Within party-list PR systems, there are a variety of different methods that can be used to determine how many seats are allocated to each party for a given vote breakdown. The method used to allocate seats within party-list proportional representation vary. Some
apportionment methods may favor small parties; others may favor large parties: •
D'Hondt method (biased towards large parties) •
Sainte-Laguë method (generally considered closest to proportional but does not ensure that a party receiving more than half the votes will win at least half the seats) •
Huntington–Hill method (biased towards small parties, automatically gives every party at least one seat) • Example (5 seats): • Result: A = 2, B = 2, C = 1
Sainte-Laguë method The
Sainte-Laguë (Webster) method is a highest averages method using odd-numbered divisors (1, 3, 5, ...) to promote more equal distribution. • Same vote totals as above. • Result: A = 2, B = 2, C = 1
Modified Sainte-Laguë method Same as Sainte-Laguë but first divisor is 1.4 to favour larger parties. • Divisors: 1.4, 3, 5, ... • Result: A = 2, B = 2, C = 1
Hare quota (largest remainder) The
Hare quota uses a quota to allocate seats, then gives remaining seats to the parties with the largest remainders. • Quota = Total votes / Seats = 2200 / 5 = 440 • Remaining 2 seats to C and B (highest remainders) • Result: A = 2, B = 2, C = 1
Imperiali quota (largest remainder) The
Imperiali quota is rarely used; favors large parties more. • Quota = Total votes / (seats + 2) = 2200 / 7 = ~314.29 • 1 leftover seat to B • Result: A = 3, B = 2, C = 1
Huntington–Hill method The
Huntington–Hill method is used for US congressional apportionment, based on geometric mean. Too specialized for vote quotas, usually used with population. The apportionment methods can be classified into two categories: • The
highest averages method (or divisor method), including the
D'Hondt method (Jefferson method) is used in
Armenia,
Austria,
Brazil,
Bulgaria,
Cambodia,
Croatia,
Estonia,
Finland,
Poland, and
Spain; and the
Sainte-Laguë method (Webster method) is used in
Indonesia,
New Zealand,
Norway, and
Sweden. • The
largest remainder (LR) methods, including the Hamilton (Hare) method and Droop method. While the allocation formula is important, equally important is the district magnitude (number of seats in a constituency). The higher the district magnitude, the more proportional an electoral system becomes, with the most proportional results being when there is no division into constituencies at all and the entire country is treated as a single constituency. In some countries the electoral system works on two levels:
at-large for parties, and in constituencies for candidates, with local party-lists seen as fractions of general, national lists. In this case, magnitude of local constituencies is irrelevant, seat apportionment being calculated at national level. List proportional representation may also be combined with other apportionment methods in various mixed systems, using either
additional member systems or
parallel voting.
Example Below it can be seen how different apportionment methods yield different results when apportioning 100 seats. Webster's method yields the same result (though this is not always the case). Otherwise, all other methods give a different number of seats to the parties. Notice how the D'Hondt method breaks the
quota rule (shown in red text) and favors the largest party by "rounding" an ideal apportionment of 35.91 up to 37. Adams' method greatly favors smaller parties, giving 2 seats to the smallest party, and would give at least 1 seat to every party receiving at least one vote.
Electoral threshold == List of countries using party-list proportional representation ==