Highest averages method

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The highest averages, divisor, or divide-and-round methods^[1] are a family of apportionment rules, i.e. algorithms for fair division of seats in a legislature between several groups (like political parties or states).^[1][2] More generally, divisor methods are used to round shares of a total to a fraction with a fixed denominator (e.g. percentage points, which must add up to 100).^[2]

The methods aim to treat voters equally by ensuring legislators represent an equal number of voters by ensuring every party has the same seats-to-votes ratio (or divisor).^[3]: 30 Such methods divide the number of votes by the number of votes needed to win a seat. The final apportionment. In doing so, the method approximately maintains proportional representation, meaning that a party with e.g. twice as many votes will win about twice as many seats.^[3]: 30

The divisor methods are generally preferred by social choice theorists and mathematicians to the largest remainder methods, as they produce more-proportional results by most metrics and are less susceptible to apportionment paradoxes.^[3][4][5][6] In particular, divisor methods avoid the population paradox and spoiler effects, unlike the largest remainder methods.^[5]