Editing Highest averages method (section)

{{Short description|Rule for proportional allocation}}
{{good article}}

{{Use American English|date=December 2024}}

{{Electoral systems|expanded=Proportional representation}}
The '''highest averages''', '''divisor''', or '''divide-and-round methods'''<ref name="Pukelsheim-2017-1" /> are a family of [[Apportionment (politics)|apportionment]] rules, i.e. algorithms for [[fair division]] of seats in a legislature between several groups (like [[Political party|political parties]] or [[State (sub-national)|states]]).<ref name="Pukelsheim-2017-1" />'''<ref name="Pukelsheim-2017-5" />''' More generally, divisor methods are used to round shares of a total to a [[Ratio|fraction]] with a fixed [[denominator]] (e.g. percentage points, which must add up to 100).'''<ref name="Pukelsheim-2017-5" />'''

The methods aim to treat voters equally by ensuring legislators [[One man, one vote|represent an equal number of voters]] by ensuring every party has the same [[seats-to-votes ratio]] (or ''divisor'').<ref name="Balinski-1982" />{{Rp||page=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.<ref name="Balinski-1982" />{{Rp||page=30}}

The divisor methods are generally preferred by [[Social choice theory|social choice theorists]] and mathematicians to the [[largest remainder method]]s, as they produce more-proportional results by most metrics and are less susceptible to [[apportionment paradox]]es.<ref name="Balinski-1982" /><ref name="Ricca-2017" /><ref name="Pukelsheim-2017-7" /><ref name="Dancisin-2017" /> In particular, divisor methods avoid the [[vote-ratio monotonicity|population paradox]] and [[spoiler effect]]s, unlike the largest remainder methods.<ref name="Pukelsheim-2017-7" />