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In mathematics, economics, and social choice theory, the highest averages or divisor methods, sometimes called divide-and-round,[1] are a family of apportionment algorithms that aim to fairly divide a legislature between several groups, such as political parties or states.[1][2] More generally, divisor methods can be used to round shares of a total, e.g. percentage points (which must add up to 100). The two names for these methods—highest averages and divisors—reflect two different ways of thinking about them, and their two independent inventions. However, both procedures are equivalent and give the same answer.[1]
Divisor methods aim to treat voters equally by ensuring every legislator represents an equal number of voters, as nearly as practicable, by iteratively assigning additional representatives to whichever party is most underrepresented.[3]: 30 In doing so, the method maintains proportional representation, so that a party with (say) twice as many votes as another should win twice as many seats.[3]: 30
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