Highest averages method

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The highest averages, divisor, or divide-and-round methods^[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).^[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-per-seat, then round the total to get the final apportionment. In doing so, the method approximately maintains proportional representation, so that a party with e.g. twice as many votes as another should win twice as many seats.^[3]: 30

The divisor methods are generally preferred by social choice theorists to the largest remainder methods, as they produce more-proportional results by most metrics and are less susceptible to apportionment paradoxes.^[4][5][6] In particular, divisor methods satisfy vote-ratio monotonicity and participation, i.e. voting for a party can never cause it to lose seats, unlike in the largest remainders methods; in addition, they are not sensitive to spoiler effects.^[5]