzstan: ‘no single party could gain more than 65 seats in the new 120-member unicameral parliament’ (Huskey and Hill 2011: 877).

（16）　Martin and Vanberg argue that voters can influence policy-making under multi-party governance if there are strong legislative institutions (Martin and Vanberg 2011: 165).

（17）　As for the historical change in government stability in Italy, see Chiaramonte 2015: 21-23.（18）　Giovanni Sartori proposes the stipulation that ‘the premium is forfeited for all the parties

that have benefitted from it, if and when their governmental coalition breaks down’ (Sartori 1997: 7). Note that Sartori is critical of the PR with a majority bonus that was adopted in 2005 (see Massetti 2006: 266-267).

（19）　The competitiveness created by PR with a limited majority bonus, which I have

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mentioned in Section 3, will be a good condition for members of the House of Citizens to compare various arguments on a bill.

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