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«Since the work of Maurice Duverger (1954), one of the most fundamental ideas in political science is that a party system is shaped by the electoral ...»

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Since the work of Maurice Duverger (1954), one of the most fundamental ideas in

political science is that a party system is shaped by the electoral institution that it

possesses. The particular effects of each electoral system can be systematically derived

and predictions made of the normative consequences. Duverger states in his famous Law

that plurality electoral systems favor two-party systems while systems of Proportional

Representation (PR) are associated with multi-party systems. While the deterministic nature of this relationship between electoral system and party system is debatable, it is generally accepted (Riker, 1976, 1982, 1986; Sartori, 1976, 1986; Taagepera and Shugart, 1989; Lijphart, 1994).

Perhaps the most fruitful and encompassing work in a similar vein is that of Douglas Rae (1967). He makes bold observations about not only the properties of each electoral system (his "similarity propositions"), but also about the comparisons between different electoral systems (his "differential propositions"). Rae finds that in all electoral systems there exists "a relative advantage of strong elective parties over weak ones" (Similarity Proposition One). Rae defines a "large" (i.e., "strong elective") party as any party with greater than 20 percent of the vote and that all systems slightly favor the top two vote-getting parties (hereafter referred to as "large parties").

By Rae's definition of a "large" party, Similarity Proposition One usually pertains to not only the largest party, but also to the second largest party as well. Both parties, individually and collectivesly, benefit from their size. The political significance of this over-representation is the "manufacturing" of majorities (i.e., a party obtaining a majority of seats without a majority of votes) (Similarity Proposition Three).

Rae determines that the large party seat bonus is more pronounced in plurality/majority electoral systems than in proportional electoral systems (Differential Proposition One). He also illustrates the role that district magnitude (i.e., the number of seats awarded in the district) plays, stating that a positive relationship exists between district magnitude and proportionality (Differential Proposition Ten). Thus, there should be a positive incentive for large parties to desire more majoritarian systems, while the smaller parties should prefer more proportional systems.

Other work has confirmed and extended Rae's findings. Sartori (1976) emphasizes Rae's predicted correlation between proportionality and district magnitude.

The logic of his argument is that a small district magnitude allows only a small number of parties to gain effective representation, while a larger district magnitude allows a greater number of parties to win seats. Sartori (1976, 1986) posits that all electoral systems possess incentives for strategic voting. The more proportional the electoral system, the fewer incentives exist. Therefore, as the district magnitude increases, proportionality and the number of parties increases.

In a comprehensive and systematic examination of democratic legislatures, Taagepera and Shugart (1989) develop a "generalized Duverger's Rule." In an exhaustive empirical analysis they find a positive relationship between district magnitude and the size of the party system. Moreover, they confirm both Rae's similarity propositions and differential propositions. First, they show that all systems award large parties a seat bonus. Second, this over-representation leads to disproportional results for the party system as a whole. Third, plurality/majority electoral systems produce greater overrepresentation and disproportionality than party-list PR electoral systems.

Lijphart (1986, 1994) illustrates that disproportionality is sensitive to electoral system rules. He confirms Rae's differential propositions in two ways. First, he shows that plurality/majority systems are less proportional than PR systems. Second, he provides evidence that different PR electoral formulas can be differentiated by their degree of proportionality. Lijphart states that some PR formulas (e.g., D'Hondt) are clearly less proportional than other PR formulas (e.g., Hare). Third, he agrees with Sartori (1976, 1986) and Taagepera and Shugart (1989) in the positive relationship between district magnitude and proportionality.

Cox (1990) develops a formal proof of the connection between district magnitude and the number of parties. He finds that if political parties can be arranged on a onedimensional spectrum, lowering district magnitude will cause a centripetal effect (lowering the number of parties), while increasing district magnitude will create a centrifugal effect (increasing the number of parties). Cox's model thus confirms both Duverger's Mechanical effect and the influence of the district magnitude on electoral outcomes found in the empirical studies. Blais and Carty (1987, 1991) demonstrate the empirical reality of Duverger's Mechanical and Psychological effects and also the manufacturing of majorities by plurality/majority electoral systems.

In general, these works attempt to find electoral system "equilibria." These authors assume that institutions matter and that they produce predictable results.

Moreover, each electoral system's unique set of procedures favors a singular set of outcomes. For example, multi-member district party-list PR produces multi-party systems with coalition governments. PR with small-member districts (or restrictive thresholds) creates three-party systems with one dominant party. Candidate-choice procedures (e.g., Single Non-Transferable Vote) produce clientalism and/or party fractionalization (Katz, 1980; Lijphart, 1984, 1994; Taagepera and Shugart, 1989).





Given the general consensus of the current literature with Rae's propositions, this paper address whether Rae's First Differential Proposition accurately describes four political systems with unusual electoral formulas: the Single Transferable Vote (STV) as employed in the Republic of Ireland, the Australian State of Tasmania and the Australian Senate, as well as the use of the Alternative Vote (AV) in the Australian House of Representatives.

I have chosen these systems for three compelling reasons. First, STV lies midway between majoritarian and list-PR systems (I explain this later), allowing me to compare a shift in electoral system in both directions. Second, all four party systems have

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occupation/colonization. Last, both STV and AV allow aggregation of votes within the district (which I shall use later to construct party shares), while also presenting information on the electoral strength of individual candidates.

I do not use closed-list PR systems because voters cannot mark a preference for individual candidates. I also refrain from including traditional open-list PR systems (i.e., voters may mark a preference for a candidate) for two reasons: first, often the choice to vote for an individual candidate is optional (e.g., pre-1994 Italy, Switzerland and Luxembourg) and second, the voters choice is ineffective in overturning the party's default order (e.g., Austria, Belgium, the Netherlands, Norway, Sweden) (Taagepera and Shugart, 1989; Gallagher, Laver and Mair, 1995). I also do not include quasi-list PR (i.e., voters are required to mark a candidate preference yet the seats are awarded by party totals) despite its close similarity to STV. My rationale is that in two cases (Chile and Brazil) continuous elections were either interrupted by military regimes or so short-lived that "each (electoral) period was so different and so largely unrelated that any trends are elusive" (MacDonald and Ruhl, 1989) and in another case (Poland) the system has operated for only a short period. This leaves only Finland, which I shall not consider alone versus the "transferable" systems of STV and AV. I also have excluded the use of SNTV systems (multi-member plurality) because an STV election cannot be approximated from the voting results (while admittedly tentative SNTV results can be derived from STV results).1 I compare the actual results in these party systems with predicted results for more majoritarian and more proportional electoral systems. My approach is see how results differ under a variety of electoral rules and infer whether a given party would have an incentive to change the electoral rules.2 From this comparison, I conclude that not all large parties prefer a shift from their current electoral system to a more majoritarian system. In fact, it is often to the advantage of the second largest party (and sometimes the largest) to maintain an electoral system with a transfer of votes rather than replace the current system with either a more majoritarian or more proportional system. Such parties are at an "electoral equilibrium" in which no change of the electoral system will benefit them. In other words, Rae's Differential Proposition One seems unable to define adequately the position of certain large parties in these systems.

The Single Transferable Vote and the Alternative Vote The Single Transferable Vote and Alternative Vote possess the same electoral formula for electing members. Both electoral systems work in the following manner. Each voter casts a single vote by ordering her3 preferences among the available candidates.4 The number of first-preference votes for each candidate is counted and any candidate receiving the necessary quota is elected.5 Any surplus votes over this total are transferred to the other remaining candidates. Then the candidate with the lowest number of first preference votes is eliminated and the ballots supporting him are transferred to the other candidates based on the next marked preferences. The procedure repeats itself until all of the parliamentary seats are filled.6 The electoral formulae of STV and AV thus differ in only their district magnitude;

the former being multi-member and the latter single-member. However, this difference has important consequences. AV is a majoritarian system that favors the larger parties,

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disproportional electoral outcomes (Lijphart, 1994).

On the other hand, STV can be called tentatively a proportional system (O'Leary, 1979; Katz, 1980; Chubb, 1982; Riker, 1986; Lijphart, 1986). Rae classifies STV as a proportional formula, saying that while it lacks the party-list, categorical voting method, the system operates quite proportionally (based on seat/vote ratios and only minimal exclusion of electoral parties from the legislature). Other authors give similar evidence of the high degree of proportionality exhibited by elections with STV (Blondel 1969;

Loosemore and Hanby, 1971; Lijphart 1986). More recent literature are in general agreement, listing STV as a purely proportional system (Gallagher, 1986; Taagepera and Shugart, 1989; Lijphart, 1994; Farrell, Mackerras and McAllister, 1996).7 Grofman and Bowler (1996) claim that STV is "intermediate between first-past-the-post systems and list PR, albeit more like the latter than the former"(pg. 43). This essay agrees with this assessment.

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From the above collective work, one can think of electoral systems as lying along a single spectrum from the more majoritarian on one end to the more proportional on the other (see Figure 1).8 On one theoretical end is the proportional goal of one seat for each vote (or perfect proportionality). The closet approximations are the PR systems with a large average district magnitude9and party-list ballot procedures. STV is included in the PR systems with a small average district magnitude and/or candidate-list ballot procedures. Crossing over to the majoritarian side of the spectrum, one finds the multimember district plurality of the Single Non-Transferable Vote (SNTV) as employed in Japan previous to 1994. Next are the single-member district pluralities (e.g., Great Britain) in which a simple plurality of the vote is necessary for victory. Last are the majority formulae in which a candidate must obtain greater than fifty percent of the vote.

AV is such a system.10 Support for such a spectrum, and the placement of the different electoral formulae, is also found in Grofman (1996) who lays out the logic for the continuum. Cox (1997) also suggests that there exists a continuum of systems from those with the greatest incentives for voters to display strategic behavior (e.g., majoritarian electoral rules) to those with fewer/no incentives (e.g., party-list PR).11 Given Rae's Differential Propositions, large parties should prefer more majoritarian systems while small parties should prefer more proportional systems. For example, In a system using SNTV, large parties would want to replace the electoral system with simple plurality while small parties would want perhaps a small-district PR formula. If parties are instrumental, i.e., that they view the electoral institution as just a rule (albeit an important one) in the larger "game" of party conflict, it is plausible that each party would work towards changing the system in its favor.

The Data: Elections in Four Party Systems To test Rae's propositions I examine data in four different party systems in the post-war period. As such, I look at thirteen Irish elections from 1954 to 1992, ten Tasmanian elections from 1950 to 1982, fifteen Australian Senate elections from 1949 to 1984 and sixteen Australian House elections from 1949 to 1984.12 As aforementioned, the first three party systems employ STV while the last uses AV. 13

THE RESULTS OF THE ACTUAL ELECTIONS

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Figure 2 presents a condensed review of the results of the fifty-four elections. It displays the average first-preference vote share, the average parliamentary seat share and the average deviation of the two obtained by each party. The parties are aligned on the horizontal axis by their ordinal size ranking, with the left-most party being the largest, the next party on the right, the second largest, etc... The right-most designation is reserved for the collective of "other" smaller parties. The solid line represents the average vote share (i.e., first preferences), the dotted line the average seat share and the dashed line the seat bonus/deficit (i.e., seat share minus vote share).

From Figure 2 it appears that two party dominance is the rule in these legislatures.



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