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The Mathematics of Apportionment:...
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In Europe, many countries elect representatives to congress or parliament using a type of voting called the Party List Method.

Like the single transferable vote method, the party list method is considered a type of proportional representation, because it gives groups of voters power in proportion to their numbers. However, the party list method leads directly to apportionment problems, since a parliament doesn't have fractional seats. One way to minimize such problems is to allow variations in the total number of seats and to use simple rounding.

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