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| Gallagher index | |
|---|---|
| Name | Gallagher index |
| Other names | Least squares index |
| Introduced | 1991 |
| Field | Electoral studies |
| Formula | √(½ Σ (v_i − s_i)²) |
Gallagher index The Gallagher index is an electoral disproportionality measure used to quantify the difference between vote shares and seat shares in representative assemblies such as parliaments and legislatures. Developed in the context of comparative electoral studies and applied by scholars of electoral systems, voting behavior, and political parties, it provides a single-number summary that is widely reported in analyses of elections in countries like the United Kingdom, United States, Germany, France, and Spain.
The index was proposed to compare the proportionality of different electoral systems and to evaluate outcomes across elections, jurisdictions, and reforms involving actors such as the Electoral Commission (United Kingdom), the Federal Election Commission (United States), and national electoral authorities in states like India, Japan, and Brazil. It serves practitioners including political scientists studying institutions at places such as the European Parliament and observers from organizations like the Organization for Security and Co-operation in Europe and the International Foundation for Electoral Systems. Analysts employ the index alongside measures derived from scholars connected to the Institute for Democracy and Electoral Assistance and research centers like the Brookings Institution.
Formally, the index is computed by taking vote shares v_i and seat shares s_i for each party i represented in an election such as those for the House of Commons, Bundestag, Knesset, or Dáil Éireann, calculating the squared differences, summing them, halving the sum, and finally taking the square root. The computation is implemented in software packages maintained by institutions such as the R Project for Statistical Computing community, the Oxford University Press-hosted journals, and data repositories curated by the Inter-university Consortium for Political and Social Research and the European University Institute.
Values of the index are interpreted in relation to benchmarks used by commentators at outlets such as the Financial Times, The Economist, and academic journals like the American Political Science Review and Electoral Studies. The index has properties including non-negativity, symmetry between votes and seats when applied consistently across entities like the Supreme Court of the United States in analyses of institutional representation, and scale invariance under total-seat normalization used in comparisons between assemblies like the Senate of Canada and the Australian House of Representatives. It is sensitive to tail-party effects observed in systems dominated by parties such as the Conservative Party (UK), the Social Democratic Party of Germany, the Liberal Democratic Party (Japan), and the Workers' Party (Brazil).
Researchers apply the index to study outcomes of landmark contests including elections like the 1997 United Kingdom general election, the 2009 European Parliament election, the 2016 United States elections, and episodes of electoral reform such as the adoption of proportional representation in countries like New Zealand and Italy. It is used by comparative teams at institutions such as the Centre for European Policy Studies, the Carnegie Endowment for International Peace, and university departments at Harvard University, University of Oxford, and Sciences Po to assess how systems—first-past-the-post, mixed-member proportional, single transferable vote—affect translation of votes to seats. Policy debates in legislatures like the Irish Dáil and commissions like the Constitutional Commission (Iceland) have cited the index when considering districting, thresholds, and ballot design.
Critics appearing in journals like Journal of Politics and forums such as the London School of Economics's pages note limitations when dealing with independent candidates as seen in elections in India or Kenya, and with regional parties active in contexts such as Scotland, Catalonia, and Quebec. Other critiques focus on normative interpretation when applied alongside measures of disproportionality like those developed by scholars associated with Rein Taagepera and Arend Lijphart, and with indices used in work from the National Democratic Institute. The index does not capture geographic concentration effects highlighted in studies of constituencies like Bucaramanga or Bihar nor the strategic behavior analyzed by theorists at the Massachusetts Institute of Technology and the University of California, Berkeley.
Related measures include the Loosemore–Hanby index, indices derived from concepts by Mancur Olson-inspired scholars, and global measures used by the International Institute for Democracy and Electoral Assistance. Alternative summaries applied in comparative work originate from researchers affiliated with the Center for Strategic and International Studies and the Inter-Parliamentary Union; these include measures based on mean absolute deviations, entropy-based metrics used by analysts at United Nations agencies, and adapted least-squares variants used in studies of systems such as Denmark's and Norway's proportional frameworks.
Category:Electoral systems Category:Voting theory