Apportionment and districting by Sum of Ranking Differences

Area of Science:

• Statistics
• Political Science
• Computational Social Science

Background:

• Democratic elections require fair apportionment and districting.
• Existing methods for measuring malapportionment and constituency shape lack a definitive best approach.
• The Sum of Ranking Differences (SRD) offers a novel statistical framework for ranking solutions.

Purpose of the Study:

• To apply the Sum of Ranking Differences method to evaluate apportionment and districting techniques.
• To compare the performance of established methods in electoral processes using real-world data.
• To identify superior methods for fair representation in democratic systems.

Main Methods:

• Utilized the Sum of Ranking Differences (SRD) statistical method.
• Applied SRD to case studies from Norway and the US for both apportionment and districting.
• Ranked established heuristics for malapportionment and constituency compactness.

Main Results:

• In apportionment, Leximin and the Imperiali method tied for the best performance.
• Classical apportionment methods showed subtle but significant differences in effectiveness.
• For districting, the Lee-Sallee index and the novel Moment Invariant method demonstrated superior performance.
• The Moment Invariant method's effectiveness is influenced by parameter selection.

Conclusions:

• The Sum of Ranking Differences provides a robust framework for comparing electoral methods.
• Specific methods like Leximin and Moment Invariant show promise for improving fairness in democratic processes.
• Further research may refine parametric methods for optimal districting outcomes.