Circular Societies Visualization Tool

Kristen Mazur, Mutiara Sondjaja, Matthew Wright, and Carolyn Yarnall

This github repostory contains a set of python tools for visualizing and generating examples of "circular societies" in approval voting.

Try online: examples-Google_Colab.ipynb

Contents

• Background
• The circularsocieties module
  • Documentation
  • Requirements

Background

The development of this tool is motivated by the following papers, which study approval voting in a mathematical context.

• Deborah E. Berg, Serguei Norine, Francis Edward Su, Robin Thomas, and Paul Wollan. "Voting in agreeable societies." The American Mathematical Monthly 117, no. 1 (2010): 27-39. [link]
• Christopher S. Hardin, "Agreement in circular societies." The American Mathematical Monthly 117, no. 1 (2010): 40-49. [link]
• Kristen Mazur, Mutiara Sondjaja, Matthew Wright, and Carolyn Yarnall. "Approval voting in product societies." The American Mathematical Monthly 125, no. 1 (2018): 29-43.[link]
• Francis Edward Su and Shira Zerbib. "Piercing numbers in approval voting." Mathematical Social Sciences 101 (2019): 65-71. [link]

The circularsocieties module

• circularsocieties.py
• Examples (local Jupyter notebook): examples.ipynb
• Examples (online): examples-Google_Colab.ipynb

Documentation

• DOCUMENTATION.md

Requirements

• numpy (for linear algebra computations)
• matplotlib (for plotting/visualization)
• cvxpy (for computing piercing numbers via integer programming)
• cvxopt (allows cvxpy to use the open source mixed-integer program solver 'GLPK_MI')
• itertools (for generating combinations of k objects from a collection of m objects)