Electoral Formulas Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

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Electoral formulas determine the allocation of representation to candidates or parties, given the tally in an election. They can be simple, with the candidate receiving the most votes winning the seat in a single-member district, or complex, with an elaborate mathematical formula in multimember districts. Indeed, because seat allocation is so straightforward in plurality systems—the candidate with the most votes in a given district wins the seat—the term electoral formula is generally used with respect to proportional representation systems.

The simplest element of an electoral formula is the threshold of votes required to qualify for at least one seat, although some formulas do not set a threshold. For example, in state primary elections to allocate delegates to the 2008 Democratic National Convention, the body that formally nominated the Democratic candidate for president of the United States, 15 percent of the state primary vote was required to earn delegates from that state. Where thresholds are set, they typically vary with the number of seats allocated. In elections for the European Parliament, which use variants of proportional representation from country to country, thresholds vary from none to 5 percent.

There are two major families of electoral formulas: highest-averages and largest-remainder methods. Under highest averages methods, the first step after votes are tallied is to calculate a quotient for each party with the numerator equaling the number of votes received by that party. The formula for the denominator varies across specific methods. For example, in the D’Hondt formula, a highest-averages method used in most European systems, the denominator for each party is the number of seats already allocated to that party plus one. Initially, all parties start with zero seats allocated and a denominator equal to one. The first seat is assigned to the party with the highest quotient; then its quotient is recalculated using the new denominator (two). The second seat is assigned to the party that now has the highest quotient, which could be the party with the first seat if it received more than twice as many votes as its nearest competitor but otherwise will be the party with the second-highest vote total. The quotient is again recalculated, and the process is repeated until all seats are allocated. An alternative to D’Hondt is the Sainte-Laguë formula, for which the denominator equals two times the number of seats already allocated, plus one. This variation makes Sainte-Laguë more favorable to smaller parties than D’Hondt.

The key element of the largest-remainder method is the enhances the representation of smaller parties more than the Droop quota. In wide use are the Droop quota and the Hare (or simple) quota. Each party’s vote tally is divided by the quota, and the result is a whole-number quotient plus a remainder (it is possible for a party’s remainder to equal zero). Each party receives, at a minimum, the number of seats equal to the whole-number quotient. Unallocated seats are then awarded sequentially to the party with the largest remainder. As with the denominator of a highest-averages method, the choice of a specific quota in a largest-remainder method can alter the seat allocation. To wit, the Hare quota

Bibliography:

Benoit, Kenneth. “Which Electoral Formula Is the Most Proportional? A New Look with New Evidence.” Political Analysis 8 (July 2000): 381–388.
Blais, André, and Louis Massicotte. “Electoral Formulas: A Macroscopic Perspective.” European Journal of Political Research 32 (August 1997): 107–129.
Golder, Matt. “Democratic Electoral Systems around the World, 1946–2000.” Electoral Studies 24 (March 2005): 103–121.
Lijphart, Arend. Electoral Systems and Party Systems: A Study of Twenty-seven Democracies, 1945–1990. New York: Oxford University Press, 1995. See esp. Appendix A.