Math 217, Mathematics, Voting, & Democracy, Spring 2022

Be sure to check back, because this will be updated during the semester.

- PS due refers to Problem Sets uploaded to onCourse
- Check PCA refers to the Pre-Class Assignments, that consist of readings you should complete and/or videos you should watch before class that day.

Week | Major Topics | Tuesday 11:00 - 12:20 |
Thursday 11:00 - 12:20 |
||
---|---|---|---|---|---|

1 | Welcome to Math 217! | 1/25 | 1/27 | Course overview and logistics | |

2 | Introduction to apportionment methods | 2/1 |
Apportionment methods of Hamilton, Jefferson, and Webster
Check PCA |
2/3 |
Divisor methods as step functions
Check PCA |

3 | The theory of apportionment | 2/8 |
Hill's method
Check PCA |
2/10 |
Apportionment paradoxes
Check PCA PS #1 due @ midnight |

4 |
Finishing up apportionment
Congressional redistricting in the U.S. |
2/15 | Systematically evaluating apportionment methods | 2/17 |
Basics of redistricting
Measures of compactness Check PCA |

5 | Analyzing the 2010 redistricting process | 2/22 |
Case studies from the 2010 cycle: Wisconsin, Pennsylvania, North Carolina Check PCA |
2/24 |
Measures of partisan gerrymandering
Check PCA State for presentation due PS #2 due @ midnight |

6 | Measures of gerrymandering | 3/1 | More with the Efficiency Gap | 3/3 |
The GEO metric
Check PCA |

7 | What's happening right now? | 3/8 |
Student Presentations: Pick a state! |
3/10 |
Student Presentations: Pick a state! |

3/14 | Spring Break | 3/16 | Spring Break | ||

8 | Examples from some other countries | 3/22 |
Proportional Represenation Systems
Check PCA |
3/24 | Proportional Represenation Systems |

9 | Introduction to multicandidate elections | 3/29 |
Elections with three candidates
Check PCA |
3/31 |
The representation triangle and procedure line
Check PCA |

10 | A geometric framework for voting | 4/5 |
A fundamental decomposition of ℝ^{6}
Check PCA |
4/7 |
The pairwise space ℝ^{3}
Check PCA PS #3 due @ midnight |

11 |
Why do different voting methods give different outcomes?
Extending to higher dimensions |
4/12 | Creating paradoxical examples | 4/14 |
Elections with four candidates
PS #4 due @ midnight |

12 | What is a "fair" election? | 4/19 |
Plurality runoffs
"Ranked choice voting" Statement of Arrow's Theorem Check PCA |
4/21 |
Understanding what Arrow's Theorem says. . .and doesn't say
Topic for presentation due |

13 | Elections with more than one winner | 4/26 |
Electing committees, City Councils, School Boards
Check PCA |
4/28 | Single transferable vote in Cambridge, MA |

14 | Group presentations | 5/3 | Student presentations | 5/5 | Student presentations |

5/10 | Finals Period | 5/12 |
Final Assignment due @ midnight |