What is a low Gallagher index?

A Gallagher LSq below 2 is very proportional (Netherlands, Denmark). Values of 5–10 indicate moderate disproportionality (Germany, Ireland). Values above 10–15 indicate highly disproportional systems (UK FPTP typically 15–20).

Who developed the Gallagher index?

Michael Gallagher developed the least squares index in 1991 as an improvement over earlier deviation measures. It squares differences (penalising large deviations more) and normalises by taking the square root of half the sum.

Gallagher Disproportionality Index (LSq)

Calculate the Gallagher least squares index LSq = √(½∑(vᵢ – sᵢ)²) measuring electoral disproportionality between vote shares vᵢ and seat shares sᵢ. Lower values indicate more proportional systems.

Data set — comma or newline separated

Statistical Results — n = 8

Count (n)8

Sum (Σx)40

Min2

Max9

Range7

Q14

Q35.5

IQR1.5

Mean (μ)5

Median4.5

Mode4

Pop. Variance (σ²)4

Pop. Std Dev (σ)2

Sample Variance (s²)4.571428571

Sample Std Dev (s)2.138089935

Skewness0.65625

Excess Kurtosis-0.21875

How to Use

Enter the values for the scenario you are assessing. Calculate the Gallagher least squares index LSq = √(½∑(vᵢ – sᵢ)²) measuring electoral disproportionality between vote shares vᵢ and seat shares sᵢ. Lower values indicate more proportional systems. Use the gallagher index result to inform your calculation.

Gallagher Disproportionality Index (LSq)

How to Use

Frequently Asked Questions

What is a low Gallagher index?

Who developed the Gallagher index?