Gallagher Index Calculator

The Gallagher Index is a statistical measure used to evaluate disproportionality in electoral systems. It quantifies the difference between the percentage of votes received by political parties and the percentage of seats they win in a legislature. A lower index value indicates a more proportional system, while higher values suggest greater electoral distortion.

Historical Background

The Gallagher Index was proposed by political scientist Michael Gallagher in 1991 as a tool to measure electoral fairness. It is widely used in political science to assess the proportionality of various electoral systems, particularly in countries that use forms of proportional representation.

Calculation Formula

The formula for the Gallagher Index is as follows:

\[ \text{Gallagher Index} = \sqrt{\frac{1}{2} \sum_{i=1}^{n} (V_i - S_i)^2} \]

Where:

• \( V_i \) is the percentage of votes received by party \( i \)
• \( S_i \) is the percentage of seats won by party \( i \)
• \( n \) is the number of parties in the election

Example Calculation

Suppose three parties receive the following vote and seat percentages:

• Party A: 40% of votes, 45% of seats
• Party B: 35% of votes, 30% of seats
• Party C: 25% of votes, 25% of seats

The discrepancies for each party are:

• Party A: \( (40 - 45)^2 = 25 \)
• Party B: \( (35 - 30)^2 = 25 \)
• Party C: \( (25 - 25)^2 = 0 \)

Summing and dividing by 2:
\[ \frac{1}{2} \times (25 + 25 + 0) = 25 \]

The Gallagher Index is:
\[ \sqrt{25} = 5 \]

Importance and Usage Scenarios

The Gallagher Index is crucial for analyzing the fairness of electoral systems. It helps policymakers and researchers understand how well votes are translated into seats, promoting democratic fairness. The index is often used to compare different electoral systems or track changes over time within a country.

Common FAQs

1. What is a "good" Gallagher Index score?
   A lower Gallagher Index score, close to zero, is considered "good," as it reflects high proportionality. Higher values indicate greater distortion in how votes translate into seats.

2. Can the Gallagher Index be negative?
   No, the Gallagher Index is always positive or zero, as it is based on squared differences between vote and seat shares.

3. What is the ideal scenario for a Gallagher Index?
   The ideal score is 0, which occurs when the percentage of votes exactly matches the percentage of seats for all parties, indicating perfect proportionality.

The Gallagher Index calculator is a helpful tool for political analysts, researchers, and anyone interested in understanding electoral fairness.