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Predicting Party SizesThe Logic of Simple Electoral Systems$

Rein Taagepera

Print publication date: 2007

Print ISBN-13: 9780199287741

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199287741.001.0001

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How Electoral Systems Matter

How Electoral Systems Matter

(p.1) 1 How Electoral Systems Matter
Predicting Party Sizes

Rein Taagepera (Contributor Webpage)

Oxford University Press

Abstract and Keywords

An electoral system helps determine the number and size distribution of parties in a country, as well as cabinet duration. Electoral systems are expressed in electoral laws. Their impact depends on the way politicians and voters make use of these laws. Flawed electoral laws can lead to breakdown of democracy or to staleness.

Keywords:   number of parties, size distribution, cabinet duration, electoral laws, breakdown of democracy

For the practitioner of politics:

  • Electoral systems help determine how many parties a country has, how cohesive they are, who forms the government, and how long the government cabinets tend to last.

  • Electoral systems are expressed in electoral laws. Their impact depends on the way politicians and voters make use of these laws.

  • At times, flawed electoral laws can undo democracy or lead to staleness.

Who governs? Electoral systems matter in democracies because they affect the answer to this question Robert Dahl (1961) posed in a different context. In the January 2006 Palestinian elections, the electoral system used gave Hamas 70 percent of the seats and hence threw the Palestinian–Israeli relations into turmoil. Yet Hamas received only about 45 percent of the list votes, as against about 41 percent for the more moderate Fatah.1 With proportional representation rules, no party would have won an absolute majority of the seats, leading to a more balanced coalition government. In contrast, the actual, heavily majoritarian electoral system was bound to boost the seats for whichever party received even slightly more votes. The answer to the question ‘Who governs?’ was determined as much by the electoral system as by popular votes.

Elections are one way to determine who the leaders will be. This method is more peaceful than fighting it out, more credible in modern times than (p.2) claims of divine favor, and more systematic than estimating the loudness of noise made by various factions at an open‐air meeting. Only transfer of power from parent to offspring can compete with elections in orderliness of procedure; and in the modern world, elections have become a more widespread practice. The supposed goal is to have the ‘people’ express their will.

By electoral system, we mean the set of rules that specify how voters can express their preferences (ballot structure) and how the votes are translated into seats. The system must specify at least the number of areas where this translation takes place (electoral districts), the number of seats allocated in each of these areas (district magnitude), and the seat allocation formula. All this will be discussed in more detail later.

This book deals only with elections that offer some choice. It bypasses fake elections where a single candidate for a given post is given total or overwhelming governmental support, while other candidates are openly blocked or covertly undermined. It also largely overlooks pathologies of electoral practices such as malapportionment and gerrymander, except for pointing out which electoral systems are more conducive to such manipulation.

The physical conditions of elections matter, such as ease of registration of voters and candidates, location and opening times of polling stations, the timing of elections, and ballot design—see Mozaffar and Schedler (2002) and Reynolds and Steenbergen 2006). It is presumed in this book that such conditions of electoral governance are satisfactory. My only concern is to explain, in what are considered fair elections, how electoral systems affect the translation of votes into seats, how the results also affect the distribution of the votes in the next elections, and what it means for party systems. Moreover, the book largely limits itself to first or only chambers of legislatures, except for one chapter on second chambers and supranational assemblies, plus incidental comments on presidential and local elections.

This scope may look narrow, but translation of votes into seats by different electoral systems can lead to drastically different outcomes. We already saw what it meant for Palestine. Also, with a different electoral system (and traditions in applying it), a mere 36.3 percent of the total vote would not have made Salvador Allende president of Chile in 1970, and Chile's history could have taken a very different course.

Around 1930, the vote shares of the British Liberals and the Icelandic Progressives were practically the same: 23.4 percent for the Liberals in 1929 and 23.9 percent for the Progressives in 1933. But the rules for (p.3)

                   How Electoral Systems Matter

Figure 1.1 The opposite impacts of electoral systems and current party politics

allocating assembly seats on the basis of popular votes differed. The Icelandic Progressives won 33 percent of the seats and played a leading role in the country's politics, while the British Liberals won less than 10 percent of the seats. The resulting disappointment affected the votes in the next election and sent the Liberals down to near‐oblivion.

Thus, electoral systems can sometimes make or break a party—or even a country. In less spectacular ways, they affect party strengths in the representative assembly and the resulting composition of the governing cabinet. They can encourage the rise of new parties, bringing in new blood but possibly leading to excessive fractionalization, or they can squeeze out all but two parties, bringing clarity of choice but possibly leading to eventual staleness. It is well worth discovering in quantitative detail how electoral systems and related institutions affect the translation of votes into seats.

Electoral Systems, Seats, Votes, and Party Politics

Figure 1.1 shows the opposite impacts of electoral systems and party politics on the distribution of seats and votes among parties. Electoral systems restrict directly the way seats can be distributed. In particular, when single‐seat districts are used, only one party can win a seat in the given district. The impact on votes is more remote. When a party fails to obtain seats in several elections, it may lose votes because voters give up on it, or it may decide not to run in the given district. The impact on party system and hence on politics in general is even more remote. Still, if a party fails to win seats all across the country, over many elections, it may fold, reducing the number of parties among which the voters can choose.

The impacts of the existing party system and current politics are attenuated in the reverse direction. The total number of meaningful parties may be limited by the workings of the electoral system, but current politics determines which parties obtain how many votes. The impact of current (p.4) politics on the seats distribution is weaker, as the electoral system may restrict the numberof parties that can win seats. Still, current politics determines which parties win seats. Finally, current politics has no impact at all on the electoral system, most of the times. Yet, infrequently, it has a major impact, when a new electoral system is worked out from scratch, or when protest against the existing electoral system builds up for any reason.

At all stages, political culture plays a role. The same electoral laws play out differently in different political cultures, shaping different party systems. Along with the initial party system, political culture shapes the adoption of electoral laws. If stable electoral and party systems succeed in lasting over a long time, this experience itself can alter the initial political culture—a connection not shown in Figure 1.1. This book mentions political culture rarely, but not because I underestimate it. I just do the relatively easy things first, and political culture is harder to tackle.

In the study of current politics, votes come first, and seats follow—the arrows at the top of Figure 1.1. This direction may look natural, but it is reversed when we study the impact of electoral systems. Now seats are restricted directly, and restrictions on votes follow in a slow and diffuse way—the arrows at the bottom of Figure 1.1. Recognition of such reversal is essential for elucidating the impact of electoral systems.

The Limiting Frames of Political Games

Politics takes place in time and space—both the immutable physical space and the institutional space that politics can alter, but with much inertia. The physical size of polities matters for their functioning, as stressed early on by Robert Dahl and Edward Tufte (1973). Institutional size also places constraints on politics. For instance, in a five‐seat electoral district, at least one party and at most five parties can win seats. Within these bounds, politics is not predetermined, but the limiting frame still restricts the political game. It is rare for one party to win all seats in a five‐seat district, while such an outcome is inevitable in a single‐seat district. This observation may look obvious and hence pointless, but it will be seen that it leads to far‐reaching consequences.

Institutions are containers within which the political processes take place. Containers matter. True, the content matters more, and containers do not decide what is poured into them. But if they leak, crack, overflow, (p.5) or corrode, they do affect the outcome. Indirectly, they even affect the content, because one learns from experience not to pour, for instance, the proverbial new wine into old wineskins. It would be false dichotomy to ask whether containers matter or not. It is a question of how much they matter, and how.

So it is with political institutions. An excellent institutional framework cannot compensate for flawed political culture, but inadequate institutions can make it worse. Such a risk is high when political culture is corrosively intolerant and does not value cooperation and compromise. To maximize stability, institutions should be congruent with political culture, to use Harry Eckstein's terminology (Eckstein 1966, 1998), but not so congruent as to help perpetuate an undemocratic culture. Electoral systems are part of such institutions.

Electoral Systems and Party Systems

Here I use ‘electoral systems’ with some hesitation. In systems theory, a system divides the world into external and internal, and it has some capacity to restore internal equilibrium when disturbed by external factors. If so, then one could speak of an electoral system only when the electoral rules have been embedded in a political culture where voters and politicians have acquired reasonable skills in handling the rules to their enlightened self‐interest, which includes most actors’ long‐term interest in preserving a modicum of stability. Such skills are based on experience. A set of electoral rules can be promulgated as laws overnight, but it takes several electoral cycles for politicians and voters to learn how to handle these laws to their best advantage. Hence electoral rules become a stable limiting frame for the electoral game only when they have been used a fair number of times.

In this light, should we define ‘electoral systems’ as not only a set of rules but also include the skills people exert in using them? There is some merit in such a definition (Taagepera 1998a), but it also leads to new difficulties in telling electoral and party systems apart. Therefore, I adhere to the generally accepted definition of electoral system as the set of rules that govern ballot structure and seat allocation.

Electoral system thus defined is inextricably intertwined with party system. Even the earliest election in a new democracy is bound to take place in the context of some constellation of proto‐parties, but to talk of a party system truly serves a purpose only when some degree of stability (p.6) has set in regarding the identity, size, and interaction of parties. Early party constellations are often kaleidoscopic configurations of individual politicians, devoid of anything akin to a system. During early democratization, major parties may vanish completely and new ones may arise. Thus, the early party constellations can be even more fleeting than a kaleidoscope, where at least the pieces remain the same (Grofman, Mikkel, and Taagepera 2000). Such party constellations become a party system only slowly.

What is involved in a party system? It is more than just the number and sizes of parties. It also includes their interactions. Peter Mair (1997: 214–20) offers two convincing examples of decoupling between parliamentary strengths of parties and their interaction patterns regarding government formation and maintenance. A long‐standing feature of the Irish party system was Fianna Fail's refusal to engage in coalition cabinets, which constrained the voters to vote either for Fianna Fail and single‐party cabinets or for coalition cabinets by ‘The Rest’. When a variety of reasons induced Fianna Fail to participate in coalitions, starting in 1989, the entire pattern of possible combinations expanded. Party system changed without any change in electoral system or any appreciable shift in seat shares of parties.

Denmark is Mair's contrary example (1997) of party system remaining the same despite shifts in party strengths. Instead of previous 5 parties, 10 parties won seats in 1973, and the combined vote share of the established 5 dropped from 93 percent to 65. Yet the interaction pattern of parties changed little, as another minority cabinet replaced the previous one. Note, however, that the electoral system did not change either—only the electoral outcomes did.

The fact that a party system also involves interaction patterns among parties does not do away with the importance of the number and sizes of parties. A two‐party system offers inherently different options, compared to a multiparty system. The shift in Ireland 1989 and the non‐shift in Denmark 1973 both played themselves out within the usual range of options available in multiparty systems. When describing party systems, it would needlessly be limiting to claim either that only party sizes matter or, conversely, that party sizes do not matter at all.

The initial electoral system can play a major role in determining the party system, but it is not the only factor. This book does focus on the impact of electoral systems on representation and party systems, because the workings of electoral systems are relatively well understood qualitatively and also with some quantitative rigor. But we should remember (p.7) that historical and cultural factors may produce a different party system on the basis of the same electoral system.

Electoral systems affect politics, but they are also products of politics. Political pressures can alter them. This is well known, but after an initial bow to this two‐way causality, most researchers treat electoral systems as causes of party systems rather than results. Consider the famous Duverger's law (to which I will return), saying that plurality rule for seat allocation tends to produce a two‐party system. How often does this allocation rule produce a two‐party constellation, and how often does it result from a preexisting two‐party constellation? Indeed, if the dawn of democracy in a given country finds the decision‐makers divided into two parties, these parties may wish to choose the plurality rule so as to block entry of new competitors. If, on the contrary, the initial decision‐makers are split into many parties, they may wish to play it safe and adopt proportional representation (PR) so as to reduce their risk of total elimination.

Only recently this issue has been addressed systematically (Boix 1999; Benoit 2002; 2004; Colomer 2005). Party constellations do tend to precede and determine the electoral systems. Once in place, though, the electoral system helps to preserve the initial party constellation and to freeze it into a party system. To avoid causal implications in either direction, we may reword Duverger's law: ‘Seat allocation by plurality rule tends to go with two major parties.’

Chess Rules and Electoral Rules

Electoral laws establish the rules for how the electoral game is carried out and how the winners are determined. In this, they are somewhat akin to chess rules (Taagepera 1998a). But there is one marked difference. Chess rules are extraneous to the game, while electoral rules are interwoven with the game. In his classic Fights, Games, and Debates (1960), Anatol Rapoport imagines going to a statistics‐oriented person to analyze chess. The latter reports items like the distribution of duration of games and the attrition rates of chess figures at successive moves. Rapoport, however, mumbles: ‘But is this what we want to know about chess?’ In particular, does this enable us to play better chess? Guess not.

Still, such statistical information on chess would be of interest. It certainly would, if proposals arose for changing the chess rules. Would the change make the game boringly long or, to the contrary, awkwardly (p.8) short? But even then, the rules would not be part of the game. Before sitting down at the chessboard, a player will not negotiate for fairer rules to prevail on the chessboard, threatening otherwise with boycott. No player will declare that, if s/he wins, s/he will change the rules. These rules are quite constant in space and time. They define the game rather than being part of the game. The loser cannot claim that the rules were biased.

Electoral rules also define the game, but they are part of it. They vary in space and time. Losers can blame them, and at times do. Change in electoral rules can be part of an election platform. Because these rules can be changed through political processes, the statistical and logical analysis of the properties of electoral systems is part of the study of politics, while the study of the consequences of various conceivable chess rules is not part of learning chess.

This is not to deny the strategic aspects of politics, which are subject to game‐theoretical approaches and conditioned by political culture and various path‐dependent factors. One need not even claim equal importance for institutional aspects and for electoral systems in particular. They are merely the limiting frames for political games. A good electoral system cannot save a polity where many other institutions, attitudes, and policies have broken down. And on the other hand, a healthy polity can find ways to compensate for a poor electoral system. However, an inadequate electoral system can contribute to crisis in the case of shaky polities—and most polities have their fragile aspects and periods.

My approach to electoral systems is very much in line with what made Rapoport ask ‘But is this chess?’ For chess, the response would be ‘No’, but for the study of politics, it is ‘Yes’, because here the rules are themselves part of the game.

The Study of Electoral Systems

Within political science, electoral studies are a relatively mature field of study. They are located at the core of political science:

Although there are many concerns of political science that do not center around elections, the study of democratic practices—to which elections indisputably are central—is certainly one of the most crucial topics for the discipline as a whole. The study of elections is more than the study of electoral systems, and the study of electoral systems is more than ‘seats and votes’, but the numerical values of (p.9) seats and votes for individual political parties and candidates are among the most important quantitative indicators that we, as political scientists, employ in our work. (Shugart 2006)

For political scientists, electoral laws offer a further attraction: the possibility of institutional engineering. For the given votes, one can calculate the extent to which different electoral laws would have altered the composition of the representative assembly, and one can propose changes in laws. Of course, under different laws voters may have voted differently. For instance, a shift from plurality to PR may encourage voters to shift to third parties. Such tendencies also must be taken into account.

Actually, fundamental changes in electoral laws are infrequent, because they usually require agreement by representatives chosen under the old laws—and why should they change laws that served them well in getting elected? Still, electoral laws may well be more conducive to institutional engineering than institutions firmly stipulated in constitutions, not to mention political culture.

The quantitative nature of many features of electoral systems—the numbers of seats and votes, precise allocation algorithms, and the like—may attract those political scientists who yearn to discover quantitative regularities akin to those that have paid off in natural sciences. For the same reason, electoral studies may repel those who consider the study of politics an art rather than a science, or at most a science that thrives on richness of details rather than broad generalizations—zoology rather than molecular biology. Students of politics are largely reduced to nonrepeatable observations in vivo instead of repeatable in vitrolaboratory tests. Hence any general scientific laws in politics, if they exist at all, are bound to be hidden, submerged underneath considerable random scatter in data. This scatter may easily be construed as absence of general laws. This book, however, presents evidence that logical models can be constructed in the context of electoral systems, and that they lead to specific quantitative predictions, which are confirmed empirically by the averages of many elections, and even more by averages of many electoral systems.

This book first reviews the typology of electoral systems and introduces some analytical tools that make a comparative study of electoral systems possible. This overview of rules and tools is a prelude to the ‘Duvergerian agenda’ which has dominated the electoral studies for the last half‐century—the attempt to express the impact of the main features of electoral systems on representation and party system.

(p.10) The central part of the book presents recent advances in the macroscopic aspect of the Duvergerian agenda. These advances help us understand the logic of simple electoral systems to the degree that specific quantitative predictions can be made for the average of many elections carried out under the same rules. Individual elections, of course, can vary wildly, just as daily weather can vary within a well‐defined climatic pattern. All this applies to simple systems. We are still far from being able to predict in detail the impact of complex electoral systems, but we have made marked progress during the last few decades.

In this light, the final part of the book broadens the agenda and asks: What can we expect from electoral laws? It briefly describes advances in studying more complex electoral systems and lays out the agenda for extending our predictive ability from simple to complex systems. Once we have a firm grip on the impact of institutions, we can separate it from the impact of political culture and study the latter in relative isolation from confusing side effects. We are then in a position to attempt to design electoral laws so as to obtain specific average outcomes—and also to have a sober awareness of the limits to our ability to design. The aforementioned quantitative nature of many features of electoral systems enables us to build and test logical quantitative models more extensively than has been the case in other studies of politics. Can we transfer some of the methodology developed for electoral systems? The book concludes with this provocative issue: To what extent can electoral studies supply a ‘Rosetta Stone’ to some other parts of political science?


(1) Matthew S. Shugart, ‘The magnitude of the Hamas sweep: The electoral system did it’ (http://fruitsandvotes.com, visited on February 28, 2006), calculates the Hamas list vote as 44.5 percent. The complex multi‐seat nontransferable vote system, with many other embellishments, makes an exact count for candidates difficult. See also Steven Hill, ‘Vote system gave Hamas huge victory’, Hartford Courant, February 8, 2006, The Prague Post, February 15, 2006.