Electoral Systems

How much do seats actually track votes? The Gallagher index of disproportionality for every legislative election in the atlas, from South Africa's near-perfect 0.50 to Britain's record 23.68 in 2024, set against the system each country uses.

1,028 legislative elections scored across 55 polities · built 2026-09-08

One number, and what it measures

The Gallagher index takes every party's share of the vote, subtracts its share of the seats, squares the differences, halves the total and takes the root. Zero means the chamber is a photograph of the electorate. The scale below is conventional, not invented here.

under 2seats track votes

2–5mildly disproportional

5–10clearly disproportional

10–15heavily disproportional

over 15seats barely track votes

The extreme: Ethiopia 1995 at 37.15. A plurality system meeting a five-party electorate produces the widest gap between votes and seats in this atlas.

The other end: Belgium 1852 at 0.05. A single national district with no threshold is what near-zero looks like.

By family

Mean of each country's median, so a country with two centuries on file does not drown one with three elections. The ordering is the argument: the systems designed to convert votes into seats do it, and the ones designed to produce a winner do that instead.

Single transferable vote4.27

1 country

Party-list proportional5.96

27 countries

Other or non-competitive6.25

2 countries

Proportional with a majority bonus6.98

2 countries

Mixed-member proportional7.15

2 countries

Two-round majority8.27

1 country

Mixed-member majoritarian9.38

7 countries

Instant-runoff (preferential)11.22

1 country

First past the post14.03

11 countries

Every polity with a series

Median across each country's scored elections, with its most recent and its most extreme. Sham votes are kept in the series and out of the median: a ritual that hands one party every seat scores well and means nothing. Every column sorts.


East Germany	Other or non-competitiveno threshold	0.24	1990 · 0.24	1990 · 0.24	1
Denmark	Party-list proportionalthreshold: 2%	1.15	2019 · 1.92	1884 · 21.75	49
Netherlands	Party-list proportionalthreshold: one seat, about 0.67%	1.86	2025 · 1.34	1894 · 10.33	34
Indonesia	Party-list proportionalthreshold: 4% nationally	2.51	2024 · 8.68	2024 · 8.68	11
Sweden	Party-list proportionalthreshold: 4% nationally or 12% in one constituency	2.81	2022 · 0.64	1887 · 10.95	44
Austria	Party-list proportionalthreshold: 4% or one regional seat	2.90	2024 · 3.24	1923 · 4.87	28
Finland	Party-list proportionalno threshold	3.03	2023 · 3.99	1987 · 4.99	39
Colombia	Party-list proportionalthreshold: 3% of the national vote since 2003	3.42	2026 · 3.58	1991 · 12.61	21
Israel	Party-list proportionalthreshold: 3.25%	3.57	2022 · 6.85	2019 · 7.06	25
Ireland	Single transferable voteno threshold	4.27	2016 · 6.51	1922 · 8.92	30
Japan	Mixed-member majoritarianno threshold	4.33	1993 · 6.39	1949 · 9.96	24
Brazil	Party-list proportionalthreshold: party performance clause	4.47	1990 · 4.62	1945 · 8.18	8
Germany	Mixed-member proportionalthreshold: 5% or three constituencies	4.53	2025 · 7.32	2013 · 10.80	30
Switzerland	Party-list proportionalno threshold	4.54	2023 · 4.31	1917 · 17.88	50
Belgium	Party-list proportionalthreshold: 5% per constituency	4.57	2024 · 3.56	1884 · 36.03	56
Venezuela	Mixed-member majoritarianno threshold	4.67	2010 · 9.85	2005 · 13.34	12
Norway	Party-list proportionalthreshold: 4% for levelling seats	4.86	2025 · 4.08	1915 · 24.22	39
Iraq	Party-list proportionalno threshold	5.53	2010 · 6.57	2010 · 6.57	3
Czech Republic	Party-list proportionalthreshold: 5% for a party, higher for coalitions	5.75	2025 · 5.36	1948 · 26.51	17
DR Congo	Party-list proportionalthreshold: no effective threshold	5.78	2023 · 5.78	1965 · 12.74	3
Morocco	Party-list proportionalno threshold	6.18	2021 · 4.26	1963 · 11.32	9
Italy	Proportional with a majority bonusthreshold: 3% party, 10% coalition	6.38	2008 · 29.70	2006 · 31.21	12
Thailand	Mixed-member majoritarianno threshold	6.41	2026 · 17.62	2026 · 17.62	15
Portugal	Party-list proportionalno threshold	6.53	2019 · 9.81	1969 · 11.20	14
Slovakia	Party-list proportionalthreshold: 5%	6.57	2023 · 7.44	2020 · 12.36	14
Romania	Party-list proportionalthreshold: 5%	6.67	2024 · 4.70	1946 · 35.80	19
Mexico	Mixed-member majoritarianthreshold: 3%	6.68	2021 · 8.38	2003 · 17.93	11
Chile	Party-list proportionalthreshold: no national threshold	6.81	2025 · 7.55	1949 · 13.87	15
Turkey	Party-list proportionalthreshold: 7% for an alliance	6.89	2023 · 9.26	2023 · 9.26	3
Poland	Party-list proportionalthreshold: 5% party, 8% coalition	6.90	2023 · 6.76	2015 · 15.79	10
Spain	Party-list proportionalthreshold: 3% within a province	7.09	2023 · 6.11	1977 · 12.79	19
Greece	Proportional with a majority bonusthreshold: 3%	7.58	2023 · 7.43	1952 · 27.36	35
France	Two-round majoritythreshold: 12.5% of the roll to reach round two	8.27	1986 · 8.18	1919 · 10.78	4
Singapore	First past the postno threshold	9.61	1951 · 18.71	1951 · 18.71	2
New Zealand	Mixed-member proportionalthreshold: 5% or one electorate	9.78	1993 · 18.32	1935 · 18.70	32
South Africa	Party-list proportionalno threshold	9.82	2024 · 0.50	1933 · 24.41	24
Canada	First past the postno threshold	10.01	2025 · 5.05	1935 · 22.20	40
Kenya	First past the postno threshold	10.44	2017 · 10.44	1961 · 27.71	3
United Kingdom	First past the postno threshold	10.55	2024 · 23.68	2024 · 23.68	49
Ukraine	Party-list proportionalthreshold: 5%	10.71	2012 · 10.71	2012 · 10.71	1
South Korea	Mixed-member majoritarianthreshold: 3%	11.15	1978 · 14.52	1960 · 30.03	7
Australia	Instant-runoff (preferential)no threshold	11.22	2025 · 23.64	2025 · 23.64	44
Jamaica	First past the postno threshold	11.48	2025 · 4.87	1993 · 26.40	19
Pakistan	First past the postno threshold	11.79	2024 · 11.79	1977 · 19.62	11
Nigeria	First past the postno threshold	12.25	2011 · 7.96	1933 · 21.35	10
Egypt	Other or non-competitiveno threshold	12.27	1950 · 13.37	1923 · 29.66	10
Peru	Party-list proportionalthreshold: 5% of the national vote	13.71	2021 · 14.02	2016 · 15.23	6
Hungary	Mixed-member majoritarianthreshold: 5% party, 10% two-party alliance	14.66	2026 · 15.45	1825 · 23.75	21
Palestine	Party-list proportionalthreshold: 2%	16.30	2006 · 10.00	1996 · 22.59	2
Bangladesh	First past the postno threshold	17.37	2018 · 10.51	1979 · 24.10	9
Malaysia	First past the postno threshold	17.47	2022 · 7.92	2004 · 23.93	14
Russia	Mixed-member majoritarianthreshold: 5%	17.76	2021 · 17.76	2016 · 18.00	3
India	First past the postno threshold	19.49	1991 · 8.77	1951 · 23.51	10
Ethiopia	First past the postno threshold	23.85	2021 · 10.55	1995 · 37.15	3
Cuba	plurality/listno threshold	—	2018 · 19.56	2018 · 19.56	4

Most proportional on the median: East Germany at 0.24. Least: Ethiopia at 23.85.

Turnout, every polity

The other half of how a system behaves. The landing page charts six countries over a century; this is all 63 that record turnout at all, on the same series each hub leads with. Rituals are kept out of the medians and left in the highs, which is where a reported 99% is worth seeing. Every column sorts.


Vietnam	99.5%	2026 · 99.7%	1960 · 99.9%ritual	1981 · 98.0%	14
Australia	95.0%	2025 · 90.7%	1943 · 96.3%	1903 · 39.0%	48
Singapore	94.0%	2025 · 92.8%	1997 · 95.9%	1951 · 52.0%	19
East Germany	93.4%	1990 · 93.4%	1986 · 99.7%ritual	1990 · 93.4%	11
Ethiopia	91.3%	2026 · 95.7%	2026 · 95.7%	2005 · 82.6%	8
Austria	91.1%	2024 · 77.7%	1949 · 96.8%	2013 · 74.9%	30
Belgium	90.8%	2024 · 88.5%	1987 · 93.4%	2019 · 88.4%	10
Italy	88.4%	2022 · 63.9%	1953 · 93.8%	1919 · 56.6%	21
New Zealand	86.0%	2023 · 78.2%	1949 · 96.3%	1884 · 60.6%	46
Sweden	85.9%	2022 · 84.2%	1976 · 91.8%	1872 · 19.1%	39
Denmark	85.8%	2026 · 84.0%	1968 · 89.3%	1879 · 47.2%	31
Turkey	84.1%	2023 · 87.0%	1987 · 93.3%	1927 · 20.0%	23
Indonesia	83.0%	2024 · 82.0%	1955 · 91.5%	2009 · 71.0%	8
Germany	82.5%	2025 · 82.5%	1938 · 99.6%ritual	1871 · 51.0%	48
Peru	82.3%	2026 · 73.8%	1963 · 94.4%	2021 · 70.0%	14
Argentinapresidential	82.3%	2023 · 78.3%	1958 · 90.9%	1922 · 56.4%	21
Brazil	82.1%	1945 · 82.1%	1945 · 82.1%	1945 · 82.1%	1
Netherlands	81.0%	2025 · 78.3%	1959 · 95.6%	1917 · 38.0%	40
South Vietnam	80.8%	1966 · 80.8%	1966 · 80.8%	1966 · 80.8%	1
Chile	80.6%	2025 · 85.4%	1989 · 94.7%	1945 · 34.6%	21
Norway	79.1%	2025 · 80.1%	1894 · 90.2%	1865 · 41.8%	58
Philippinespresidential	78.0%	2022 · 83.1%	1946 · 89.6%	1949 · 69.7%	15
Israel	77.4%	2022 · 70.6%	1949 · 86.9%	1925 · 57.0%	27
Greece	76.3%	2023 · 61.8%	1963 · 83.2%	2023 · 53.7%	28
Taiwanpresidential	74.9%	2024 · 71.9%	2000 · 82.7%	1954 · 53.2%	9
Malaysia	74.7%	2022 · 74.1%	2013 · 84.6%	1986 · 70.0%	14
Finland	74.2%	2023 · 72.6%	1962 · 85.1%	1913 · 51.1%	39
Venezuela	74.0%	2025 · 42.7%	1968 · 96.7%	2005 · 25.3%	15
United Kingdom	72.8%	2024 · 59.7%	1910 · 86.8%	1918 · 57.2%	38
South Korea	72.7%	2024 · 67.0%	1948 · 95.5%	2008 · 46.1%	22
Ireland	72.1%	2024 · 59.7%	1933 · 81.3%	2024 · 59.7%	32
Palestine	71.4%	2006 · 71.2%	1996 · 71.7%	2006 · 71.2%	2
Canada	70.3%	2025 · 69.5%	1958 · 79.4%	2008 · 58.8%	45
Spain	69.7%	2023 · 66.6%	1982 · 80.0%	1971 · 42.3%	30
France	69.6%	2024 · 66.7%	1936 · 84.5%	2022 · 47.5%	29
Hungary	69.3%	2026 · 79.0%	1967 · 98.8%ritual	1998 · 56.2%	23
South Africa	69.1%	2024 · 58.6%	1999 · 89.3%	1989 · 23.3%	26
Japan	68.8%	2026 · 56.3%	1930 · 82.3%	2014 · 52.6%	32
Slovakia	68.5%	2023 · 68.5%	1976 · 99.8%ritual	2006 · 54.7%	17
Czech Republic	67.2%	2025 · 69.0%	1976 · 99.7%ritual	2002 · 58.0%	20
Kenya	65.2%	2022 · 64.8%	2013 · 85.9%	1988 · 40.7%	7
Jamaica	65.2%	2025 · 40.0%	1980 · 86.9%	1983 · 2.7%	19
Ukraine	64.8%	2019 · 49.2%	1994 · 75.8%	2019 · 49.2%	8
Portugal	64.3%	2025 · 58.3%	1975 · 91.7%	2019 · 48.6%	23
Thailand	61.4%	2026 · 71.4%	2023 · 75.6%	1948 · 29.5%	28
Bangladesh	60.3%	2026 · 59.4%	2008 · 87.1%	1996 · 21.0%	13
Russia	60.1%	2021 · 51.7%	1989 · 89.8%	1922 · 22.3%	11
India	60.0%	2024 · 66.1%	2019 · 67.4%	1957 · 45.4%	17
Iran	59.7%	2024 · 40.6%	1996 · 71.1%	2024 · 40.6%	11
United Statespresidential	59.4%	2024 · 64.3%	1876 · 82.6%	1792 · 6.3%	60
DR Congo	59.0%	2023 · 42.6%	1970 · 97.6%ritual	2023 · 42.6%	7
Iraq	56.0%	2025 · 56.0%	2014 · 62.0%	2021 · 43.3%	3
Romania	55.5%	2024 · 52.5%	1980 · 100.0%ritual	2020 · 31.9%	28
Morocco	55.0%	2021 · 50.4%	1977 · 82.4%	2007 · 37.0%	10
Poland	52.1%	2023 · 74.3%	1952 · 95.0%	2005 · 40.5%	18
European Union	50.7%	2024 · 50.7%	1979 · 62.0%	2014 · 42.5%	10
Mexico	50.2%	2021 · 52.7%	2021 · 52.7%	2015 · 47.7%	2
Switzerland	46.5%	2023 · 46.6%	1983 · 48.9%	1995 · 42.2%	12
Pakistan	45.2%	2024 · 47.8%	1970 · 58.0%	1997 · 35.8%	11
Egypt	44.4%	2015 · 28.3%	1923 · 96.9%	2005 · 28.1%	18
Colombia	43.5%	2026 · 50.6%	1958 · 68.1%	1994 · 32.7%	22
United Arab Emirates	35.3%	2023 · 44.0%	2006 · 74.4%	2011 · 27.8%	5
Cuba	—	2023 · 75.8%	1993 · 99.6%ritual	1901 · 63.5%	8

What this cannot measure yet

An empty row would read as an oversight, so here is why each one is empty. Two of these are not limits of the method: the atlas records the seats but not the vote shares, and adding them would produce the series in full.

United Arab EmiratesSeats are on file but vote shares are not, so the index cannot be computed. Adding the shares would unlock the whole series.

ArgentinaThis hub records single-winner contests, which have no seat share to compare a vote share against.

ChinaNo election met the scoring rules; the commonest reason was: no vote shares recorded.

European UnionNo election met the scoring rules; the commonest reason was: no parties recorded.

IranNo election met the scoring rules; the commonest reason was: no seat total.

PhilippinesThis hub records single-winner contests, which have no seat share to compare a vote share against.

TaiwanThis hub records single-winner contests, which have no seat share to compare a vote share against.

United StatesThis hub records single-winner contests, which have no seat share to compare a vote share against.

Vatican CityThis hub records single-winner contests, which have no seat share to compare a vote share against.

South VietnamNo election met the scoring rules; the commonest reason was: no vote shares recorded.

VietnamNo election met the scoring rules; the commonest reason was: no vote shares recorded.

West Indies FederationSeats are on file but vote shares are not, so the index cannot be computed. Adding the shares would unlock the whole series.

Spain24 of its elections record seats without vote shares, which is why the series stops at 2023. The system did not change; the data ran out.

Norway23 of its elections record seats without vote shares, which is why the series stops at 2025. The system did not change; the data ran out.

France23 of its elections record seats without vote shares, which is why the series stops at 1986. The system did not change; the data ran out.

Greece21 of its elections record seats without vote shares, which is why the series stops at 2023. The system did not change; the data ran out.

Gallagher least-squares index of disproportionality, computed from the vote shares and seat counts already recorded for every legislative election in this atlas. Unlisted parties are folded into one residual bucket; an election whose listed vote shares total under 80% is not scored. Parties are those recorded in each hub, so the index is computed on the same figures the hub pages show, and can be checked against them. Built by scripts/elections/build_systems.py, which carries a self-test covering the hand-computable cases.