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| Loosemore–Hanby index | |
|---|---|
| Name | Loosemore–Hanby index |
| Other names | LHI |
| Introduced | 1971 |
| Creators | Rodney D. Loosemore; R. J. Hanby |
| Field | Electoral studies; Political science |
| Formula | Sum of absolute vote–seat differences / 2 |
Loosemore–Hanby index The Loosemore–Hanby index measures disproportionality between United Kingdom-style vote shares and seat shares in pluralist electoral systems. It was introduced to quantify divergence in systems such as the first-past-the-post, and has been applied in comparative studies involving countries like United States, Canada, Australia, India, and New Zealand. The index is used by analysts at institutions such as the International Institute for Democracy and Electoral Assistance, the Conservative Party, and research groups affiliated with London School of Economics and University of Oxford.
The index defines electoral disproportionality as the aggregate absolute difference between party vote shares and party seat shares. It was created to assess fairness and representativeness in assemblies such as the House of Commons, the House of Representatives, the Lok Sabha, and the Australian House of Representatives. Practitioners in organizations including Electoral Commission, European Parliament, and think tanks like Chatham House and Brookings Institution use the measure to compare outcomes across systems like STV and Mixed-member proportional representation.
For a legislature with parties indexed by i, let v_i denote the party's vote share and s_i denote its seat share. The Loosemore–Hanby index L is given by L = (1/2) * Σ_i |v_i − s_i|. This formulation is equivalent to summing positive deviations across parties and dividing by two, a property familiar to researchers at Massachusetts Institute of Technology, Harvard University, and Stanford University. In practice the index ranges from 0 (perfect proportionality, e.g., in some Proportional representation lists) to 1 (maximum disproportionality as in extreme winner-take-all cases), a scale used in comparative datasets maintained by groups at Oxford Internet Institute and University of Michigan.
The Loosemore–Hanby index is nonnegative, symmetric with respect to exchange of votes and seats, and additive across parties in terms of absolute deviations. It equals zero for systems where vote shares equal seat shares, a property discussed in literature from Institute for Advanced Study and cited in analyses by scholars at Princeton University. It is sensitive to large deviations by small or large parties, and it treats overrepresentation and underrepresentation equally due to the absolute value. Comparative studies across jurisdictions such as Germany, France, Spain, Italy, Sweden, and Norway interpret L alongside measures like the Gallagher index and the Sainte-Laguë method to provide nuanced assessments of representativeness.
Researchers apply the Loosemore–Hanby index to elections in parliaments like the Knesset, the Bundestag, the Sejm, and regional assemblies such as the Catalan Parliament. Empirical examples include analyses of 1979 UK election outcomes, 2016 US election seat-vote distortions in state legislatures, and proportionality in the New Zealand reform transition. Political scientists at institutions including Yale University, Columbia University, and University of Chicago use L in cross-national datasets such as those compiled by Inter-Parliamentary Union and the Comparative Study of Electoral Systems.
Critics note that the Loosemore–Hanby index ignores district magnitude, ballot structure, and regional concentration effects that matter in systems like Canada's provinces or the United Kingdom's constituencies. It also does not weight deviations by party size beyond absolute difference, a concern raised by scholars at University of California, Berkeley and in reports by International IDEA. Alternative indices such as the Gallagher index or measures developed at European University Institute address sensitivity to large parties and squaring deviations, while practitioners from Princeton University emphasize combining L with district-level analyses and seat allocation rules such as D'Hondt method.
Related measures include the Gallagher index, Loosemore–Hanby’s absolute-sum variant without the 1/2 normalization, and indices derived from the Sainte-Laguë and D'Hondt allocation comparisons. Other related statistics are the effective number of parties (Laakso–Taagepera), the Rae index, and measures used by World Bank analysts for electoral quality. Comparative frameworks combine L with incentive-focused metrics like the disproportionality-adjusted indices developed at London School of Economics and with seat-vote curve modeling used by researchers at University of California, Los Angeles.
Category:Electoral systems Category:Political science