Highest averages method

The highest averages, divisor, or divide-and-round methods 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). 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).

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).^: 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.^: 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. In particular, divisor methods avoid the population paradox and spoiler effects, unlike the largest remainder methods.