Rein Taagepera

“Effective” Number of Parties A Measure with Application to West Europe

The qEffectiveq Number of Parties: qA Measure with Application to West Europeq Laakso, Markku;Taagepera, Rein Comparative Political Studies; Apr 1, 1979; 12, 1; Proouest pg. 3 “EFFECTIVE” NUMBER OF PARTIES A Measure with Application to West Europe MARKKU LAAKSO University of Helsinki REIN TAAGEPERA University of California, Irvine I s a large number of parties bound to destabilize a political system (Duverger, 1954) or is it not (e.g., Lijphart, 1968; Nilson, 1974)? Before this question can be answered, the number of parties must be operationally defined in a way that takes into account their relative size. Such a number is also needed if one wants to detect trends toward fewer or more numerous parties over time, or the effects of a proposed change in electoral rules. This article presents ways to calculate this important political variable, calculates it for I42 post-1944 elections in 15 West European countries, and analyzes its possible effect on stability. We often talk of two-party and multiparty systems. We further dis- tinguish three~ or four—party systems in some countries, and even talk (e. g., Blondel, 1969: 535) of a two-and-a-half-party system whenthere is a third party of marginal size. Mexico could be viewed as a one-and-a- half-party system because the PR1 is so much larger than all other parties. Rather than take the number of all existing parties, including even the very smallest, one visibly has a need for a number that takes into account their relative size. We will call this number the “effective number of parties,” using the word “effectiveq somewhat in the sense pressure group literature uses it when talking about “effective access” (Truman, 195]: 506), but even more in the operational sense physicists give it when they talk about effective current (Richards et al., 1960: 594), COMPARATIVE POLITICAL STUDIES. Vol. I2 No. I. April 1979 3-27

Arend Lijphart's dimensions of democracy: Logical connections and institutional design

Lijpharts (1999) analysis maps countries along two dimensions of democratic institutions: ‘executives-parties’ or ‘joint-power’, and ‘federal-unitary’ or ‘divided-power’. My ‘meta-study’ maps the methodology of Lijpharts mapping: the nature of indices (inputs or outputs), their logical interconnections, their susceptibility to institutional design (‘constitutional engineering’), and their suitability for expressing the intended underlying concepts. Strikingly, the joint-power indicators are highly correlated and mostly logically connected output measures, which are not susceptible to institutional design, while the opposite is true for the divided-power dimension. For this dimension most indices are expert estimates of inputs, marginally correlated, yet subject to institutional design, limited by size dependence. Surprisingly, the parliamentary-presidential aspect of institutional design does not affect the picture. The connection between cabinet life and the number of parties is even stronger than found by Lijphart. Interest groups and central bank independence fit his dimensions empirically but less so logically. In sum, institutional design may be more difficult than sometimes assumed, but offers hope.

Effective number of parties for incomplete data

Abstract In the presence of a large lumped category of ‘Other’ parties the effective number of parties cannot be known exactly. Some approaches used produce large discrepancies. This note shows how the effective number still can be estimated with fair accuracy. The same issue arises with the measures of disproportionality between seats and votes.

Mapping the indices of seats-votes disproportionality and inter-election volatility

Measures of electoral system disproportionality and of party system volatility (as well as malapportionment and vote splitting) present similar statistical issues in terms of deciding what index is most appropriate, but it is not common to view indices of disproportionality and volatility as serving similar ends. Making use of 12 different criteria, we evaluate 19 indices that have been previously proposed as measures of either disproportionality of electoral seats–votes results or over-time volatility of party vote (or seat) shares. We suggest that, on balance, Gallagher’s (1991) index, which has achieved increasing acceptance in the seats–votes literature on disproportionality (see esp. Lijphart, 1994) offers the most desirable combination of features, although the advantages it offers over the Loosemore-Hanby index are not large and are debatable. We also find that Dalton’s principle of transfers presents an ambiguity when one party has a larger number of excess seats, while another has a larger proportion of them.

Size and duration of empires: Systematics of size

Abstract Areas of the worlds three largest empires or states at any given time are listed at 100- or 50-year intervals, from 3000 b.c. on. Area measurement definitions and techniques are described. Major empire size has tended to increase, approaching the worlds dry earth area in an approximately logistic way. This pattern suggests that a world state is still many centuries away. Sudden increases in empire size have occurred around 2800 b.c. due to emergence of cities, around 600 b.c. due to a power delegation breakthrough, and around 1600 a.d. due to a communication speed revolution. A graph of the worlds largest empire areas throughout times offers somewhat novel perspectives on world history, making one realize the Western bias of many “world history” texts. Areas of 20 largest states that ever existed are listed. Subsequent papers will deal with historical periods in more detail.

The number of parties as a function of heterogeneity and electoral system

What determines the number of parties in a national assembly? Previous work has emphasized either sociopolitical heterogeneity or electoral system permissiveness, or brought them together on an empirical basis. Here an equation is developed that satisfies two theoretical boundary conditions and expresses the effective number of assembly parties (N) in terms of both the number of politicized issue dimensions (I) and effective magnitude (M) of electoral system: N = I .6 M .15 + 1. Actually, depending on circumstances, any of the three variables could become the dependent one, affected by the two others. Empirical evidence is presented, based on Lijpharts (1984) data on 22 stable regimes.

Nationwide threshold of representation

How large must parties be to achieve minimal representation in a national assembly? The degree of institutional constraints is reflected indirectly by the number of seat-winning parties (n) and more directly by the threshold of representation (T), defined as the vote level at which parties have a 50–50 chance to win their first seat. The existing theoretical threshold formulas use district-level reasoning and therefore overestimate the nationwide threshold. This study extends the theory to the nationwide level. In addition to district magnitude (M), the number of electoral districts and hence assembly size (S) emerge as important variables. When all seats are allocated in M-seat districts, T=75%/[(M+1)(S/M)0.5] and n=(MS)0.25. T and n are connected by T=75%/[n2+(S/n2)]. These theoretical expectation values are tested with 46 durable electoral systems.

Expansion and Contraction Patterns of Large Polities: Context for Russia

Over 5,000 years of history, the effective number of separate political entities has decreased from close to a million to 24, if going by geographical area, and from about a thousand to 15, if going by population. These changes have followed interconnected exponential patterns which extrapolate to a single world polity around year 4000. Within this long-term trend, three sudden increases in polity sizes occur: around 3000 BC, 600 BC, and AD 1600. This study tests the exponential model against area and population data for five millennia. It also gives tables and graphs of area versus time for all major polities since AD 600. The median duration of large polities at more than half the peak size has been 130 years, and it has not changed over 5,000 years. Polities that expand slower tend to last slightly longer. The prospects of the Moscow-centered state are discussed in the light of these findings.

Plurality Versus Majority Election of Presidents A Proposal for a “Double Complement Rule”

Under plurality rule, presidents may be elected with narrow support whenever there are more than two “serious” candidates. Even under majority-runoff rules, the eventual winner may have received the backing of only a small minority in the first round. This article shows that majority runoff rules tend to be associated with an “effective” number of presidential candidates greater than three. The effective number for plurality is, on average, less; however, a nontrivial share of such elections have resulted in close multicandidate races. The article proposes an alternative “double complement rule,” which is derived as the arithmetic average of majority runoff and plurality criteria. This rule stipulates that a front-runner with less than a majority of the votes wins without need of a second round if the shortfall of the runner-up from a majority of votes is more than double the leading candidates shortfall from a majority. Possible effects and desirable conditions of this rule are assessed in light of the existing debate about electoral methods.

Seats and votes: A generalization of the cube law of elections

Abstract The empirical “cube law” applies to parliamentary elections in Anglo-Saxon countries. It says that the ratio of assembly seats of two major parties is approximately the cube of the ratio of votes. This paper presents a more general semi-empirical “seat-vote equation” which includes the cube law as a special case but which also applies to the U.S. Electoral College, labor union, direct presidential, and proportional representation elections. The paper defines “constituency” as the smallest unit within which the party with plurality wins all the seats. The smaller the number of such constituencies is, the more dramatic is the attrition of minority party representation. Thus changes in the number of constituencies can be used to bring about a desired degree of minority representation. The prediction of the average long-range effects of such changes could be an important practical application of the seat-vote equation.