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.

1,095 legislative elections scored across 59 polities · built 2026-10-24

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 proportional5.94
31 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 majoritarian9.28
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-competitive · latest 1990 0.24
0.24
median
Denmark
Party-list proportional · latest 2019 1.92
1.15
median
Netherlands
Party-list proportional · latest 2025 1.34
1.86
median
Indonesia
Party-list proportional · latest 2024 8.68
2.51
median
Sweden
Party-list proportional · latest 2026 0.68
2.73
median
Austria
Party-list proportional · latest 2024 3.24
2.90
median
Finland
Party-list proportional · latest 2023 3.99
3.03
median
Colombia
Party-list proportional · latest 2026 3.58
3.42
median
Israel
Party-list proportional · latest 2022 6.85
3.57
median
Slovenia
Party-list proportional · latest 2026 4.71
4.11
median
Brazil
Party-list proportional · latest 2026 3.29
4.17
median
Ireland
Single transferable vote · latest 2016 6.51
4.27
median

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 67 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
latest 2026 99.7% · high 99.9% · low 98.0%
99.5%
median since 1945
Australia
latest 2025 90.7% · high 96.3% · low 39.0%
95.0%
median since 1945
Singapore
latest 2025 92.8% · high 95.9% · low 52.0%
94.0%
median since 1945
East Germany
latest 1990 93.4% · high 99.7% · low 93.4%
93.4%
median since 1945
Ethiopia
latest 2026 95.7% · high 95.7% · low 82.6%
91.3%
median since 1945
Austria
latest 2024 77.7% · high 96.8% · low 74.9%
91.1%
median since 1945
Belgium
latest 2024 88.5% · high 93.4% · low 88.4%
90.8%
median since 1945
Italy
latest 2022 63.9% · high 93.8% · low 56.6%
88.4%
median since 1945
New Zealand
latest 2023 78.2% · high 96.3% · low 60.6%
86.0%
median since 1945
Sweden
latest 2026 84.9% · high 91.8% · low 19.1%
85.8%
median since 1945
Denmark
latest 2026 84.0% · high 89.3% · low 47.2%
85.8%
median since 1945
Turkey
latest 2023 87.0% · high 93.3% · low 20.0%
84.1%
median since 1945

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.