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In mathematics, economics, and social choice theory, the highest averages methods, also called the divisor methods,^[1] are a family of apportionment methods. These methods seek to fairly divide a legislature between several groups, such as political parties or states.^[1]^[2] The two names for these methods—highest averages and divisors—reflect two different ways to 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, i.e. a party with twice as many votes should win twice as many seats.^[3]^: 30

^ ^a ^b ^c Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), "Divisor Methods of Apportionment: Divide and Round", Proportional Representation: Apportionment Methods and Their Applications, Cham: Springer International Publishing, pp. 71–93, doi:10.1007/978-3-319-64707-4_4, ISBN 978-3-319-64707-4, retrieved 2021-09-01
^ Pukelsheim, Friedrich (2017), "From Reals to Integers: Rounding Functions, Rounding Rules", Proportional Representation: Apportionment Methods and Their Applications, Springer International Publishing, pp. 71–93, doi:10.1007/978-3-319-64707-4_4, ISBN 978-3-319-64707-4, retrieved 2021-09-01
^ ^a ^b Balinski, Michel L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.