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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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Gallagher, Michael, Laver, Michael and Peter Mair. 1995. Representative Government in Modern Europe. New York: McGraw Hill.

Grofman, Bernard. 1996. "STV's Place in the Family of Electoral Systems: Theoretical Comparisons and Contrasts." Paper delivered at the Conference on Australia, Ireland and Malta under the Single Transferable Vote. December 14-15, Laguna

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Grofman, Bernard and Shaun Bowler. 1996. "STV's Place in the Family of Electoral Systems: The Theoretical Comparisons and Contrasts." Representation. vol. 34,

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Hughes, Colin A. 1977. A Handbook of Australian Government and Politics 1965-1974.

Canberra: Australian National University Press.

-------. 1986. A Handbook of Australian Government and Politics 1975-1984. Canberra:

Australian National University Press.

Hughes, Colin A. and B. D. Graham. 1968. A Handbook of Australian Government and Politics 1890-1964. Canberra: Australian National University Press.

Jesse, Neal. 1996. The Single Transferable Vote and Duverger's Law: Impact on Party Systems and Voting Behavior. Dissertation. University of California, Los Angeles.

Katz, Richard. 1980. A Theory of Parties and Electoral Systems. Baltimore: John

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-------. 1981. "But How Many Candidates Should We Have in Donegal? Number of Nominees and Electoral Efficiency in Ireland." British Journal of Political Science.

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Lijphart, Arend. 1984. Democracies: Patterns of Majoritarian and Consensus Government in Twenty-One Countries. New Haven: Yale University Press.

-------. 1986. "Degrees of Proportionality of Proportional Representation Formulas." In Electoral Laws and Their Political Consequences. ed. B. Grofman and A. Lijphart.

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-------. 1994. Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies 1945-1990. Oxford: Oxford University Press.

Lijphart, Arend and Galen A. Irwin. 1979. "Nomination Strategies in the Irish STV System: The Dail Elections of 1969, 1973 and 1977." British Journal of Political Science. vol. 9, no. 3. pg. 362-369.

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Mair, Peter. 1987. "Policy Competition." In. How Ireland Voted: The Irish General Election, 1987. Eds. M. Laver, P. Mair, and R. Sinnott. Dublin: PSAI press.

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Marsh, Michael. 1996. "Candidate Centered but Party Wrapped: Campaigning in Ireland under STV." Paper delivered at the Conference on Australia, Ireland and Malta under the Single Transferable Vote. December 14-15, Laguna Beach, CA.

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Riker, William H. 1976. "The Number of Political Parties: A Reexamination of Duverger's Law." Comparative Politics. Vol. 9. pg. 93-106.

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The author would like to thank George Tsebelis, Mark Hallerberg and three anonymous readers for comments on earlier drafts of this paper.

This similar logic also works for the quasi-list PR elections. The results of STV elections can be transformed into quasi-list PR, but the reverse is not possible.

My approach is thus similar to that of Bawn (1993) and her analysis of German electoral laws.

For the purpose of clarity, I use male gender pronouns when referring to party candidates and female gender pronouns when referring to voters.

In other words, each voter places the number one beside her most preferred candidate, the number two beside the next preferred, and so on until she no longer wishes to mark further preferences or the list of candidates is exhausted. If a voter's ballot is to be transferred but no further preferences are listed (or only preferences for eliminated candidates are listed) the ballot becomes "non-transferable".

This is calculated using the Droop Quota. The mathematical formula is as follows:

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magnitude equals one).

There are, of course, special provisions for extraordinary situations (e.g. when not enough candidates meet the quota). A good summary of the entire electoral procedure can be found in Mair (1987) or Sinnott (1995).

Katz (1980) is the lone dissenting opinion. He states that STV is really either a plurality formula (due to voting for individual candidates and not party lists) or an intermediate system between plurality and proportional systems. I do not find Katz’s argument persuasive due to his confounding of the electoral system, ballot structure and district magnitude in his classification of STV.

Since district magnitude is positively correlated with the degree of proportionality, for the purposes of Figure 1, I have combined the two variables into a single axis (Rae 1967, Lijphart 1984, Taagepera and Shugart, 1989).

The Average District Magnitude is the size of the legislature (i.e., the number of seats) divided by the number of districts. (Rae 1967, Taagepera and Shugart, 1989).

Similarity Proposition Seven says that all properties of plurality formula apply to the Alternative Vote as well.

To be accurate, Cox (1997) is referring to strategic incentives that would limit the number of political parties in the party system. This is congruent to my Figure 1 and its reference to under-/over-representation.

Elections are to the Irish lower house (Dail), Tasmanian lower house (House of Assembly), Australian lower house (House of Assembly) and the Australian upper house (Senate), I have not included more recent Australian elections due to a change in the electoral laws. Voters may now cast a single vote for a party-list, which allows the parties to pre-determine the destination of most intra-party candidate transfers.

In Ireland, Fianna Fail is the largest party and Fine Gael the second largest. In the three other party systems, Labour is the largest party and the Liberals the second largest.

It can be argued that the size of the second-largest party in these systems is unusually large, perhaps due to historical coincidence. The implication being that my cases are at best a prejudicial examination of Rae and at worst a confounding of my selected variable (electoral formula) with the historical party system size.

Let me say in my defense, first, that the size of the second largest party in these systems is not that unusual (see the following fn.). Second, much of the literature shows that a seat bonus will accrue to these parties once they have obtained at least a 20% vote share, a limit cleared by most other second parties (e.g., see Taagepera and Shugart, 1989). And last, the large size of the second-largest parties only strengthens Rae's argument and weakens my hypothesis, thus creating a stronger "straw man" for me to knock down, which I welcome.

Note that this pattern occurs in a number of other parliamentary democracies. A brief (and by no means exhaustive) examination of the seat shares of the top two parties in other European democracies reveals that in their most recent pre-1995 elections the top two parties in Greece, Portugal, Spain and the United Kingdom obtained over 85% of the seats and the top two parties in Germany and Austria obtained over 75%. The exceptions are Belgium, the Netherlands, France and Switzerland (Gallagher, Laver and Mair, 1995).

In fact, if D'Hondt is substituted for STV in the 1992 Irish elections, the largest party (Fianna Fail) would gain 17 seats at the expense of the other parties.

Largest-Remainder formulas are detailed in Rae (1967), Lijphart (1986, 1994), and Taagepera and Shugart (1989).

Note that AV leads to a type of strategic voting by supporters of a third party similar to that produced by plurality elections. It is not inevitable that votes would transfer to the second largest party, but it is reasonable to assume that they would transfer to one of the two (but not both) large parties. Thus, the transferability of votes may inevitably create one party that defies Rae's predictions.

I do not look at SNTV in the Australian House for two reasons. First, it would not be a more majoritarian shift, but rather a more proportional one. As such it would be a weaker test than that in Table

1. Second, it would involve creating multi-member districts where none exist. As such, there is no reasonable method to create SNTV elections from the current data. I do not look at the Australian Senate because an approximation of a more majoritarian system cannot be accomplished from the actual elections.

Parties are allowed in the Senate to list their candidates in a specified order. Voters may choose these "lists" if they so wish. The first-preference of any voter marking the "list" goes to the first candidate on the list. If the vote has to be transferred, it moves down the list in the pre-determined order. As such, SNTV cannot be approximated as the votes for the candidate on the top of the list are overstated and the votes for the lower candidates are understated.

SNTV has been used in Japan (1949-1994) and Taiwan.

This is often determined by summing up the party's total votes and dividing by the D'Hondt formula.

Holding voters constant assumes that voters do not respond to incentives contained in different electoral systems. However, some work has shown that plurality electoral systems should elicit a particular form of voting behavior that does not exist under proportional formulas (Duverger, 1954; Downs, 1957; Cox, 1987). Other work shows that even PR, and specifically STV, can elicit sophisticated voter responses (Jesse, 1996). Thus, the assumption may too strong. However, it is useful in this study as a way of limiting the effects of the voter and highlighting the effects of the electoral system.

A Labour government would be replaced with a Liberal government in the 1955, 1956 and 1976 elections, while the Liberal-Centre Coalition in 1969 would be replaced by a Labour Government.

In fact, Fine Gael would lose seats in eleven of the thirteen elections, and there would be no change in the number of seats in the other two elections (1957 & 1977).

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