Social Choice Mathematics



Part 1a - Introduction, Deductive and Inductive Reasoning
Common Origins of Mathematics and Democracy
Part 1b - Fairness Criteria and Methods of Voting
Part 2 - Examples of Voting Methods
Part 3 - Problems with Voting, Criteria for Voting
Example: Plurality Fails IIA
Part 4 - Problems with Approval Voting & Arrow's Impossibility Theorem
Example: The Voting Paradox of Condorcet
Proving Criteria False
List of Voting Criteria
Real-life example of Sequential Pairwise Voting
Common Test #1 mistakes
Additional example questions on voting

Electing the President

Electing the President in Plain English (video)
Presidential Election Process and The 2008 Election
The Electoral College and Ending the Electoral College
Primary Elections and Caucuses
Delegates and Superdelegates - Election Predictions - Polling Analysis - Historical Voting Data

Analysis of Weighted Voting Systems

Counting Techniques
Part 1 - Weighted Voting Systems
Part 2 - Banzhaf Index
Part 3 - Shapley-Shubik Index
Part 4 - Minimal Winning Coalitions
Theorem: Equal Weight Implies Equal Power
Calculating power in large systems
Calculating Power in Large Systems - Another Example
Classification of Weighted Voting Systems with Four Voters
Practicing calculating power with large systems

Methods of Apportionment

Part 1 - Introduction to Apportionment
Part 2 - Hamilton's Method
Part 3 - Jefferson's Method
Part 4 - More on History
Part 5 - Webster's Method
Part 6 - Huntington-Hill Method
Part 7 - Which Method is Better?
Paradoxes of Apportionment
Examples of Paradox in Apportionment
More Examples of Paradox in Apportionment
Apportionment - Overview
Excel file - apportionment calculator
Excel file - current U.S. apportionment

Introduction to Game Theory

Part 1 - Introduction to Game Theory
Part 2 - Zero Sum Games
Part 3a - The Minimax Theorem
Part 3b - Finding Mixed Strategy Saddle Points
Part 3c - A Formula for Mixed Strategy Saddle Points
Part 4 - Dominant Strategies
Part 5 - Nash's Theorem


Methods of Fair Division

Part 1 - the Adjusted Winner Procedure
Part 2 - the Knaster Inheritance Procedure
Part 3 - Taking Turns and Divide and Choose
Part 4 - Divide and Choose with more than 2 players
Part 5 - Defining Fairness
Additional notes on the Selfridge-Conway fair division method
Selfridge-Conway fair division method is envy-free
Additional example questions on fair division


Nassau County Weighted voting systems:

Florida Congressional Districts
Individual Maps of Congressional Districts

South Florida Congressional Representatives:
District 17: Kendrick Meek
District 18: Ileana Ros-Lehtinen
District 19: Robert Wexler
District 20: Debbie Wasserman Schultz
District 21: Lincoln Diaz-Balart
District 22: E. Clay Shaw, Jr.
District 23: Alcee Hastings
District 25: Mario Diaz-Balart