Gallagherindex

The Gallagher index, also known as the Gallagher index or the least-squares index, is a measure of disproportionality in election results. It assesses how closely the distribution of seats in a legislature matches the distribution of votes among the represented parties in a given election. The index was introduced by political scientist Michael J. Gallagher in 1991 and has since become a standard tool in comparative electoral analysis.

The index is defined as 100 times the square root of one-half the sum, over all parties, of the squared differences between vote shares and seat shares. More precisely, if Vi denotes the vote share of party i and Si its seat share, both expressed as fractions of the total votes and seats (Vi, Si ∈ [0,1] and ∑Vi = ∑Si = 1), then LSq = 100 × sqrt(0.5 × Σ (Vi − Si)²) across all parties. The resulting score ranges from 0 to 100, where 0 indicates perfect proportionality (votes and seats align exactly) and 100 indicates maximum disproportionality (e.g., one party wins all seats with only a small share of votes).

Usage and interpretation: The Gallagher index is widely used to compare disproportionality across elections and across countries with different party systems. It provides a single numeric summary of the overall mismatch between votes and seats and is commonly employed in academic research on electoral systems and reform debates.

Limitations: Like any single-number measure, the Gallagher index abstracts away details of the distribution of disproportionality. It can be influenced by the number of parties and by thresholds or electoral rules, and it does not capture how disproportionality is distributed among parties or regions. It should be complemented with other indicators and qualitative analysis for a fuller picture.