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Ed Scheinerman
This course is aimed at anyone who has interest in the lens through which mathematicians view democracy. You will learn theories and approaches to the mathematics of voting.
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OpenCourser.com/course/incapa/mathematics
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What's inside
Syllabus
Module 1
This module sets the stage for the entire Teach Out. We begin by discussing the nature of mathematics (as opposed to arithmetic) and develop a workable abstract model for democracy: a function that takes individual preferences and returns a group decision. We then look closely at different methods for two-party elections, fairness criteria we want these functions to have, and conclude that only the Simple Majority method satisfies those criteria.
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Syllabus
Module 1
This module sets the stage for the entire Teach Out. We begin by discussing the nature of mathematics (as opposed to arithmetic) and develop a workable abstract model for democracy: a function that takes individual preferences and returns a group decision. We then look closely at different methods for two-party elections, fairness criteria we want these functions to have, and conclude that only the Simple Majority method satisfies those criteria.
Read more
Traffic lights
Traffic lights
Read about what's good
what should give you pause and
possible dealbreakers
Touches on the history and foundation of mathematics
Develops a functional model for democracy, highlighting the mathematics involved in the process
Explores the complexity of voting systems with multiple candidates and examines the challenges they present
Introduces key concepts and theories related to voting, preference, and decision making
Examines the mathematical foundations of representative democracies and the challenges of fair representation
Requires a strong understanding of mathematics, particularly in the area of abstract reasoning and set theory
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Reviews summary
Mathematics and democracy: a unique perspective
According to learners, 'Mathematics and Democracy Teach Out' offers a thought-provoking exploration of the mathematical principles underlying democratic systems. Students consistently highlight the instructor's clear and engaging explanations, which make complex theories accessible, especially the insights into voting systems and apportionment. While it provides a strong theoretical foundation for those seeking intellectual enrichment, some learners noted the pace could be challenging, particularly for those without a strong mathematical background, and that it leans more towards abstract concepts than practical applications.
Explores topics with significant relevance to current political and societal discussions.
"A truly thought-provoking 'Teach Out.' The material on apportionment in Module 4 was highly relevant to current political discussions."
"This course provides valuable insights into voting paradoxes that helped me understand real-world political issues better."
"It's not just for math geeks; it's for anyone who votes and wants to understand the underlying complexities of our systems!"
The course provides a deep, mathematical understanding of democratic processes and voting theory.
"This course opened my eyes to the complexities of democracy. The mathematical approach was brilliant, and the instructor was fantastic."
"It wasn't always easy, but the way it challenges conventional wisdom about voting systems was very insightful. Arrow's Theorem was particularly eye-opening."
"I gained a solid theoretical foundation in the mathematics of voting and apportionment, which I found fascinating."
The instructor excels at making complex mathematical concepts accessible and engaging.
"The instructor's ability to explain complex mathematical concepts in the context of democracy was outstanding."
"Dr. Smith has a gift for making abstract math accessible. The examples were clear, and the non-transitive preferences section was mind-bending in a good way."
"Engaging and incredibly well-presented. I really appreciated how complex topics were broken down into digestible parts."
Some learners found the course pace challenging or desired more practical applications.
"Good content, but sometimes the pace felt a bit rushed, especially in Module 2 when covering Arrow's Theorem. I had to rewatch a few lectures."
"The mathematical proofs were sometimes hard to follow without a stronger math background, but the concepts were still valuable."
"I found it a bit too theoretical for my taste. While the concepts were important, I was hoping for more practical examples or case studies related to modern electoral processes."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Mathematics and Democracy Teach Out with these
activities:
Review Basic Probability and Statistics
Show steps
Refresh and strengthen foundational skills in probability and statistics to enhance understanding of concepts related to voting methods.
Browse courses on
Probability
Show steps
-
Review lecture notes or textbooks on probability and statistics.
-
Solve practice problems to test understanding.
-
Identify areas where further review is needed.
Linear Algebra Basics
Show steps
Review basic linear algebra skills to enhance understanding of mathematical foundations of voting systems
Browse courses on
Linear Algebra
Show steps
-
Review matrix operations and properties
-
Refresh concepts of determinants
Organize and Review Course Materials
Show steps
Improve retention and understanding by organizing and reviewing notes, assignments, and course materials.
Browse courses on
Learning Strategies
Show steps
-
Review and summarize lecture notes.
-
Organize assignments and quizzes by topic.
-
Highlight key concepts and make connections between different topics.
Seven other activities
Expand to see all activities and additional details
Show all ten activities
Review 'Social Choice and Welfare'
Show steps
Gain a comprehensive understanding of the foundations of social choice theory, including Arrow's Theorem and its implications for democratic decision-making.
Show steps
-
Read and comprehend the text.
-
Take notes and highlight key concepts.
-
Work through the exercises and problems provided in the book.
Solve Practice Problems on Voting Paradoxes
Show steps
Strengthen problem-solving skills and gain a deeper understanding of voting paradoxes by solving a variety of practice problems.
Show steps
-
Review course materials on voting paradoxes.
-
Find practice problems online or in textbooks.
-
Solve the problems and check your answers.
-
Identify patterns and common pitfalls.
Participate in Discussion Groups on Voting Theory
Show steps
Gain different perspectives and deepen understanding by engaging in discussions with peers about the concepts and applications of voting theory.
Browse courses on
Voting Systems
Show steps
-
Join online or local discussion groups related to voting theory.
-
Actively participate in discussions, sharing insights and asking questions.
-
Collaborate with peers on projects or presentations related to voting theory.
Explore Online Tutorials on Arrow's Theorem
Show steps
Supplement the course material by exploring online tutorials that provide in-depth explanations and interactive demonstrations of Arrow's Theorem.
Show steps
-
Identify reputable sources for online tutorials on Arrow's Theorem.
-
Go through the tutorials, taking notes and working through the examples.
-
Participate in online forums or discussions related to Arrow's Theorem.
Election Prediction Modeling
Show steps
Conduct modeling to predict election outcomes by applying principles of voting systems and decision functions studied in the course
Show steps
-
Gather election data and voter preference data
-
Choose and apply prediction models, e.g., logistic regression, decision tree
-
Train and evaluate the models
Simulate Voting Methods
Show steps
Develop a deeper understanding of the mathematical properties of voting methods by simulating them using a programming language.
Browse courses on
Computer Simulation
Show steps
-
Choose a programming language.
-
Implement various voting methods in the chosen programming language.
-
Design test cases with different sets of voter preferences.
-
Run simulations and analyze the results.
Compile Resources on Voting Methods
Show steps
Summarize key concepts and arguments from the course by compiling resources on different voting methods.
Browse courses on
Democratic Theory
Show steps
-
Review course materials on various voting methods.
-
Search for additional articles, books, and websites on the topic.
-
Organize and categorize the resources in a structured manner.
Review Basic Probability and Statistics
Show steps
Refresh and strengthen foundational skills in probability and statistics to enhance understanding of concepts related to voting methods.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Review lecture notes or textbooks on probability and statistics.
- Solve practice problems to test understanding.
- Identify areas where further review is needed.
Linear Algebra Basics
Show steps
Review basic linear algebra skills to enhance understanding of mathematical foundations of voting systems
Browse courses on
Linear Algebra
Show steps
Show steps
Show steps
- Review matrix operations and properties
- Refresh concepts of determinants
Organize and Review Course Materials
Show steps
Improve retention and understanding by organizing and reviewing notes, assignments, and course materials.
Browse courses on
Learning Strategies
Show steps
Show steps
Show steps
- Review and summarize lecture notes.
- Organize assignments and quizzes by topic.
- Highlight key concepts and make connections between different topics.
Seven other activities
Expand to see all activities and additional details
Show all ten activities
Review 'Social Choice and Welfare'
Show steps
Gain a comprehensive understanding of the foundations of social choice theory, including Arrow's Theorem and its implications for democratic decision-making.
Show steps
Show steps
Show steps
- Read and comprehend the text.
- Take notes and highlight key concepts.
- Work through the exercises and problems provided in the book.
Solve Practice Problems on Voting Paradoxes
Show steps
Strengthen problem-solving skills and gain a deeper understanding of voting paradoxes by solving a variety of practice problems.
Show steps
Show steps
Show steps
- Review course materials on voting paradoxes.
- Find practice problems online or in textbooks.
- Solve the problems and check your answers.
- Identify patterns and common pitfalls.
Participate in Discussion Groups on Voting Theory
Show steps
Gain different perspectives and deepen understanding by engaging in discussions with peers about the concepts and applications of voting theory.
Browse courses on
Voting Systems
Show steps
Show steps
Show steps
- Join online or local discussion groups related to voting theory.
- Actively participate in discussions, sharing insights and asking questions.
- Collaborate with peers on projects or presentations related to voting theory.
Explore Online Tutorials on Arrow's Theorem
Show steps
Supplement the course material by exploring online tutorials that provide in-depth explanations and interactive demonstrations of Arrow's Theorem.
Show steps
Show steps
Show steps
- Identify reputable sources for online tutorials on Arrow's Theorem.
- Go through the tutorials, taking notes and working through the examples.
- Participate in online forums or discussions related to Arrow's Theorem.
Election Prediction Modeling
Show steps
Conduct modeling to predict election outcomes by applying principles of voting systems and decision functions studied in the course
Show steps
Show steps
Show steps
- Gather election data and voter preference data
- Choose and apply prediction models, e.g., logistic regression, decision tree
- Train and evaluate the models
Simulate Voting Methods
Show steps
Develop a deeper understanding of the mathematical properties of voting methods by simulating them using a programming language.
Browse courses on
Computer Simulation
Show steps
Show steps
Show steps
- Choose a programming language.
- Implement various voting methods in the chosen programming language.
- Design test cases with different sets of voter preferences.
- Run simulations and analyze the results.
Compile Resources on Voting Methods
Show steps
Summarize key concepts and arguments from the course by compiling resources on different voting methods.
Browse courses on
Democratic Theory
Show steps
Show steps
Show steps
- Review course materials on various voting methods.
- Search for additional articles, books, and websites on the topic.
- Organize and categorize the resources in a structured manner.
Career center
Learners who complete Mathematics and Democracy Teach Out will develop knowledge and skills
that may be useful to these careers:
For more career information including salaries, visit:
OpenCourser.com/course/incapa/mathematics
Reading list
We haven't picked any books for this reading list yet.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/incapa/mathematics
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Effort
4 weeks of study, 1-2 hours per week
Level
Introductory
Via
Coursera
Institution
Johns Hopkins University
Instructor
Ed Scheinerman
Language
English
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